Mathematics Education Research Blog

I have moved!!!

2010-06-09T07:25:00.001+02:00

The headline of this post is not completely correct, since it is really not a matter of me having moved personally. The thing is, however, that this blog - The Mathematics Education Research Blog - has now moved to a different place! I have been considering this for quite some time actually, and I have now decided to move the blog to a Wordpress platform. Reasons for this decision are many, I guess, but here are the two most important reasons:

Wordpress is a very flexible blogging platform (even more so than Blogger)!
And I needed some change myself too...

There has also been a long process during some very busy months this Spring, where I have spent some time discussing with myself whether or not to continue working on this blog or not. I have come to a decision, and I will keep on blogging, but in a different place, and I hope that I will (gradually) be able to change and hopefully also improve the blog. In the two-year phase, the main purpose of the blog was for it to be useful to me. To me, this is still an important reason to blog! In the future, however, I also want the blog to become more useful to you as a reader. If you want to know how, you have no other choice but to update your bookmarks and start following my "new" blog over at: http://mathedresearch.wordpress.com :-)

First Sourcebook on Nordic Research in Mathematics Education

2010-05-21T20:50:00.004+02:00

The First Sourcebook on Nordic Research in Mathematics Education is going to be released in July this year, and I have been given the opportunity by the main editor, Professor Bharath Sriraman, to publish the cover photo and the table of contents first, here on this blog!

Being the first one to provide this news is of course great, and I guess that I am also enthusiastic about the book because I am one of the authors. The main reason why I am really enthusiastic about this book, however, is that it is going to be a monumental documentation of Nordic research and contributions to the field of mathematics education research. Putting together a book like this is a feature in itself, and I tip my hat to Bharath and the co-editors for this effort! I am happy that I have been able to be a part of it, and I am looking forward to digging into it! And I am quite certain that the hopes, which are expressed by the main editor in the foreword, are going to become true when it comes to this book. It will be "of use to many generations of mathematics education researchers inside and outside the Nordic world" (p. xii).

So, keep an eye on the publisher's website at http://www.infoagepub.com/products/First-Sourcebook-Nordic-Research-Mathematics-Education to make sure you don't miss the release date! And, in the meantime you can build your expectations by reading the table of contents as well as the foreword below:

TheFirstNordicSourcebook_TOC

New issue of Journal of Mathematics Teacher Education

2010-05-19T10:33:00.001+02:00

A new issue of Journal of Mathematics Teacher Education has been published (See SpringerLink - Journal Issue). The issue contains five interesting articles, all of them with a strong focus on inquiry:

The challenge in developing in mathematics teachers an inquiry stance to teaching, by Peter Sullivan.
Collaborative teacher inquiry as a tool for building theory on the development and use of rich mathematical tasks, by David Slavit and Tamara Holmlund Nelson.
The effect of video-based approach on prospective teachers' ability to analyze mathematics teaching, by Othman N. Alsawaie and Iman M. Alghazo.
Learning to teach mathematics through inquiry: a focus on the relationship between describing and enacting inquiry-oriented teaching, by Jo Towers.
Conceptions of effective mathematics teaching within a cultural context: perspectives of teachers from China and the United States, by Jinfa Cai and Tao Wang.

Theories of Mathematics Education - Recommendations from Reuben Hersh

2010-05-19T10:25:00.000+02:00

"Theories of Mathematics Education: Seeking new frontiers" is the first book in the series: Advances in Mathematics Education. The book was published a while ago, and it has already received good reviews and recommendations. The last in line to recommend the book is Reuben Hersh, and he has some very positive things to say about it:

A very impressive new book, "Theories of Mathematics Education" (Springer) edited by Sriraman and English is meant to inaugurate a new series, "Advances in Mathematics Education" . This first book in the series is a massive and ambitious undertaking, a very wide-ranging survey written in a dialogic format. (See this link for more!)

JMTE, April 2010

2010-04-12T13:07:00.000+02:00

The April issue of Journal of Mathematics Teacher Education has recently been published. This issue contains 6 interesting articles:

Crossing the divide: reflecting on the benefits of international collaboration, by Anne D. Cockburn
Secondary mathematics cooperating teachers’ perceptions of the purpose of student teaching, by Keith R. Leatham and Blake E. Peterson
Analyzing and attempting to overcome prospective teachers’ difficulties during problem-solving instruction, by Alexander Karp
Developing teachers’ knowledge of students as learners of mathematics through structured interviews, by Oliver F. Jenkins
The influence of video clubs on teachers’ thinking and practice, by Elizabeth A. van Es and Miriam Gamoran Sherin
Prospective primary mathematics teachers’ learning from on-line discussions in a virtual video-based environment, by Salvador Llinares and Julia Valls

The article by van Es and Sherin is an Open Access article, so that one should be available even for non-subscribers!

New issue of IJMEST, vol 41, issue 3, 2010

2010-03-29T07:02:00.001+02:00

A new issue of International Journal of Mathematical Education in Science and Technology has been released, and it contains a whole host of interesting articles and classroom notes. This issue appears to have a particular focus on the use of technology in mathematics teaching, and here is a list of the original articles that are contained in the issue:

Sustainable student retention and gender issues in mathematics for ICT study, by Blazenka Divjak, Mirela Ostroski and Violeta Vidacek Hains
A proposal for a variation on the axioms of classical geometry, by Bjorn Schellenberg
Trends in performance of science and technology students (1997–2008) in Ireland, by Olivia Gill, John O’Donoghue, Fiona Faulkner and Ailish Hannigan
Relational understanding and paths of reasoning through a Boolean lattice classification of quadrilaterals, by J. Karakonstantis and T. Patronis
Using dynamic geometry to explore non-traditional theorems, by Arsalan Wares
A new approach for proving or generating combinatorial identities, by Luis González

Review of my blog

2010-03-29T06:51:00.001+02:00

After a slow month (on the blog - not at work!), it is great to see someone writing a nice review of this blog. This time it is Jerry Johnson from MathNEXUS who has written a very kind review. MathNEXUS is a web site particularly geared towards teachers of mathematics, and it presents itself as a mathematics portal with "news and ideas for teachers and learners of mathematics. So, if you're into teaching and/or learning of mathematics it might be worthwhile to check it out!

Thanks for the kind words, Jerry :-)

Appropriating geometric series as a cultural tool

2010-03-01T12:13:00.000+01:00

A couple of new articles have been published online in Educational Studies in Mathematics lately, amongst those a very interesting one by my good colleague Martin Carlsen from the University of Agder, Norway. His article is entitled: Appropriating geometric series as a cultural tool: a study of student collaborative learning. Carlsen, along with other colleagues in Agder, have been influenced by the focus on small-group problem solving that was advocated by Neil Davidson and others some years ago. The Agder group is also strongly influenced by theories related to sociocultural perspectives of teaching and learning mathematics, and this article provides a nice overview of some of these theoretical foundations. The research reported in this article can be placed within a qualitative, naturalistic paradigm, and the data were analyzed using a dialogical approach (Carlsen here makes use of a framework developed by two other colleagues: Maria-Luiza Cestari and Raymond Bjuland). So, if you are interested in any of the perspectives referred to above, this article should be highly relevant for you! Here is the abstract of the article:

The aim of this article is to illustrate how students, through collaborative small-group problem solving, appropriate the concept of geometric series. Student appropriation of cultural tools is dependent on five sociocultural aspects: involvement in joint activity, shared focus of attention, shared meanings for utterances, transforming actions and utterances and use of pre-existing cultural knowledge from the classroom in small-group problem solving. As an analytical point of departure, four mathematical theoretical components are identified when appropriating the cultural tool of geometric series: (1) estimating of parameters, (2) establishing of the general term, (3) composing of the sum and (4) deciding on convergence. Analyses of five excerpts focused on the students’ social processes of knowledge objectification and the corresponding semiotic means, i.e., lecture notes, linguistic devices, gestures, head movements and gaze, to obtain shared foci and meanings. The investigation of these processes unveils the manner in which the students established links to pre-existing mathematical knowledge in the classroom and how they simultaneously combined the various mathematical theoretical components that go into appropriating the cultural tool of geometric series. From the excerpts, it is evident that the students’ participation changes throughout their involvement in the problem-solving process. The students are gaining mathematical knowing through a process of transforming and by establishing shared meanings for the concept and its theoretical components.

Exploring kindergarten teachers' pedagogical content knowledge of mathematics

2010-02-26T09:08:00.001+01:00

Last week, an interesting article was published online in the International Journal of Early Childhood. The article is entitled Exploring Kindergarten Teachers’ Pedagogical Content Knowledge of Mathematics, and it has been written by Joohl Lee. The combination of teachers knowledge of mathematics and kindergarten is very interesting, and while a lot of research has been done to learn more about the type of knowledge mathematics teachers need in school, little has been done to learn more about this in kindergarten. This is also mentioned by Lee in the article. As the title of the article reveals, Lee builds upon Shulman's traditional framework of teachers' professional knowledge. What I don't understand, however, is how it is possible to write an article about teachers' pedagogical content knowledge of mathematics without making any reference to the MKT (Mathematical Knowledge for Teaching) framework, or any of the work done by Deborah Ball and her colleagues at the University of Michigan. I understand that this article has a focus on kindergarten, but still... I also think there should be some mention of how the teachers in the study were selected. 81 kindergarten teachers were assessed in the study, and 55% of these had a master's degree. I would like to know more about how representative this sample was. Still, I think it is an interesting article, and I think it is a good thing that the issue of kindergarten teachers' knowledge of mathematics is addressed.

Here is the abstract of the article:

The purpose of this study was to assess 81 kindergarten teachers’ pedagogical content knowledge of mathematics on six subcategory areas such as number sense, pattern, ordering, shapes, spatial sense, and comparison. The data showed participants possessed a higher level of pedagogical content knowledge of “number sense” (M = 89.12) compared to other mathematics pedagogical content areas. The second highest scores among six subcategories of pedagogical content knowledge of mathematics was for the pedagogical content area of “pattern” (M = 82.33). The lowest scores among those six subcategories of kindergarten teachers’ pedagogical content knowledge were obtained from the subcategory of “spatial sense” (M = 44.23), which involved the means to introduce children to spatial relationships. The second lowest score was obtained for the subcategory of “comparison” (M = 50.40) which involved the means to introduce the concept of graphing and the use of a balance scale for measurement.

Teachers attending to students' reasoning

2010-02-24T07:09:00.000+01:00

John M. Francisco and Carolyn A. Maher have written an article about Teachers attending to students’ mathematical reasoning: lessons from an after-school research program. This article was published online in Journal of Mathematics Teacher Education last Thursday. This article is interesting in several respects, amongst others because awareness of and knowledge about students' mathematical reasoning is something teachers need, and it should be part of every mathematics teacher's professional knowledge. Theoretically, it builds upon Shulman's classic framework, but they also make interesting links to a focus on practitioner-researcher collaboration. The article reports on a study that was made of "elementary and middle school teachers who participated as interns in the 1-year NSF-funded Informal Mathematical Learning Project (IML)". Here is a copy of the abstract of their article:

There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’ mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity. The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning.

Busy days...

2010-02-16T21:12:00.001+01:00

The last couple of weeks have been extremely busy - for many reasons - and I haven't been able to follow up on all the latest articles and news in the field. I apologize for this, and I hope that all the readers of the blog have patience with me! I promise that I will catch up :-)

In the meantime, you always have a couple of good options in order to stay really up-to-date:

Pay attention to my Google Reader blog (shared items)
Follow me on twitter

These two sites are a bit easier for me to update, and when I don't manage to update my blog as often as I would, I will probably continue to push new updates to these two other services. Still, as soon as I get my head above water again, I will keep providing you with information here as well :-)

Mathematically based and practically based explanations

2010-02-09T07:44:00.000+01:00

Esther Levenson, Pessia Tsamir and Dina Tirosh have written an interesting article about Mathematically based and practically based explanations in the elementary school: teachers’ preferences. Their article was published online in Journal of Mathematics Teacher Education on Friday. In this article, the authors make interesting connnections between research on teachers' knowledge and beliefs. Although their focus is on knowledge and beliefs in relation to the use of explanations (and they distinguish between mathematically and practically based explanations) in the classroom, the article makes a nice contribution to extending our understanding of the way these concepts are related. The part of teachers' knowledge (and beliefs) that the authors discuss is related to students' thinking, or even a sub-category of that. In this respect, they make valuable contributions to what Deborah Ball and her colleagues refer to as Knowledge of Content and Students, but their focus is also in the borderline of what is referred to as Knowledge of Content and Teaching. The links to research concerning teachers' beliefs is also interesting, althought the authors don't go into great detail here. They are, of course, aware of this, and explain that they have only given "a glimpse into the complexity of the relationship between teachers' knowledge and beliefs", in particular with focus on teachers' use of explanations.

Here is the abstract of their article:

This article focuses on elementary school teachers’ preferences for mathematically based (MB) and practically based (PB) explanations. Using the context of even and odd numbers, it explores the types of explanations teachers generate on their own as well as the types of explanations they prefer after reviewing various explanations. It also investigates the basis for these preferences. Results show that teacher-generated explanations include more MB explanations than PB explanations. However, many still choose to use mostly PB explanations in their classrooms, believing that these explanations will be most convincing to their students. The implications for teacher education are discussed.

ZDM, February, 2010

2010-02-03T07:15:00.001+01:00

A new issue of ZDM - The International Journal on Mathematics Education has been published. This issue has a special focus on Historical aspects of the use of technology and devices in ICMEs and ICMI, and guest editors have been Maria G. Bartolini Bussi and Marcelo C. Borba. The issue contains 15 articles which covers many aspects of the theme, from historical perspectives on the use of technology to a social perspective on technology enhanced learning. Here is an overview of the contents of this issue:

The role of resources and technology in mathematics education, by Maria G. Bartolini Bussi and Marcelo C. Borba
Historical comments on the use of technology and devices in ICMEs and ICMI, by Gert Schubring
Exploration of technologies, emerging from African cultural practices, in mathematics (teacher) education, by Paulus Gerdes
Concrete models and dynamic instruments as early technology tools in classrooms at the dawn of ICMI: from Felix Klein to present applications in mathematics classrooms in different parts of the world, by Maria G. Bartolini Bussi, Daina Taimina and Masami Isoda
Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories, by Michela Maschietto and Luc Trouche
Collectives of humans-with-media in mathematics education: notebooks, blackboards, calculators, computers and … notebooks throughout 100 years of ICMI, by Mónica E. Villarreal and Marcelo C. Borba
Charting the microworld territory over time: design and construction in mathematics education, by Lulu Healy and Chronis Kynigos
Graphic calculators and connectivity software to be a community of mathematics practitioners, by Ornella Robutti
A social perspective on technology-enhanced mathematical learning: from collaboration to performance, by George Gadanidis and Vince Geiger
Integrating technology into mathematics teaching at the university level, by Zsolt Lavicza
Place and use of new technology in the teaching of mathematics: ICMI activities in the past 25 years, by Colette Laborde and Rudolf Sträßer
Clarkson, P., Presmeg, N. (eds) (2008): Critical Issues in Mathematics Education: Major Contributions of Alan Bishop, Springer, New York, 257 pp., ISBN 978-0-387-09672-8, by Irit Peled
Acknowledgements to reviewers 2009, by Gabriele Kaiser
Acknowledgments to the members of the Editorial Board, by Gabriele Kaiser
Advances in mathematics education: new book series connected to ZDM—The International Journal on Mathematics Education, by Gabriele Kaiser and Bharath Sriraman

Combining constructions of knowledge

2010-01-27T07:53:00.001+01:00

Ivy Kidron and Tommy Dreyfus have written an article entitled Justification enlightenment and combining constructions of knowledge. The article was published online in Educational Studies in Mathematics last week. Here is a copy of the abstract of their article:

This case study deals with a solitary learner’s process of mathematical justification during her investigation of bifurcation points in dynamic systems. Her motivation to justify the bifurcation points drove the learning process. Methodologically, our analysis used the nested epistemic actions model for abstraction in context. In previous work, we have shown that the learner’s attempts at justification gave rise to several processes of knowledge construction, which develop in parallel and interact. In this paper, we analyze the interaction pattern of combining constructions and show that combining constructions indicate an enlightenment of the learner. This adds an analytic dimension to the nested epistemic actions model of abstraction in context.

Online distance mathematics education in Brazil

2010-01-27T07:51:00.001+01:00

Marcus Vinicius Maltempi and Ana Paula dos Santos Malheiros have written an article about Online distance mathematics education in Brazil: research, practice and policy. The article was recently published online in ZDM. Here is the abstract of their article:

In this article, we address online distance mathematics education research and practice in Brazil, which are relative newcomers to the educational scene. We present the national context of education in Brazil, highlighting the organization of the educational system, and also a summary of national legislation on distance education and an overview of digital inclusion in the country. We outline the potential and relevance of distance education for the Brazilian educational system and show how it could intervene in the system. With respect to research and practice in online mathematics education, we present support for research, examples of studies and highlight different aspects being addressed, including its essential components. In addition, we discuss the synergy between distance education and teacher education, and mathematics distance education and modeling, as well as other initiatives in the national scenario.

Mathematics education and democracy

2010-01-22T08:56:00.001+01:00

Adriana Cesar de Mattos and Marcelo Salles Batarce have written an article that was published online in ZDM on Wednesday. This article is about Mathematics education and democracy, and here is a copy of the abstract:

In this paper, we investigate the relationship between mathematics education and the notions of education for all/democracy. In order to proceed with our analysis, we present Marx’s concept of commodity and Jean Baudrillard’s concept of sign value as a theoretical reference in the discussion of how knowledge has become a universal need in today’s society and ideology. After, we engage in showing mathematics education’s historical and epistemological grip to this ideology. We claim that mathematics education appears in the time period that English becomes an international language and the notion of international seems to be a key constructor in the constitution of that ideology. Here, we draw from Derrida’s famous saying that “there is nothing beyond the text”. We conclude that a critique to modern society and education has been developed from an idealistic concept of democracy.

Feeling number

2010-01-22T07:36:00.001+01:00

David Wagner and Brent Davis have written an article called Feeling number: grounding number sense in a sense of quantity. The article was published online in Educational Studies in Mathematics on Monday. In this interesting article, they draw upon different theories and ideas from psychology as well as cultural and linguistic studies. Here is the abstract of their article:¨

Drawing on results from psychology and from cultural and linguistic studies, we argue for an increased focus on developing quantity sense in school mathematics. We explore the notion of “feeling number”, a phrase that we offer in a twofold sense—resisting tendencies to feel numb-er (more numb) by developing a feeling for numbers and the quantities they represent. First, we distinguish between quantity sense and the relatively vague notion of number sense. Second, we consider the human capacity for quantity sense and place that in the context of related cultural issues, including verbal and symbolic representations of number. Third and more pragmatically, we offer teaching strategies that seem helpful in the development of quantity sense coupled with number sense. Finally, we argue that there is a moral imperative to connect number sense with such a quantity sense that allows students to feel the weight of numbers. It is important that learners develop a feeling for number, which includes a sense of what numbers are and what they can do.

Engaging in problem posing activities

2010-01-19T08:30:00.002+01:00

Ilana Lavya and Atara Shrikib have written an article that was recently published online in The Journal of Mathematical Behavior. The full title of their article is: Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge. Here is the abstract of their article:

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the “What If Not?” (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs’ portfolios reveals that they believe that engaging in the inquiry-based activity enhanced both their mathematical and meta-mathematical knowledge. As to the mathematical knowledge, they deepened their knowledge regarding the geometrical concepts and shapes involved, and during the process of creating the problem and checking its validity and its solution, they deepened their understanding of the interconnections among the concepts and shapes involved. As to meta-mathematical knowledge, the PTs refer to aspects such as the meaning of the givens and their relations, validity of an argument, the importance and usefulness of the definitions of concepts and objects, and the importance of providing a formal proof.

TMME, January 2010 revisited

2010-01-15T20:41:00.003+01:00

The January issue of The Montana Mathematics Enthusiast has now been released on the journal website. The entire issue is freely available as always!

0. New Year Tidings Bharath Sriraman (USA) pp. 1-2
FEATURE ARTICLES

1. When is .999... Less Than 1? Karin Usadi Katz and Mikhail G. Katz (Israel) pp. 3-30
2. High School Teachers use of Dynamic Software to generate serendipitous mathematical relations Manuel Santos-Trigo and Hugo Espinosa-Pérez (Mexico) pp. 31-46
3. Gender and Mathematics Education in Pakistan: A situation analysis Anjum Halai (Pakistan/Tanzania) pp. 47-62
4. Early Intervention in College Mathematics Courses: A Component of the STEM RRG Program Funded by the US Department of Education Rohitha Goonatilake and Eduardo Chappa (USA) pp. 63-74
5. “What Was Really Accomplished Today?”
Mathematics Content Specialists Observe a Class for Prospective K–8 Teachers Andrew M. Tyminski, Sarah Ledford, Dennis Hembree (USA) pp. 75-92
6. Leading Learning within a PLC: Implementing New Mathematics Content Ann Heirdsfield, Janeen Lamb, Gayle Spry (Australia) pp. 93-112
7. Mathematical Reasoning in Service Courses: Why Students Need Mathematical Modeling Problems Kris H. Green & Allen Emerson (USA) pp. 113-140
8. Randomness: Developing an understanding of mathematical order. Steve Humble (UK) pp. 141-148
9. The Constructs of PhD Students about Infinity: An Application of Repertory Grids Serdar Aztekin, Ahmet Arikan (Turkey) & Bharath Sriraman (USA) pp. 149-174

TMME, No 1, 2010

2010-01-14T19:43:00.002+01:00

The next issue of THE MONTANA MATHEMATICS ENTHUSIAST is soon to appear, and it is going to be Vol.7, No.1, January 2010. This issue is particularly exciting for me, since I am introduced as one of the new members of the editorial board! As usual, it is also going to be an interesting issue. The entire issue will be available soon on the journal website.

Here is a list of the feature articles in the forthcoming issue of TMME:

When is .999... Less Than 1? by Karin Usadi Katz and Mikhail G. Katz (Israel)
High School Teachers use of Dynamic Software to generate serendipitous mathematical relations, by Manuel Santos-Trigo and Hugo Espinosa-Pérez (Mexico)
Gender and Mathematics Education in Pakistan: A situation analysis, by Anjum Halai (Pakistan/Tanzania)
Early Intervention in College Mathematics Courses: A Component of the STEM RRG Program Funded by the US Department of Education, by Rohitha Goonatilake and Eduardo Chappa (USA)
"What Was Really Accomplished Today?" Mathematics Content Specialists Observe a Class for Prospective K-8 Teachers, by Andrew M. Tyminski, Sarah Ledford, Dennis Hembree (USA)
Leading Learning within a PLC: Implementing New Mathematics Content, by Ann Heirdsfield, Janeen Lamb, Gayle Spry (Australia)
Mathematical Reasoning in Service Courses: Why Students Need Mathematical Modeling Problems, by Kris H. Green & Allen Emerson (USA)
Randomness: Developing an understanding of mathematical order, by Steve Humble (UK)
The Constructs of PhD Students about Infinity: An Application of Repertory Grids, by Serdar Aztekin, Ahmet Arikan (Turkey) & Bharath Sriraman (USA)

Below, you'll find Professor Bharath Sriraman's editorial, and the updated editorial board info:

TMME, vol7, no1, 2010, Editorial

Edboardlistandjournalinfo_vol7no1_2010

Integrating technology into mathematics teaching

2010-01-12T09:13:00.001+01:00

Zsolt Lavicza has written an article entitled Integrating technology into mathematics teaching at the university level. This article was published online in ZDM on Friday. Here is the abstract of the article:

The emergence of new computing technologies in the second half of the twentieth century brought about new potentials and promised the rapid transformation of the teaching and learning of mathematics. However, despite the vast investments in technology resources for schools and universities, the realities of schooling and the complexities of technology-equipped environments resulted in a much slower integration process than was predicted in the 1980s. Hence researchers, together with teachers and mathematicians, began examining and reflecting on various aspects of technology-assisted teaching and learning and on the causes of slow technology integration. Studies highlighted that as technology becomes increasingly available in schools, teachers’ beliefs and conceptions about technology use in teaching are key factors for understanding the slowness of technology integration. In this paper, I outline the shift of research focus from learning and technology environment-related issues to teachers’ beliefs and conceptions. In addition, I highlight that over the past two decades a considerable imbalance has developed in favour of school-level research against university-level research. However, several changes in universities, such as students declining mathematical preparedness and demands from other sciences and employers, necessitate closer attention to university-level research. Thus, I outline some results of my study that aimed to reflect on the paucity of research and examined the current extend of technology use, particularly Computer Algebra Systems (CAS) at universities, mathematicians’ views about the role of CAS in tertiary mathematics teaching, and the factors influencing technology integration. I argue that due to mathematicians’ extensive use of CAS in their research and teaching, documenting their teaching practices and carrying out research at this level would not only be beneficial at the university level but also contribute to our understanding of technology integration at all levels.

Using history as a goal

2010-01-08T21:27:00.002+01:00

Uffe Thomas Jankvist has written an article called An empirical study of using history as a ‘goal’. The article was published online in Educational Studies in Mathematics two days ago. Here is the abstract of his article:

This article discusses an empirical study on the use of history as a goal. A historical module is designed and implemented in a Danish upper secondary class in order to study the students’ capabilities at engaging in meta-issue discussions and reflections on mathematics and its history. Based on videos of the implementation, students’ hand-in essay assignments, questionnaires, and follow-up interviews, the conditions, sense, and extent to which the students are able to perform such discussions and reflections are analyzed using a described theoretical framework.

January issue of Science & Education

2010-01-04T10:50:00.003+01:00

The January issue of Science & Education has been published. One of the articles contained in the issue is of relevance to mathematics education: A Pilot Study of a Cultural-Historical Approach to Teaching Geometry. The article is written by Stuart Rowlands from the University of Plymouth. Here is the abstract of his article:

There appears to be a widespread assumption that deductive geometry is inappropriate for most learners and that they are incapable of engaging with the abstract and rule-governed intellectual processes that became the world’s first fully developed and comprehensive formalised system of thought. This article discusses a curriculum initiative that aims to ‘bring to life’ the major transformative (primary) events in the history of Greek geometry, aims to encourage a meta-discourse that can develop a reflective consciousness and aims to provide an opportunity for the induction into the formalities of proof and to engage with the abstract. The results of a pilot study to see whether 14–15 year old ‘mixed ability’ and 15–16 year old ‘gifted and talented’ students can be meaningfully engaged with two such transformative events are discussed.

Happy new year!

2010-01-01T11:09:00.000+01:00

I want to wish all readers of the Mathematics Education Research Blog a happy new year!

2009 was a nice year in many ways, and I am certain that 2010 will be a great year too! No matter what lies ahead, I will do my best to keep you up to date on what happens in the world of mathematics education research, with a particular emphasis on journals and scientific articles. Best of wishes to all of you, and I hope that 2010 will be a productive year for each and everyone of you!

Merry Christmas

2009-12-25T09:41:00.001+01:00

I wish all of my readers a merry Christmas! Things are going to be somewhat slow here on the blog for a few days, but I promise to be back in early January with more news about mathematics education research!

If you want to stay up to date, you might consider checking my shared articles on Google Reader, or you can go directly to the automatically updated articles within the field of mathematics education. Articles related to education research in general can be found here, and articles related to early childhood education can be found here. You might also consider following me on twitter, where I will also provide news and updates about mathematics education and other things of interest.

Teacher lust

2009-12-23T11:00:00.001+01:00

Andrew M. Tyminski has written an article that was recently published online in Journal of Mathematics Teacher Education. The article is entitled Teacher lust: reconstructing the construct for mathematics instruction. Here is the abstract of Tyminski's article:

Two collegiate mathematics courses for prospective elementary and middle grades teachers provide the context for the examination of Mary Boole’s construct of teacher lust. Through the use of classroom observations and instructor interviews, the author presents a refined conception of teacher lust. Two working aspects of the construct were identified: (1) enacted teacher lust; an observable action that may remove an opportunity for students to think about or engage in mathematics for themselves; and (2) experienced teacher lust; an internal impulse to act in the manner described. Empirical examples of each facet, differences between conscious and unconscious interactions with teacher lust, along with potential antecedents are discussed.

Learning to teach mathematics through inquiry

2009-12-23T10:57:00.001+01:00

Jo Towers has written an article entitled Learning to teach mathematics through inquiry: a focus on the relationship between describing and enacting inquiry-oriented teaching. The article was published online in Journal of Mathematics Teacher Education last week. Here is the abstract of the article:

This article is based on one of the several case studies of recent graduates of a teacher education programme that is founded upon inquiry-based, field-oriented and learner-focussed principles and practices and that is centrally concerned with shaping teachers who can enact strong inquiry-based practices in Kindergarten to Grade 12 classrooms. The analysis draws on interviews with one graduate, and on video data collected in his multi-aged Grade 1/2 classroom, to explore some of the ways in which this new teacher enacted inquiry-based teaching approaches in his first year of teaching and to consider his capacity to communicate his understanding of inquiry. This article presents implications for beginning teachers’ collaborative practices, for the assessment of new teachers and for practices in preservice teacher education.

TIMSS Advanced 2008

2009-12-14T07:25:00.000+01:00

Last week, the results from the TIMSS Advanced 2008 were released. The TIMSS assessment is probably well known to most, and the TIMSS video studies might also be familiar to some, but what exactly is TIMSS Advanced? The following description from the official website might explain some of the confusion:

TIMSS Advanced 2008 assesses student achievement in advanced mathematics and physics in the final year of secondary school—the twelfth grade in many countries. TIMSS Advanced is part of IEA’s series of TIMSS international assessments designed to provide comparative information about educational achievement across countries. Because TIMSS Advanced assesses students in their last year of secondary school who have studied advanced mathematics or physics to prepare them for further study of mathematics and science at the tertiary level, the results are of particular importance for educational decision making. (Source: http://timss.bc.edu/timss_advanced/index.html)

If you want to take a closer look at the full report from this study, you can check out this link (this is a direct link to a 33MB pdf file!). In case you want to dig even deeper into all the details and documentation of this study, you might want to take a look at The TIMSS Advanced 2008 Technical Report (14MB).

References
Arora, A., Foy, P., Martin, M.O., & Mullis, I.V.S. (Eds.). (2009). TIMSS Advanced 2008 Technical Report. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

Mullis, I.V.S., Martin, M.O., Robitaille, D.F., & Foy, P. (2009). TIMSS Advanced 2008 International Report: Findings from IEA's Study of Achievement in Advanced Mathematics and Physics in the Final Year of Secondary School. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

Math tutoring for low-achieving students

2009-12-14T07:11:00.000+01:00

Ronnie Karsenty has written an article entitled Nonprofessional mathematics tutoring for low-achieving students in secondary schools: A case study. This article was published online in Educational Studies in Mathematics last week. The project that is reported in the article is part of a larger project (SHLAV - Hebrew acronym for Improving Mathematics Learning). The research questions in the study are:

Will nonprofessional tutoring be effective, in terms of improving students' achievements in mathematics, and if so, to what extent?
Which factors will be identified by tutors as having the greatest impact on the success or failure of tutoring?

Here is the abstract of the article:

This article discusses the possibility of using nonprofessional tutoring as means for advancing low achievers in secondary school mathematics. In comparison with professional, paraprofessional, and peer tutoring, nonprofessional tutoring may seem less beneficial and, at first glance, inadequate. The described case study shows that nonprofessional tutors may contribute to students' understanding and achievements, and thus, they can serve as an important assisting resource for mathematics teachers, especially in disadvantaged communities. In the study, young adults volunteered to tutor low-achieving students in an urban secondary school. Results showed a considerable mean gain in students' grades. It is suggested that affective factors, as well as the instruction given to tutors by a specialized counselor, have played a major role in maintaining successful tutoring.

The increasing role of metacognitive skills in math

2009-12-10T13:28:00.000+01:00

Manita Van der Stel, Marcel Veenman, Kim Deelen and Janine Haenen have written an article entitled The increasing role of metacognitive skills in math: a cross-sectional study from a developmental perspective. This article was published online in ZDM last week. The article is an Open Access article, so it is freely available for all to read, but here is a copy of the abstract to tickle your interest:

Both intelligence and metacognitive skillfulness have been regarded as important predictors of math performance. The role that metacognitive skills play in math, however, seems to be subjected to change over the early years of secondary education. Metacognitive skills seem to become more general (i.e., less domain-specific) by nature (Veenman and Spaans in Learn Individ Differ 15:159–176, 2005). Moreover, according to the monotonic development hypothesis (Alexander et al. in Dev Rev 15:1–37, 1995), metacognitive skills increase with age, independent of intellectual development. This hypothesis was tested in a study with 29 second-year students (13–14 years) and 30 third-year students (14–15 years) in secondary education. A standardized intelligence test was administered to all students. Participants solved math word problems with a difficulty level adapted to their age group. Thinking-aloud protocols were collected and analyzed on the frequency and quality of metacognitive activities. Another series of math word problems served as post-test. Results show that the frequency of metacognitive activity, especially those of planning and evaluation, increased with age. Intelligence was a strong predictor of math performance in 13- to 14-year-olds, but it was less prominent in 14- to 15-year-olds. Although the quality of metacognitive skills appeared to predict math performance in both age groups, its predictive power was stronger in 14- to 15-year-olds, even on top of intelligence. It bears relevance to math education, as it shows the increasing relevance of metacognitive skills to math learning with age.

Visual templates in pattern generalization activity

2009-12-08T09:00:00.000+01:00

F.D. Rivera has written an article called Visual templates in pattern generalization activity. The article was published online in Educational Studies in Mathematics last Thursday. The study, which is described in the article, was carried out in an eighth-grade Algebra 1 class in California. Four and a half months after a teaching experiment on pattern generalization, 11 students were interviewed (clinical interviews). Clinical interviews were also made with these students directly before and after the teaching experiment. The article reports on results from the analyses of these clinical interviews.

Here is the abstract of the article:

In this research article, I present evidence of the existence of visual templates in pattern generalization activity. Such templates initially emerged from a 3-week design-driven classroom teaching experiment on pattern generalization involving linear figural patterns and were assessed for existence in a clinical interview that was conducted four and a half months after the teaching experiment using three tasks (one ambiguous, two well defined). Drawing on the clinical interviews conducted with 11 seventh- and eighth-grade students, I discuss how their visual templates have spawned at least six types of algebraic generalizations. A visual template model is also presented that illustrates the distributed and a dynamically embedded nature of pattern generalization involving the following factors: pattern goodness effect; knowledge/action effects; and the triad of stage-driven grouping, structural unit, and analogy.

Developing a 'leading identity'

2009-12-01T15:09:00.001+01:00

Laura Black, Julian Williams, Paul Hernandez-Martinez, Pauline Davis, Maria Pampaka and geoff Wake have written an article called Developing a ‘leading identity’: the relationship between students’ mathematical identities and their career and higher education aspirations. This article was published online in Educational Studies in Mathematics last Wednesday. Here is the abstract of their article:

The construct of identity has been used widely in mathematics education in order to understand how students (and teachers) relate to and engage with the subject (Kaasila, 2007; Sfard & Prusak, 2005; Boaler, 2002). Drawing on cultural historical activity theory (CHAT), this paper adopts Leont’ev’s notion of leading activity in order to explore the key ‘significant’ activities that are implicated in the development of students’ reflexive understanding of self and how this may offer differing relations with mathematics. According to Leont’ev (1981), leading activities are those which are significant to the development of the individual’s psyche through the emergence of new motives for engagement. We suggest that alongside new motives for engagement comes a new understanding of self—a leading identity—which reflects a hierarchy of our motives. Narrative analysis of interviews with two students (aged 16–17 years old) in post-compulsory education, Mary and Lee, are presented. Mary holds a stable ‘vocational’ leading identity throughout her narrative and, thus, her motive for studying mathematics is defined by its ‘use value’ in terms of pursuing this vocation. In contrast, Lee develops a leading identity which is focused on the activity of studying and becoming a university student. As such, his motive for study is framed in terms of the exchange value of the qualifications he hopes to obtain. We argue that this empirical grounding of leading activity and leading identity offers new insights into students’ identity development.

"Me and maths"

2009-12-01T15:06:00.001+01:00

Pietro Di Martino and Rosetta Zan have written an article entitled ‘Me and maths’: towards a definition of attitude grounded on students’ narratives. The article was published online in Journal of Mathematics Teacher Education on Friday. Here is a copy of the abstract of their article:

The attitude construct is widely used by teachers and researchers in mathematics education. Often, however, teachers’ diagnosis of ‘negative attitude’ is a causal attribution of students’ failure, perceived as global and uncontrollable, rather than an accurate interpretation of students’ behaviour, capable of steering future action. In order to make this diagnosis useful for dealing with students’ difficulties in mathematics, it is necessary to clarify the construct attitude from a theoretical viewpoint, while keeping in touch with the practice that motivates its use. With this aim, we investigated how students tell their own relationship with mathematics, proposing the essay “Me and maths” to more than 1,600 students (1st to 13th grade). A multidimensional characterisation of a student’s attitude towards mathematics emerges from this study. This characterisation and the study of the evolution of attitude have many important consequences for teachers’ practice and education. For example, the study shows how the relationship with mathematics is rarely told as stable, even by older students: this result suggests that it is never too late to change students’ attitude towards mathematics.

Graphics calculators in examination

2009-11-27T08:22:00.000+01:00

Roger G. Brown from the University of Leeds (UK) has written an article entitled Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested? This article was published online in Educational Studies in Mathematics earlier this week. Here is the abstract of his article:

The paper reports on the introduction of the graphics calculator into three centralised examination systems, which were located in Denmark, Victoria (Australia) and the International Baccalaureate. The introduction of the graphics calculator required those responsible for writing examination questions to consider how to assess mathematical skills within this new environment. This paper illustrates the types of mathematics skills that have been assessed within the graphics-calculator-assumed environment. The analysis of the examination questions indicated that only two out of the six mathematics examinations considered demonstrated any significant change in the types of skills assessed in conjunction with the introduction of the graphics calculator. The results suggest that it is possible to reduce the use of questions assessing routine procedures (mechanical skills) with a graphics calculator, but it is also evident that there have not been major changes in the way that examination questions are written nor the mathematics skills which the questions are intended to assess.

Using live, online tutoring

2009-11-25T11:22:00.000+01:00

Richard Lissaman, Sue de Pomerai and Sharon Tripconey have written an article that was recently published online in Teaching Mathematics and its Applications. The article is entitled Using live, online tutoring to inspire post 16 students to engage with higher level mathematics, and here is a copy of the article's abstract:

In recent years, there has been a decline in the number of students aged 16–18 studying and being able to access higher level mathematics in schools in the UK. The Further Mathematics Network (FMN) was set up to enable access to such mathematics to all students and to promote and encourage students to study at this level. The FMN has pioneered the use of Elluminate, a well established web-based package, for live mathematics tutoring. Small groups of students meet online with an experienced tutor to learn new aspects of mathematics and to look at ways to solve complex problems. There are also extensive online resources to support the students’ learning. The findings are discussed in the following article.

Pre-service teachers' teaching anxiety

2009-11-24T15:36:00.002+01:00

Murat Peker has written an article about Pre-Service Teachers’ Teaching Anxiety about Mathematics and Their Learning Styles. This article was published in the last issue of Eurasia Journal of Mathematics, Science & Technology Education. A main issue in the article is the combination of focus on mathematics (teaching) anxiety and learning styles. When it comes to learning styles, Peker very much builds upon the theories of Kolb (see p. 337). The theoretical overview is quite interesting, and in many respects new to me.

The study included 506 pre-service teachers from Turkey, and two instruments were used in the study: the Learning Style Inventory and the Mathematics Teaching Anxiety Scale (both questionnaires). The first questionnaire is derived from Kolb's works, whereas the anxiety scale was developed by the researcher. I miss a discussion of the rationale behind the choice of methods/instruments in the study, and I think this is an important aspect of such a research article. I also think there are a couple of issues about the Learning Style Inventory that should be discussed somewhat. My main critique towards the statements from this questionnaire (as they are presented in the article) is that they appear very general. Being faced with a statement like "When I learn, I like to watch and listen", my response would vary according to the subject and teaching/learning context I had in mind. As with research on beliefs, I think it would make more sense to investigate views that teachers (pre-service or in-service) have on teaching and learning algebra, geometry, functions etc., rather than their views on teaching and learning in general. My response to a statement like "I learn best when I am practical" would also vary a lot according to what I had in mind when giving the response. I therefore think that the questionnaire has some severe weaknesses that need to be addressed. Other than that, I think the article is interesting, and Peker obviously points to some important issues!

Abstract

The purpose of this study was to investigate the differences in the teaching anxiety of pre-service teachers in mathematics according to their learning style preferences. There were a total of 506 pre-service teachers involved in this study. Of the total, 205 were pre-service elementary school teachers, 173 were pre-service elementary mathematics teachers, and 128 were pre-service secondary mathematics teachers. In the collection of the data, the researcher employed two types of instruments: the Learning Style Inventory (LSI) and the Mathematics Teaching Anxiety Scale (MATAS). The LSI determined the participants’ learning style preference: divergent, assimilator, convergent, and accommodator. The MATAS found the participants’ mathematics teaching anxiety level. The researcher used the one-way ANOVA with α = 0.05 in the analysis of the data. The study revealed that there were statistically significant differences in mathematics teaching anxiety between
convergent and the other three types of learners: divergent, accommodator, and assimilator. The difference was in favour of convergent learners. In other words, convergent learners had less mathematics teaching anxiety than the other types of learners. The study also found that divergent learners showed the highest level of mathematics teaching anxiety.

Reference:

Peker, M. (2009). Pre-Service Teachers' Teaching Anxiety about Mathematics and Their Learning Styles. Eurasia Journal of Mathematics, Science & Technology Education, 5(4), 335-345

NOMAD, October 2009

2009-11-24T13:10:00.001+01:00

The Nordic Journal of Research in Mathematics Education (NOMAD) has recently released the October issue. This issue contains three research articles:

Leif Bjørn Skorpen: Nokre spesielle trekk ved arbeidet med matematikkfaget i begynnaropplæringa (in Norwegian)
Frode Olav Haara and Kari Smith: Practical activities in mathematics teaching – mathematics teachers’ knowledge based reasons
Diana Stentoft and Paola Valero: Identities-in-action. Exploring the fragility of discourse and identity in learning mathematics

Graphic calculators and connectivity software

2009-11-24T11:31:00.001+01:00

Ornella Robutti has written an article called Graphic calculators and connectivity software to be a community of mathematics practitioners. This article was recently published online in ZDM. Here is the abstract of the article:

In a teaching experiment carried out at the secondary school level, we observe the students’ processes in modelling activities, where the use of graphic calculators and connectivity software gives a common working space in the class. The study shows results in continuity with others emerged in the previous ICMEs and some new ones, and offers an analysis of the novelty of the software in introducing new ways to support learning communities in the construction of mathematical meanings. The study is conducted in a semiotic-cultural framework that considers the introduction and the evolution of signs, such as words, gestures and interaction with technologies, to understand how students construct mathematical meanings, working as a community of practice. The novelty of the results consists in the presence of two technologies for students: the “private” graphic calculators and the “public” screen of the connectivity software. Signs for the construction of knowledge are mediated by both of them, but the second does it in a social way, strongly supporting the work of the learning community.

Conceptions of effective mathematics ...

2009-11-23T10:57:00.001+01:00

A new article about teachers' conception of effective mathematics teaching. The article investigates the perspectives of teachers from China and the U.S., and I find it particularly interesting because it focus on the issue of cultural beliefs. I think this is an interesting concept, and I've used it before in one of my own articles. The idea of cultural beliefs comes from results of cross-national studies where researchers have identified clear differences in the teaching practices of teachers from East-Asian and Western countries.

In the study referred to in the article below, 9 Chinese teachers and 11 U.S. teachers were interviewed. The semi-structured interviews that were used in the study were constructed according to Ernest's traditional framework of three aspects of mathematics teachers' beliefs. The study showed that the teachers from these two countries held quite different beliefs about good mathematics teaching. These views were also closely connected with their views on the nature of mathematics.

Conceptions of effective mathematics teaching within a cultural context: perspectives of teachers from China and the United States

Journal   Journal of Mathematics Teacher Education
Publisher   Springer Netherlands
ISSN   1386-4416 (Print) 1573-1820 (Online)
DOI   10.1007/s10857-009-9132-1
Subject Collection   Humanities, Social Sciences and Law
SpringerLink Date   Tuesday, November 17, 2009

By Jinfa Cai and Tao Wang

Abstract This study investigates Chinese and U.S. teachers’ cultural beliefs concerning effective mathematics teaching from the teachers’ perspectives. Although sharing some common beliefs, the two groups of teachers think differently about both mathematics understanding and the features of effective teaching. The sample of U.S. teachers put more emphasis on student understanding with concrete examples, and the sample of Chinese teachers put more emphasis on abstract reasoning after using concrete examples. The U.S. teachers highlight a teacher’s abilities to facilitate student participation, manage the classroom and have a sense of humor, while the Chinese teachers emphasize a teacher’s solid mathematics knowledge and careful study of textbooks. Both groups of teachers agree that memorization and understanding cannot be separated. However, for the U.S. teachers, memorization comes after understanding, but for Chinese teachers, memorization can come before understanding. These differences of teachers’ beliefs are discussed in a cultural context.

Learning from video

2009-11-23T09:28:00.002+01:00

The last couple of days, two articles with a focus on using video as a tool for teacher learning and development have been published in Journal of Mathematics Teaching Education. The first articleinvestigates how prospective primary mathematics teachers might learn from on-line discussions.

Prospective primary mathematics teachers’ learning from on-line discussions in a virtual video-based environment

Journal   Journal of Mathematics Teacher Education
Publisher   Springer Netherlands
ISSN   1386-4416 (Print) 1573-1820 (Online)
DOI   10.1007/s10857-009-9133-0
SpringerLink Date   Wednesday, November 18, 2009

By Salvador Llinares and Julia Valls

Abstract The aim of this study was to investigate how participation and reification of ideas about mathematics teaching are constituted in on-line discussions when prospective primary mathematics teachers analysed video-cases about mathematics teaching. Prospective teachers enrolled in a mathematics methodology course participated for 4 weeks in two virtual learning environments that integrated the analysis of video-clips, on-line discussions and writing essays about key aspects of mathematics teaching. Three aspects were considered relevant to explain the prospective teachers’ learning: the way in which the theoretical information was used to frame and to interpret the events from mathematics teaching; the characteristics of engagement with others participating in the on-line discussions and the role played by prospective teachers’ beliefs. Possible reasons for the importance of these features include the specific questions posed in on-line discussions and the use of video-clips of mathematics teaching. These findings are considered useful in designing virtual learning environments and the kinds of tasks through which the understanding of mathematics teaching and learning-to-notice skills can be developed.

The other article also has a focus on using videos, by the use of so called "video clubs".

The influence of video clubs on teachers’ thinking and practice

Journal   Journal of Mathematics Teacher Education
Publisher   Springer Netherlands
ISSN   1386-4416 (Print) 1573-1820 (Online)
DOI   10.1007/s10857-009-9130-3
SpringerLink Date   Saturday, November 14, 2009

By Elizabeth A. van Es and Miriam Gamoran Sherin

Abstract This article examines a model of professional development called “video clubs” in which teachers watch and discuss excerpts of videos from their classrooms. We investigate how participation in a video club influences teachers’ thinking and practice by exploring three related contexts: (a) teachers’ comments during video-club meetings, (b) teachers’ self-reports of the effects of the video club, and (c) teachers’ instruction across the year. Data analysis revealed changes in all three contexts. In the video-club meetings, teachers paid increased attention to student mathematical thinking over the course of the year. In interviews, teachers reported having learned about students’ mathematical thinking, about the importance of attending to student ideas during instruction, and about their school’s mathematics curriculum. Finally, shifts were also uncovered in the teachers’ instruction. By the end of the year, teachers increasingly made space for student thinking to emerge in the classroom, probed students’ underlying understandings, and learned from their students while teaching.

Mathematical thinking of kindergarten boys and girls

2009-11-16T09:54:00.001+01:00

Pnina S. Klein, Esther Adi-Japha and Simcha Hakak-Benizri have written an article called Mathematical thinking of kindergarten boys and girls: similar achievement, different contributing processes. This article was recently published online in Educational Studies in Mathematics. Here is the abstract of their article:

The objective of this study was to examine gender differences in the relations between verbal, spatial, mathematics, and teacher–child mathematics interaction variables. Kindergarten children (N = 80) were videotaped playing games that require mathematical reasoning in the presence of their teachers. The children’s mathematics, spatial, and verbal skills and the teachers’ mathematical communication were assessed. No gender differences were found between the mathematical achievements of the boys and girls, or between their verbal and spatial skills. However, mathematics performance was related to boys’ spatial reasoning and to girls’ verbal skills, suggesting that they use different processes for solving mathematical problems. Furthermore, the boys’ levels of spatial and verbal skills were not found to be related, whereas they were significantly related for girls. The mathematical communication level provided in teacher–child interactions was found to be related to girls’ but not to boys’ mathematics performance, suggesting that boys may need other forms of mathematics communication and teaching.

Several studies have focused on gender differences in mathematics education, but few have focused on gender differences with small children. The study of Klein and colleagues focus on gender differences in relation to "verbal skills, variables of spatial skills, and variables related to environmental factors, including teaching methods, quality of teaching, and mathematical communication". Four research questions are posed in the study:

"Do kindergarten boys and girls differ mathematically?
Are language and spatial skills related differently to mathematics achievements of boys and girls?
Do boys and girls receive different mathematical communication by their teachers?
Are the patterns of correlation between instructional behavior (mediation) and mathematics achievements different for boys and girls?"

A test called KeyMath was used to measure the mathematical thinking of a selection of children (n=80), half of the children were boys/girls. The test is supposed to cover an age range of 4.6-21 years. There are several subtests within this set of measures. Three tests were used to evaluate the verbal ability of the children, and two were used to evaluate their spatial skills. Observations of mathematical communications in teacher-child interactions were also made in the kindergartens. The actual testing was carried out by the authors of the paper.

The results of the study are quite interesting. They did not find any differences in mathematical achievements between the boys and girls in the study. There was, however, significant gender differences in some of the factors that were related to these results. As they state: "The boys’ mathematical achievement was significantly related to their spatial reasoning, whereas the girls’ mathematical achievement was related to their verbal skills."

I find this study interesting in many ways, but there are a few issues that I would have liked to learn more about (and that the article does not address):

Were the measures translated from English into Hebrew? (If so, I would like to learn more about this process)
What are the reasons for deciding on this particular method, and using these particular measures, in the study?

Developing flexibility for teaching algebra

2009-11-15T18:35:00.001+01:00

Christopher Yakes and Jon R. Star have written an article that was recently published online in Journal of Mathematics Teacher Education. The article is entitled Using comparison to develop flexibility for teaching algebra. Here is the abstract of their article:

In this paper, we describe a one-day professional development activity for mathematics teachers that promoted the use of comparison as an instructional tool to develop students’ flexibility in algebra. Effective use of comparison in mathematics instruction involves using side-by-side presentation of problems and solution methods and subsequent student discussion of these multiple solution methods to highlight the similarities and differences among problem-solving techniques. The goals of the professional development activity were to make teachers aware of how to use comparison effectively in their instruction, as well as to impact teachers’ own flexibility in algebra by using comparison instructionally during the professional development. Our analysis of teachers’ experiences in the professional development activity suggests that when teachers were presented with techniques for effective use of comparison, their own understanding of multiple solution methods was reinforced. In addition, teachers began to question why they relied exclusively on one familiar method over others that are equally effective and perhaps more efficient and started to draw new connections between problem-solving methods. Finally, as a result of experiencing instructional use of comparison, teachers began to see value in teaching for flexibility and reported changing their own teaching practices.

Teachers' metacognitive and heuristic approaches to word problem solving

2009-11-12T12:11:00.000+01:00

Fien Depaepe, Erik De Corte and Lieven Verschaffel have written an interesting article about Teachers’ metacognitive and heuristic approaches to word problem solving: analysis and impact on students’ beliefs and performance. The article was published online in ZDM last Friday. Here is the abstract of their article:

We conducted a 7-month video-based study in two sixth-grade classrooms focusing on teachers’ metacognitive and heuristic approaches to problem solving. All problem-solving lessons were analysed regarding the extent to which teachers implemented a metacognitive model and addressed a set of eight heuristics. We observed clear differences between both teachers’ instructional approaches. Besides, we examined teachers’ and students’ beliefs about the degree to which metacognitive and heuristic skills were addressed in their classrooms and observed that participants’ beliefs were overall in line with our observations of teachers’ instructional approaches. In addition, we investigated how students’ problem-solving skills developed as a result of teachers’ instructional approaches. A positive relationship between students’ spontaneous application of heuristics to solve non-routine word problems and teachers’ references to these skills in their problem-solving lessons was found. However, this increase in the application of heuristics did not result in students’ better performance on these non-routine word problems.

JMTE, December 2009

2009-11-11T12:16:00.000+01:00

The December issue of Journal of Mathematics Teacher Education has been published (volume 12, number 6). This issue is a special issue with focus on social justice perspectives in matheamtics teacher education, and it contains the following articles:

Working with mathematics teachers and immigrant students: an empowerment perspective, by Núria Planas and Marta Civil
‘Gender games’: a post-structural exploration of the prospective teacher, mathematics and identity, by Anna Llewellyn
Engaging with issues of emotionality in mathematics teacher education for social justice, by Mark Boylan
‘The conference was awesome’: social justice and a mathematics teacher conference, by Tamsin Meaney, Tony Trinick and Uenuku Fairhall

Mathematics and positive sciences

2009-11-11T07:32:00.000+01:00

On Friday, a new article by Giorgio T. Bagni was released from Educational Studies in Mathematics. The article is entitled Mathematics and positive sciences: a reflection following Heidegger. Bagni takes Heidegger's Being and Time as a starting point in an examination of Heidegger's ideas about sciences in general and mathematics in particular. Here is the abstract of Bagni's article:

In this article, I make a case for the inputs that Martin Heidegger's theoretical perspective offers to current concerns about the nature of mathematics, its teaching and learning, and the problem of subjectivity. In particular, I consider Heidegger's notion of positive science and discuss both its applicability to mathematics and its importance to mathematics education. I argue that Heidegger's ontological position is consonant with some sociocultural approaches in mathematics education and that Heidegger's work can shed some light on the problem of knowing and being. Finally, I raise some questions concerning subjectivity and the link between language and mathematical objects.

December issue of Educational Studies in Mathematics

2009-11-09T14:16:00.000+01:00

The December issue of Educational Studies in Mathematics has just been published (volume 72, number 3), and it contains the following articles:

Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks, by Kaye Stacey and Jill Vincent
Community college students’ views on learning mathematics in terms of their epistemological beliefs: a Q method study, by Denna L. Wheeler and Diane Montgomery
Constructing mathematics in an interactive classroom context, by Paul Ngee-Kiong Lau, Parmjit Singh and Tee-Yong Hwa
The effects of cooperative learning on preschoolers’ mathematics problem-solving ability, by Kamuran Tarim
Students’ perceptions of institutional practices: the case of limits of functions in college level Calculus courses, by Nadia Hardy
Mathématiques de la vie quotidienne au Burkina Faso: une analyse de la pratique sociale de comptage et de vente de mangues, by Kalifa Traoré and Nadine Bednarz
The challenge of self-regulated learning in mathematics teachers' professional training, by Bracha Kramarski and Tali Revach

Instructional Science, November 2009

2009-11-09T10:11:00.000+01:00

The November issue of Instructional Science has been released (Volume 37, Number 6, 2009). Here is a list of articles that is published in this issue:

The effects of representational format on learning combinatorics from an interactive computer simulation, by Bas Kolloffel, Tessa H. S. Eysink, Ton de Jong and Pascal Wilhelm
Uncertainty and engagement with learning games, by Paul A. Howard-Jones and Skevi Demetriou
Are instructional explanations more effective in the context of an impasse? by Emilio Sánchez, Héctor García-Rodicio and Santiago R. Acuña
Teacher and student intrinsic motivation in project-based learning, by Shui-fong Lam, Rebecca Wing-yi Cheng and William Y. K. Ma
Graduate students’ conceptions of university teaching and learning: formation for change, by Alenoush Saroyan, Joyce Dagenais and Yanfei Zhou

New journal in mathematics education!

2009-11-06T09:57:00.001+01:00

International Journal of Studies in Mathematics Education is a new international peer-reviewed journal within the field of mathematics education. The editors of the journal are from Brazil, and the journal web-site is in both Portuguese and English. The journal also accepts submission of articles in Portuguese, English, French and Spanish. According to their own description of the journal:

The journal aims to stimulate reflection on mathematics education at all levels: to generate productive discussion; to encourage enquiry and research; to promote criticism and evaluation of ideas and procedures current in the field
It is intended for the mathematics educator who is aware that the learning and teaching of mathematics are complex enterprises about which much remains to be revealed and understood
It reflects both the variety of research concerns within the field and the range of methods used to study them. We accept for submission articles in Portuguese, English, French and Spanish. The journal emphasizes high-level articles that go beyond local or national interest.

The journal has an online submission system, and the Open Journal Systems is being used. The journal is an online journal, and it appears to have an Open Access philosophy, so that the articles will be freely available for everyone to read/download. The aims of the journal are:

to stimulate reflection on mathematics education at all levels;
to generate productive discussion;
to encourage enquiry and research;
to promote criticism and evaluation of ideas and procedures current in the field

Unfortunately, I cannot find an RSS feed yet, but I am definitely going to keep an eye on this journal even though!

The first issue of the journal is already available, and it contains several interesting articles. The following articles are in English:

Gesture, conceptual integration and mathematical talk, by Laurie Edwards
Learning in virtual environments: a methodology for the analysis of teacher discourse, by Marcello Bairral
Teacher's semiotic games in mathematics laboratory, by Ornella Robutti

New IJMEST articles

2009-11-05T07:27:00.000+01:00

A couple of new articles have been published online in International Journal of Mathematical Education in Science and Technology. Several are so-called classroom notes (see this link for full list), and then there are these two original articles:

Pilot study on algebra learning among junior secondary students, by Kin-Keung Poon and Chi-Keung Leung. Abstract: The purpose of the study reported herein was to identify the common mistakes made by junior secondary students in Hong Kong when learning algebra and to compare teachers' perceptions of students' ability with the results of an algebra test. An algebra test was developed and administered to a sample of students (aged between 13 and 14 years). From the responses of the participating students (N = 815), it was found that students in schools with a higher level of academic achievement had better algebra test results than did those in schools with a lower level of such achievement. Moreover, it was found that a teacher's perception of a student's ability has a correlation with that student's level of achievement. Based on this finding, an instrument that measures teaching effectiveness is discussed. Last but not least, typical errors in algebra are identified, and some ideas for an instructional design based on these findings are discussed.
Student connections of linear algebra concepts: an analysis of concept maps, by Douglas A. Lapp, Melvin A. Nyman and John S. Berry. Abstract: This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud's theory of conceptual fields and Pirie and Kieren's model for the growth of mathematical understanding. In addition to the existing techniques for analysing concept maps, two new techniques are developed for analysing qualitative data based on student-constructed concept maps: (1) temporal clumping of concepts and (2) the use of adjacency matrices of an undirected graph representation of the concept map. Findings suggest that students may find it more difficult to make connections between concepts like eigenvalues and eigenvectors and concepts from other parts of the conceptual field such as basis and dimension. In fact, eigenvalues and eigenvectors seemed to be the most disconnected concepts within all of the students' concept maps. In addition, the relationships between link types and certain clumps are suggested as well as directions for future study and curriculum design.

Insight into the fractional calculus via a spreadsheet

2009-11-02T10:13:00.000+01:00

David A. Miller and Stephen J. Sugden have written an article called Insight into the Fractional Calculus via a Spreadsheet. The article was published in the most recent issue of electronic journal Spreadsheets in Education. The article is freely available as a pdf download, but here is a copy of the abstract:

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

JMTE - October 2009

2009-10-28T07:50:00.000+01:00

Journal of Mathematics Teacher Education has just released the October issue (Volume 12, Number 5). This issue contains 5 interesting articles:

Conditions of progress in mathematics teacher education, by João Pedro da Ponte
Teachers’ innovative change within countrywide reform: a case study in Rwanda, by Alphonse Uworwabayeho
Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices, by Dionne I. Cross
Multiple representations as sites for teacher reflection about mathematics learning, by Amy E. Ryken
Understanding the influence of two mathematics textbooks on prospective secondary teachers’ knowledge, by Jon D. Davis

Alphonse Uworwabayeho's article abat the Rwandan case study is an Open Access article.

ZDM, November 2009

2009-10-28T07:45:00.000+01:00

ZDM - The International Journal on Mathematics Education - has published the November issue of 2009 (Volume 41, Number 6). The issue contains the following nine articles:

Curriculum research to improve teaching and learning: national and cross-national studies, by Gerald Kulm and Yeping Li
Mathematics teachers’ practices and thinking in lesson plan development: a case of teaching fraction division, by Yeping Li, Xi Chen and Gerald Kulm
Approaches and practices in developing school mathematics textbooks in China, by Yeping Li, Jianyue Zhang and Tingting Ma
Mathematics curriculum: a vehicle for school improvement, by Christian R. Hirsch and Barbara J. Reys
School mathematics curriculum materials for teachers’ learning: future elementary teachers’ interactions with curriculum materials in a mathematics course in the United States, by Gwendolyn Monica Lloyd
How a standards-based mathematics curriculum differs from a traditional curriculum: with a focus on intended treatments of the ideas of variable, by Bikai Nie, Jinfa Cai and John C. Moyer
Cross-cultural issues in linguistic, visual-quantitative, and written-numeric supports for mathematical thinking, by Karen C. Fuson and Yeping Li
Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: the case of fraction division, by Yeping Li, Xi Chen and Song An
Cross-national comparisons of mathematics curriculum materials: what might we learn? by Edward A. Silver

The article by Karen C. Fuson and Yeping Li is an Open Access article, so that one should be available to all, even non-subscribers :-)

Seminar with Bharath Sriraman

2009-10-25T18:02:00.001+01:00

On Thursday, we had a very nice seminar with Bharath Sriraman, or rather we had him as a visitor at University of Stavanger for the whole day! Bharath is professor of mathematical sciences at the University of Montana. He is also founder and editor of The Montana Mathematics Enthusiast, a great online journal within the field of mathematics education research, and editor of numerous other journals, book series, etc.

When he visited us on Thursday, he held a lecture with a focus on gifted students, one of his specialties. Here are my notes from the lecture:

Gifted students - presentation by Bharath Sriraman

How do we figure out if a student is gifted? Nature versus nurture - is it genetic, or is it due to upbringing. Why is it okay for a child to be talented in sports and not so much so in a subject like mathematics?

When it comes to funding, little money is spent on gifted education. (Less than 1% of the funding for special needs education - giftedness is viewed as a special need!)

In the U.S. there is an east versus west debate. Why are they doing so much better in the eastern systems? The western system is viewed as fostering creativity and freedom, but why is it that so many of the prodigies are from the eastern part of the world?

In the U.S., public schools are poorly funded, teachers are not held in high regard or paid well, etc.

Interesting fact: U.S. has the highest prison population proportion in the western, developed world - 30% of the prisoners are high school dropouts.

In the Asian countries, there is a lot of focus on moral, hard work, perseverance, etc. Exams are very competitive! In the East, the point of an exam is to stratify the society. Late bloomers do not have a chance within the Eastern system! The U.S. (and Western) system, however, allows for a second chance.

As a teacher, there is always the potential conflict between equity and excellence! This could be seen as a false dichotomy! Alternative perspectives:

The Hamilton tradition stressed elitism,
whereas the Jacksonian tradition suggests that everyone is equal no matter what
The Jeffersonian tradition stresses that you should give people equal opportunities, and then it is up to them to use these opportunities

Mathematical intelligence is considered as:

a strong indicator of general intelligence
numerical and spatial reasoning is part of the IQ score
...

The construct of intelligence is controversial in many ways since the psychometric testing. History of IQ-test: Binet-Simon tests --> Stanford-Binet tests, etc. The modern Stanford-Binet test is very much like a mathematical test, and you don't take into account socio-cultural and environmental variables. Still, it is very much used as a test for giftedness.

There are, however, some alternative views when it comes to discussing giftedness. Usiskin (Uni. Chicago) tried to classify the mathematical talent in the world in a hierarchy of Level 0 to Level 7.

Level 0 - no talent. Adults who know very little mathematics
Level 1 - culture level. Adults who have some number sense (comparable to grades 6-9), and they have learned it through usage
Level 2 - represent the honors high school student
Level 3 - the "terrific" student, those who score 750-800 on the SAT.
Level 4 - the "exceptional" students, those who excel in math competitions
Level 5 - represents the productive mathematician
Level 6 - the exceptional mathematician
Level 7 - the all-time greats, Fields medal winners in mathematics

Krutetskii's book is very nice - about gifted students!

Problem: a pole is 15 meters tall, another one is 10 meters tall. You have a rope from the top of one to the bottom of the other, and vice versa. How tall is the crossing point of the ropes from the ground?

There is a difference between Creativity and creativity (everyone has the latter, the former is related to being creative within a certain field).

There are lots of way to adapt the curriculum so that the gifted students get what they need.

Research shows that there are no harmful effect on early college admission - the students manage well, and they adapt well.

In the U.S. there is a lot of emphasis on the modeling-based curricula nowadays, and this gets a lot of funding. Several programs are made which are based on real-world situations. (one from Montana!)

After this interesting lecture, he gave a presentation of a new book that he has been editing together with Lyn English: Theories of Mathematics Education: Seeking new frontiers. The book is published by Springer, and has just been released. Bharath told that the book took him five years to finish, and it is definitely going to become an important contribution to our field!

Thanks a lot for the visit, Bharath, and for sharing this day with us! Hopefully, this is only going to be the first in a series of visits to Stavanger!

Mathematics curriculum: a vehicle for school improvement

2009-10-21T08:39:00.000+02:00

Christian R. Hirsch and Barbara J. Reys have written an article entitled Mathematics curriculum: a vehicle for school improvement. This article was recently published online in ZDM. Here is a copy of their article abstract:

Different forms of curriculum determine what is taught and learned in US classrooms and have been used to stimulate school improvement and to hold school systems accountable for progress. For example, the intended curriculum reflected in standards or learning expectations increasingly influences how instructional time is spent in classrooms. Curriculum materials such as textbooks, instructional units, and computer software constitute the textbook curriculum, which continues to play a dominant role in teachers’ instructional decisions. These decisions influence the actual implemented curriculum in classrooms. Various curriculum policies, including mandated end-of-course assessments (the assessed curriculum) and requirements for all students to complete particular courses (e.g., year-long courses in algebra, geometry, and advanced algebra or equivalent integrated mathematics courses) are also being implemented in increasing numbers of states. The wide variation across states in their intended curriculum documents and requirements has led to a historic and precedent-setting effort by the Council of Chief State School Officers and the National Governors Association Council for Best Practices to assist states in the development and adoption of common College and Career Readiness Standards for Mathematics. Also under development by this coalition is a set of common core state mathematics standards for grades K-12. These sets of standards, together with advances in information technologies, may have a significant influence on the textbook curriculum, the implemented curriculum, and the assessed curriculum in US classrooms in the near future.

CAS calculators in algebra instruction

2009-10-21T08:34:00.000+02:00

S. Aslι Özgün-Koca has written an article called Prospective teachers’ views on the use of calculators with Computer Algebra System in algebra instruction. This article has recently been published online in Journal of Mathematics Teacher Education. Here is the abstract of the article:

Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This study investigated the views of Turkish prospective secondary mathematics teachers on the use of advanced calculators with CAS in algebra instruction. An open-ended questionnaire and group interviews revealed prospective teachers’ views and beliefs about when and why they prefer three possible uses of CAS—black box, white box, or Symbolic Math Guide (SMG). The results showed that participants mainly preferred the white box methods and especially SMG to the black box method. They suggested that while the black box method could be used after students mastered the skills, the general white box method and SMG could be used to teach symbolic manipulation.

MTL, Volume 11, Issue 4

2009-10-20T08:11:00.000+02:00

A new issue of Mathematical Thinking and Learning has appeared: Volume 11, Issue 4, 2009. The issue contains three research articles (along with an editorial by Lyn D. English and a book review):

Learning Mathematics via a Problem-Centered Approach: A Two-Year Study, by Candice L. Ridlon
Efficacy of Different Concrete Models for Teaching the Part-Whole Construct for Fractions, by Kathleen Cramer; Terry Wyberg
Reasoning-and-Proving in School Mathematics Textbooks, by Gabriel J. Stylianides

100 open lectures

2009-10-20T07:37:00.000+02:00

Yesterday, a very nice blogpost appeared over at onlinecollege.org: 100 Incredible Open Lectures for Math Geeks. In this post, they have collected and organized 100 sets of lectures within several fields of mathematics, like Algebra, Calculus, Geometry, etc. Towards the very end of the list, there is even a collection of lectures related to teaching! The lectures are from some of the best universities in the world, like Stanford, MIT, Princeton, Harvard, Berkeley, UCLA, etc. The lecturers are of course also extremely good. For instance, you'll find a lecture that includes Professor Terrence Tao from UCLA. Professor Tao is arguably one of the best mathematicians of our days, and he has received numerous awards, like the Fields Medal (in 2006). I also recommend the lectures of Professor Gilbert Strang (MIT) in Linear Algebra. Several of the lectures from the list are from Academic Earth, so you might want to check out that site as well.

This is a very useful list, and as it is said in the original post:

You can indulge your love of mathematics in these great lectures and lecture series. Some are meant to review the basics and others will keep you on the cutting edge of what renowned researchers are doing in the field, but all will help you expand your knowledge and spend a few hours enjoying a topic you love.

Teachers' perceptions about the purpose of student teaching

2009-10-20T07:26:00.000+02:00

Keith Leatham from Brigham Young University in Utah, U.S., is one of the scholars who have made important contribution to research of teachers' beliefs in mathematics education research in the last couple of years. I very much like his proposed framework for viewing teachers' beliefs as sensible systems (from his 2006 article in Journal of Mathematics Teacher Education). Now he has written a new article with focus on beliefs (or this time it is referred to as perceptions), and he has co-written this article with a colleague from Brigham Young University: Blake E. Peterson. Their article is entitled Secondary mathematics cooperating teachers’ perceptions of the purpose of student teaching, and it was published online in Journal of Mathematics Teacher Education last week. Here is their article abstract:

This article reports on the results of a survey of 45 secondary mathematics cooperating teachers’ perceptions of the primary purposes of student teaching and their roles in accomplishing those purposes. The most common purposes were interacting with an experienced, practising teacher, having a real classroom experience, and experiencing and learning about classroom management. The most common roles were providing the space for experience, modeling, facilitating reflection, and sharing knowledge. The findings provided insights into the cooperating teachers’ perceptions about both what should be learned through student teaching and how it should be learned. These findings paint a picture of cooperating teachers who do not see themselves as teacher educators—teachers of student teachers. Implications for mathematics teacher educators are discussed.

A case study in Rwanda

2009-10-19T17:20:00.000+02:00

I haven't read many scientific articles in mathematics education from or about Rwanda, but here is one! Alphonse Uworwabayeho from Kigali Institute of Education in Rwanda, and University of Bristol, UK, has written an article entitled Teachers’ innovative change within countrywide reform: a case study in Rwanda. The article was published online in Journal of Mathematics Teacher Education on Wednesday. This is even an Open Access article, so everyone should have full access to it! Here is the abstract of the article:

This article presents practical perspectives on mathematics teacher change through results of collaborative research with two mathematics secondary school teachers in order to improve the teaching and learning of mathematics in Rwanda. The 2006 national mathematics curriculum reform stresses pedagogies that enhance problem-solving, critical thinking and argumentation. Teachers need to use new teaching strategies. This article is a case study looking at issues around developing teachers’ use of interactions in mathematics classrooms independently of the national programme. Outputs of the study include teachers’ awareness of the need for change and their increased flexibility to accept learners’ autonomy in shifting from teacher-centred to learner-centred pedagogy. Geometer’s Sketchpad challenged teachers’ practice and then provoked reflection to improve student learning.

Teachers' use of representation

2009-10-19T07:16:00.000+02:00

An article called Prospective elementary teachers use of representation to reason algebraically has recently been published online in The Journal of Mathematical Behavior. The article was written by Kerri Richardson, Sarah Berenson and Katrina Staley. Here is the abstract of their article:

We used a teaching experiment to evaluate the preparation of preservice teachers to teach early algebra concepts in the elementary school with the goal of improving their ability to generalize and justify algebraic rules when using pattern-finding tasks. Nearly all of the elementary preservice teachers generalized explicit rules using symbolic notation but had trouble with justifications early in the experiment. The use of isomorphic tasks promoted their ability to justify their generalizations and to understand the relationship of the coefficient and y-intercept to the models constructed with pattern blocks. Based on critical events in the teaching experiment, we developed a scale to map changes in preservice teachers’ understanding. Features of the tasks emerged that contributed to this understanding.

Students’ perceived sociomathematical norms

2009-10-18T19:16:00.001+02:00

Esther Levenson, Dina Tirosh and Pessia Tsamir (all from Tel Aviv University in Israel) have written an article that was recently published in The Journal of Mathematical Behavior. The article is entitled Students’ perceived sociomathematical norms: The missing paradigm. Here is the article abstract:

This study proposes a framework for research which takes into account three aspects of sociomathematical norms: teachers’ endorsed norms, teachers’ and students’ enacted norms, and students’ perceived norms. We investigate these aspects of sociomathematical norms in two elementary school classrooms in relation to mathematically based and practically based explanations. Results indicate that even when the observed enacted norms are in agreement with the teachers’ endorsed norms, the students may not perceive these same norms. These results highlight the need to consider the students’ perspective when investigating sociomathematical norms.

ESM - November issue

2009-10-14T09:26:00.000+02:00

A new issue of Educational Studies in Mathematics has been released, Volume 72, Number 2 / November, 2009. This issue contains seven interesting articles:

Using the onto-semiotic approach to identify and analyze mathematical meaning when transiting between different coordinate systems in a multivariate context, by Mariana Montiel, Miguel R. Wilhelmi, Draga Vidakovic and Iwan Elstak
Changing practice, changing minds, from arithmetical to algebraic thinking: an application of the concerns-based adoption model (CBAM), by Jeanne Tunks and Kirk Weller
Conditional inference and advanced mathematical study: further evidence, by Matthew Inglis and Adrian Simpson
Didactical designs for students’ proportional reasoning: an “open approach” lesson and a “fundamental situation”, by Takeshi Miyakawa and Carl Winsløw
Bridging the macro- and micro-divide: using an activity theory model to capture sociocultural complexity in mathematics teaching and its development, by Barbara Jaworski and Despina Potari
Proof constructions and evaluations, by Andreas J. Stylianides and Gabriel J. Stylianides
Researchers’ descriptions and the construction of mathematical thinking, by Richard Barwell

Maths week in Ireland

2009-10-13T10:05:00.001+02:00

The 4th annual Maths Week Ireland takes place this week, and it is presented as an "all island celebration of mathematics" at the official website. The Irish Times published an interesting article about this yesterday. There are several activities going on during the week, and it is all "timed to coincide with the annual Hamilton Day" on October 16th. William Rowan Hamilton (1805-1865) was one of Ireland's most famous mathematicians, and he was also a physicist and astronomer.

Make sure to check out the official website for a list of events!

Sudoku: Strategy versus structure

2009-10-13T09:54:00.001+02:00

"You don't have to know any mathematics to solve a Sudoku puzzle," one of the major Norwegian newspaper claimed when the Sudoku wave started a couple of years ago. I have always disagreed strongly with this, and it seems that Provan J. Scott, who has written an article about this in American Mathematical Monthly, has a similar opinion. The article is entitled Sudoku: strategy versus structure. Here is the article abstract:

Sudoku puzzles, and their variants, have become extremely popular in the last decade. They can now be found in major U.S. newspapers, puzzle books, and web sites; almost as pervasive are the many guides to Sudoku strategy and logic. We give a class of solution strategies-encompassing a dozen or so differently named solution rules found in these guides-that is at once simple, popular, and powerful. We then show the relationship of this class to the modeling of Sudoku puzzles as assignment problems and as unique nonnegative solutions to linear equations. The results provide excellent applications of principles commonly presented in introductory classes in finite mathematics and combinatorial optimization, and point as well to some interesting open research problems in the area.

Teachers' difficulties during problem-solving instruction

2009-10-13T09:49:00.001+02:00

Alexander Karp has written an article that was published online in Journal of Mathematics Teacher Education on Saturday. The article is called Analyzing and attempting to overcome prospective teachers’ difficulties during problem-solving instruction. Here is the abstract of Karp's article:

This article analyzes the experiences of prospective secondary mathematics teachers during a teaching methods course, offered prior to their student teaching, but involving actual teaching and reflexive analysis of this teaching. The study focuses on the pedagogical difficulties that arose during their teaching, in which prospective teachers lacked pedagogical content knowledge and skills. It also analyzes the experience of the course itself, which was aimed at scaffolding the work of prospective teachers on developing their pedagogical content knowledge and skills.

Curriculum research to improve teaching and learning

2009-10-06T07:33:00.001+02:00

Gerald Kulm and Yeping Li have written an article entitled Curriculum research to improve teaching and learning: national and cross-national studies. The article was recently published online in ZDM. Here is the abstract of their article:

Curriculum, as a cultural and system-specific artifact, outlines mathematics teaching and learning activities in school education. Studies of curriculum and its changes are thus important to reveal the expectations, processes and outcomes of students’ school learning experiences that are situated in different cultural and system contexts. In this article, we aim to propose a framework that can help readers to develop a better understanding of curriculum practices and changes in China and/or the USA that have been reported and discussed in articles published in this themed issue. Going beyond the selected education systems, further studies of curriculum practices and changes are much needed to help ensure the success of educational reforms in the different cultural and system contexts.

Mathematics instruction for students with learning disabilities

2009-10-03T08:23:00.000+02:00

Russel Gersten and colleagues have written an article called Mathematics Instruction for Students With Learning Disabilities: A Meta-Analysis of Instructional Components. This article was published in the recent issue of Review of Educational Research. Here is the abstract of their article:

The purpose of this meta-analysis was to synthesize findings from 42 interventions (randomized control trials and quasi-experimental studies) on instructional approaches that enhance the mathematics proficiency of students with learning disabilities. We examined the impact of four categories of instructional components: (a) approaches to instruction and/or curriculum design, (b) formative assessment data and feedback to teachers on students' mathematics performance, (c) formative data and feedback to students with LD on their performance, and (d) peer-assisted mathematics instruction. All instructional components except for student feedback with goal-setting and peer-assisted learning within a class resulted in significant mean effects ranging from 0.21 to 1.56. We also examined the effectiveness of these components conditionally, using hierarchical multiple regressions. Two instructional components provided practically and statistically important increases in effect size–teaching students to use heuristics and explicit instruction. Limitations of the study, suggestions for future research, and applications for improvement of current practice are discussed.

Multiple solution methods and multiple outcomes

2009-10-02T08:19:00.000+02:00

Pessia Tsamir, Dina Tirosh, Michal Tabach and Esther Levenson have written an article about Multiple solution methods and multiple outcomes—is it a task for kindergarten children? This article was recently published online in Educational Studies in Mathematics. Here is a copy of their article abstract:

Engaging students with multiple solution problems is considered good practice. Solutions to problems consist of the outcomes of the problem as well as the methods employed to reach these outcomes. In this study we analyze the results obtained from two groups of kindergarten children who engaged in one task, the Create an Equal Number Task. This task had five possible outcomes and five different methods which may be employed in reaching these outcomes. Children, whose teachers had attended the program Starting Right: Mathematics in Kindergartens, found more outcomes and employed more methods than children whose teachers did not attend this program. Results suggest that the habit of mind of searching for more than one outcome and employing more than one method may be promoted in kindergarten.

How syntactic reasoners can develop understanding

2009-10-02T08:15:00.000+02:00

Keith Weber has written an article that was recently published in The Journal of Mathematical Behavior. The article is entitled How syntactic reasoners can develop understanding, evaluate conjectures, and generate counterexamples in advanced mathematics. Here is the abstract of Weber's article:

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes exercises about it. The paper focuses on how Isaac developed an understanding of this concept, how he evaluated whether a mathematical assertion is true or false, how he generated counterexamples to disprove a statement, and the general role examples play for him in concept development and understanding.

What's sophisticated about elementary mathematics?

2009-10-01T08:02:00.000+02:00

The current issue of American Educator includes a very interesting article about mathematics teaching in the elementary grades. The article is entitled What's Sophisticated about Elementary Mathematics? Plenty—That's Why Elementary Schools Need Math Teachers, and it is written by Hung-Hsi Wu, who is professor emeritus of mathematics at UC Berkeley. I should probably say a lot more about him, because his list of merits is impressive, but I will leave it to you to find out more.

It appears to be a rather common impression that teaching elementary mathematics is ... well, rather elementary. I mean, the mathematics is quite simple, so how hard can it be? In this article, Wu provides a very nice introduction to how challenging it can actually be. In the introductory part of the article, he claims: "The fact is, there's a lot more to teaching math than teaching how to do calculations." In the article, he provides examples of how hard it can actually be to teach something as "elementary" as place value and fractions.

I am tempted to quote more or less the entire article, because so many interesting issues are presented here, but I will not. I am, however, going to recommend that you take the time and read this excellent article. If you are somewhat interested in teaching mathematics, I am sure you will find this interesting!

Thanks a lot to Assistant Editor Jennifer Dubin for telling me about this article, by the way! I appreciate it :-)

Developing school mathematics textbooks in China

2009-10-01T07:41:00.000+02:00

Yeping li, Jianyue Zhang and Tingting Ma have written an article entitled Approaches and practices in developing school mathematics textbooks in China. This article was published online in ZDM a couple of days ago. This article gives a very interesting overview of how Chinese textbooks are developed, but it also provides nice insights into how mathematics teaching has developed (or is developing) in China. Here is the abstract of this article:

In this study, we aim to examine and discuss approaches and practices in developing mathematics textbooks in China, with a special focus on the development of secondary school mathematics textbook in the context of recent school mathematics reform. Textbook development in China has its own history. This study reveals some common practices and approaches developed and used in selecting, presenting and organizing content in mathematics textbooks over the years. With the recent curriculum reform taking place in China, we also discuss some new developments in compiling and publishing high school mathematics textbooks. Implications obtained from Chinese practices in textbook development are then discussed in a broad context.

The productive notion of mathematics laboratories

2009-10-01T07:36:00.000+02:00

Michela Maschietto and Luc Trouche have written an article called Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories. The article was published online in ZDM on Monday. Although they start with a glimpse from a babylonian clay tablet, their main focus is on the development of tools and use of tools in the last century. In the main part of their article, they have a strong focus on the so-called mathematics laboratories. Here is the abstract of their article:

In our research work, we have looked at the way in which artefacts become, for teachers as well as for students, instruments of their mathematical activity. The issues related to the use of tools and technologies in mathematical education are now widely considered. A look to history highlights the different ways in which the same questions have been studied at different times and in different places. This suggests that the contribution of artefacts to mathematics learning should be considered in terms of various contexts. Our “visits” to these contexts will be guided by the coordination of two main theoretical frameworks, the instrumental approach and the semiotic mediation approach from the perspective of mathematics laboratory. This journey through history and schooling represents a good occasion to address some questions: Are there “good” contexts in which to develop mathematical instruments? Are there “good” teaching practices which assist students’ instrumental geneses and construct mathematical meanings? How is it possible to promote such teaching practices? Some study cases are discussed.

IJSME, October 2009

2009-09-26T10:36:00.001+02:00

A new issue of International Journal of Science and Mathematics Education has been published, Volume 7, Number 5, October 2009. The issue contains nine articles, several of which are related to mathematics education:

CREATING OPTIMAL MATHEMATICS LEARNING ENVIRONMENTS: COMBINING ARGUMENTATION AND WRITING TO ENHANCE ACHIEVEMENT, by Dionne I. Cross
APPROACHES TO TEACHING MATHEMATICS IN LOWER-ACHIEVING CLASSES, by Ruhama Even and Tova Kvatinsky
ANALYSIS OF THE LEARNING EXPECTATIONS RELATED TO GRADE 1–8 MEASUREMENT IN SOME COUNTRIES, by Jung Chih Chen, Barbara J. Reys and Robert E. Reys
EPISTEMOLOGICAL OBSTACLES IN COMING TO UNDERSTAND THE LIMIT OF A FUNCTION AT UNDERGRADUATE LEVEL: A CASE FROM THE NATIONAL UNIVERSITY OF LESOTHO, by Eunice Kolitsoe Moru

Addition and subtraction of three-digit numbers

2009-09-26T10:29:00.001+02:00

Aiso Heinze, Franziska Marschick and Frank Lipowsky have written an article that was published in the recent issue of ZDM. The article is entitled Addition and subtraction of three-digit numbers: adaptive strategy use and the influence of instruction in German third grade. Here is the abstract of their article:

Empirical findings show that many students do not achieve the level of a flexible and adaptive use of arithmetic computation strategies during the primary school years. Accordingly, educators suggest a reform-based instruction to improve students’ learning opportunities. In a study with 245 German third graders learning by textbooks with different instructional approaches, we investigate accuracy and adaptivity of students’ strategy use when adding and subtracting three-digit numbers. The findings indicate that students often choose efficient strategies provided they know any appropriate strategies for a given problem. The proportion of appropriate and efficient strategies students use differs with respect to the instructional approach of their textbooks. Learning with an investigative approach, more students use appropriate strategies, whereas children following a problem-solving approach show a higher competence in adaptive strategy choice. Based on these results, we hypothesize that different instructional approaches have different advantages and disadvantages regarding the teaching and learning of adaptive strategy use.

Flexible and adaptive use of strategies and representations

2009-09-26T10:18:00.001+02:00

Aiso Heinze, Jon R. Star and Lieven Verschaffel have written an article entitled Flexible and adaptive use of strategies and representations in mathematics education. The article was published in ZDM, Volume 41, Number 5 on Wednesday. Here is the abstract of their article:

The flexible and adaptive use of strategies and representations is part of a cognitive variability, which enables individuals to solve problems quickly and accurately. The development of these abilities is not simply based on growing experience; instead, we can assume that their acquisition is based on complex cognitive processes. How these processes can be described and how these can be fostered through instructional environments are research questions, which are yet to be answered satisfactorily. This special issue on flexible and adaptive use of strategies and representations in mathematics education encompasses contributions of several authors working in this particular field. They present recent research on flexible and adaptive use of strategies or representations based on theoretical and empirical perspectives. Two commentary articles discuss the presented results against the background of existing theories.

How Do Parents Support Preschoolers’ Numeracy Learning Experiences at Home?

2009-09-24T21:59:00.000+02:00

A new and interesting article has been published in Early Childhood Education Journal: How Do Parents Support Preschoolers’ Numeracy Learning Experiences at Home? The article is written by Sheri-Lynn Skwarchuk.

Abstract

This study described the kinds of early numeracy experiences that parents provide for their preschoolers, and determined the extent to which parental experiences and involvement in home activities enhanced preschoolers’ numeracy knowledge. Twenty-five parents completed a home activity questionnaire, a 2-week diary study, and a videotaped play session where they were asked to draw out numerical content. Preschoolers’ numeracy scores were predicted by: (1) parental reports of positive personal experiences with mathematics and (2) involvement in activities with complex (versus basic) numeracy goals. Parents felt that most activities had important or essential mathematical value, but focused on number sense goals. Finally, parents who reportedly spent more time on numeracy tasks received high quality interaction ratings in the videotaped sessions; but these variables did not predict numeracy scores. The findings are discussed in terms of educating parents about incorporating numeracy concepts.

Finnish pre-service teachers’ and upper secondary students’ understanding of division and reasoning strategies used

2009-09-24T21:54:00.001+02:00

New article in Educational Studies in Mathematics, written by Raimo Kaasila, Erkki Pehkonen and Anu Hellinen: Finnish pre-service teachers’ and upper secondary students’ understanding of division and reasoning strategies used

Abstract

In this paper, we focus on Finnish pre-service elementary teachers’ (N = 269) and upper secondary students’ (N = 1,434) understanding of division. In the questionnaire, we used the following non-standard division problem: “We know that 498:6 = 83. How could you conclude from this relationship (without using long-division algorithm) what 491:6 = ? is?” This problem especially measures conceptual understanding, adaptive reasoning, and procedural fluency. Based on the results, we can conclude that division seems not to be fully understood: 45% of the pre-service teachers and 37% of upper secondary students were able to produce complete or mainly correct solutions. The reasoning strategies used by these two groups did not differ very much. We identified four main reasons for problems in understanding this task: (1) staying on the integer level, (2) an inability to handle the remainder, (3) difficulties in understanding the relationships between different operations, and (4) insufficient reasoning strategies. It seems that learners’ reasoning strategies in particular play a central role when teachers try to improve learners’ proficiency.

Teachers' conceptions of creativity

2009-09-21T13:56:00.000+02:00

David S. Bolden, Tony V. Harries and Douglas P. Newton have written an article entitled Pre-service primary teachers' conceptions of creativity in mathematics. This article was recently published online in Educational Studies in Mathematics. The issues concerning creativity that are raised in this article are interesting. I also find it interesting to observe how the authors make use of concepts like "beliefs" and "conceptions". As far as I can tell, they don't make a distinction between these concepts, and they also talk about teachers "views" without making a clear distinction between this concept in relation to the two former. Although attempts have been made in the past by researchers to define and distinguish between these concepts, I think we still have a challenge here!

Here is the abstract of their article:

Teachers in the UK and elsewhere are now expected to foster creativity in young children (NACCCE, 1999; Ofsted, 2003; DfES, 2003; DfES/DCMS, 2006). Creativity, however, is more often associated with the arts than with mathematics. The aim of the study was to explore and document pre-service (in the UK, pre-service teachers are referred to as ‘trainee’ teachers) primary teachers’ conceptions of creativity in mathematics teaching in the UK. A questionnaire probed their conceptions early in their course, and these were supplemented with data from semi-structured interviews. Analysis of the responses indicated that pre-service teachers’ conceptions were narrow, predominantly associated with the use of resources and technology and bound up with the idea of ‘teaching creatively’ rather than ‘teaching for creativity’. Conceptions became less narrow as pre-service teachers were preparing to enter schools as newly qualified, but they still had difficulty in identifying ways of encouraging and assessing creativity in the classroom. This difficulty suggests that conceptions of creativity need to be addressed and developed directly during pre-service education if teachers are to meet the expectations of government as set out in the above documents.

Self-efficacy beliefs regarding mathematics and science teaching

2009-09-21T13:45:00.000+02:00

Murat Bursal has written an article about Turkish preservice elementary teachers' self-efficacy beliefs regarding mathematics and science teaching. This article was published online in International Journal of Science and Mathematics Education on Thursday. A key finding is that the preservice teachers in this study had "adequate" self-efficacy beliefs when they graduated. These findings are linked with a recent reform in Turkish teacher education. Here is the abstract of the article:

This study investigated Turkish preservice, elementary teachers’ personal mathematics teaching efficacy (PMTE), and science teaching efficacy (PSTE) beliefs at the end of their teacher education program. A majority of the participants believed they were well prepared to teach both elementary mathematics and science, but their PSTE scores were significantly lower than their PMTE scores. However, a significant correlation was found between the PMTE and PSTE scores. No significant gender effect on PMTE and PSTE scores was observed, but unlike the results from other countries, Turkish female preservice elementary teachers were found to have slightly higher PMTE and PSTE scores than their male peers. High school major area was found to be a significant predictor of participants’ PMTE and PSTE scores. Participants with mathematics/science high school majors were found to have significantly higher PMTE and PSTE scores than those with other high school majors.

Three new ZDM articles

2009-09-20T19:54:00.001+02:00

Three new articles have been published online in ZDM lately. One of these articles is entitled The role of fluency in a mathematics item with an embedded graphic: interpreting a pie chart, and it is written by Carmel Mary Diezmann and Tom Lowrie. Here is the abstract of their article:

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

The other is written by Alan T. Graham, Maxine Pfannkuch and Michael O.J. Thomas. Their article is called Versatile thinking and the learning of statistical concepts. In the abstract you learn more about the main ideas in this article:

Statistics was for a long time a domain where calculation dominated to the detriment of statistical thinking. In recent years, the latter concept has come much more to the fore, and is now being both researched and promoted in school and tertiary courses. In this study, we consider the application of the concept of flexible or versatile thinking to statistical inference, as a key attribute of statistical thinking. Whilst this versatility comprises process/object, visuo/analytic and representational versatility, we concentrate here on the last aspect, which includes the ability to work within a representation system (or semiotic register) and to transform seamlessly between the systems for given concepts, as well as to engage in procedural and conceptual interactions with specific representations. To exemplify the theoretical ideas, we consider two examples based on the concepts of relative comparison and sampling variability as cases where representational versatility may be crucial to understanding. We outline the qualitative thinking involved in representations of relative density and sample and population distributions, including mathematical models and their precursor, diagrammatic forms.

Finally, George Gadanidis and Vince Geiger have written an article about A social perspective on technology-enhanced mathematical learning: from collaboration to performance. Here is the abstract of their article:

This paper documents both developments in the technologies used to promote learning mathematics and the influence on research of social theories of learning, through reference to the activities of the International Commission on Mathematical Instruction (ICMI), and argues that these changes provide opportunity for the reconceptualization of our understanding of mathematical learning. Firstly, changes in technology are traced from discipline-specific computer-based software through to Web 2.0-based learning tools. Secondly, the increasing influence of social theories of learning on mathematics education research is reviewed by examining the prevalence of papers and presentations, which acknowledge the role of social interaction in learning, at ICMI conferences over the past 20 years. Finally, it is argued that the confluence of these developments means that it is necessary to re-examine what it means to learn and do mathematics and proposes that it is now possible to view learning mathematics as an activity that is performed rather than passively acquired.

A study on the teaching of the concept of negative numbers

2009-09-17T09:25:00.000+02:00

Kemal Altiparmak and Ece Özdogan have written an article that was recently published online in International Journal of Mathematical Education in Science and Technology. The article is entitled A study on the teaching of the concept of negative numbers. Here is the abstract of their article.

This study mainly aims to develop an effective strategy to overcome the known difficulties in teaching negative numbers. Another aim is to measure the success of this teaching strategy among a group of elementary level pupils in Idotzmir, Turkey. Learning negative concepts are supported by computer animations. The academic achievement test developed by the researchers was administered to 150 sixth-grade pupils at the beginning of and following the learning period. The teaching strategy was applied to the experiment group (n = 75) as stated above, while the traditional teaching model most frequently used in Turkey was applied to the control group (n = 75). At the end of the study, a significant difference was found in favour of the experiment group (t = 17.51, df = 148, p = 0.000 < 0.05).

Honoring Paul Ernest

2009-09-17T08:57:00.000+02:00

Information Age Publishing is about to publish a "Festschrift in honor of Paul Ernest's 65th Birthday". This is a volume in the monograph series of The Montana Mathematics Enthusiast, and it is edited by Bharath Sriraman and Simon Goodchild. Paul Ernest has a big name in the community of mathematics education researchers, and his main field of interest is within the area of philosophy of mathematics and philosophy of mathematics education. Here is a copy of the publisher's description of the book:

Paul Ernest’s name is synonymous with social constructivism as a philosophy of mathematics. His contributions to mathematics education have occurred at a very fundamental level and to a extent shaped theory development in this field. His research addresses fundamental questions about the nature of mathematics and how it relates to teaching, learning and society. For the last three decades Paul has been a prolific scholar who has published in a wide array of topics such as the relationship between the philosophy of mathematics and mathematics education, and more generally the philosophy of mathematics education, ethics and values in mathematics education, and the philosophy of research methodology.

The title of this Festschrift is meant to be a pun to convey the sometimes relativistic dimension to mathematical certainty that Paul argued for in developing his philosophy, and also a play on words for the fact that absolute “earnestness” may perhaps be a Platonic construct, and not possible in the realm of language and human discourse! Paul Ernest’s scholarly evolution and life can best be summarized in the words of Walt Whitman “Do I contradict myself? Very well then I contradict myself” (I am large, I contain multitudes). Indeed his presence has been large and multitudinous and this Festschrift celebrates his 65th Birthday with numerous contributions coming from the mathematics, philosophy and mathematics education communities around the world.

What the eyes already know

2009-09-16T12:22:00.001+02:00

Angela Heine and colleagues have written an article called: What the eyes already 'know': using eye movement measurement to tap into children's implicit numerical magnitude representations. The article has recently been published in Infant and Child Development. The authors make interesting links between eye movements and childrens understanding of numbers. Here is the abstract of their article:

To date, a number of studies have demonstrated the existence of mismatches between children's implicit and explicit knowledge at certain points in development that become manifest by their gestures and gaze orientation in different problem solving contexts. Stimulated by this research, we used eye movement measurement to investigate the development of basic knowledge about numerical magnitude in primary school children. Sixty-six children from grades one to three (i.e. 6-9 years) were presented with two parallel versions of a number line estimation task of which one was restricted to behavioural measures, whereas the other included the recording of eye movement data. The results of the eye movement experiment indicate a quantitative increase as well as a qualitative change in children's implicit knowledge about numerical magnitudes in this age group that precedes the overt, that is, behavioural, demonstration of explicit numerical knowledge. The finding that children's eye movements reveal substantially more about the presence of implicit precursors of later explicit knowledge in the numerical domain than classical approaches suggests further exploration of eye movement measurement as a potential early assessment tool of individual achievement levels in numerical processing.

Students' understanding of a logical structure in the definition of limit

2009-09-11T07:58:00.000+02:00

Kyeong Hah Roh has written an article entitled An empirical study of students’ understanding of a logical structure in the definition of limit via the ε-strip activity. This article was published online in Educational Studies in Mathematics last Thursday. Here is the abstract of the article:

This study explored students’ understanding of a logical structure in defining the limit of a sequence, focusing on the relationship between ε and N. The subjects of this study were college students who had already encountered the concept of limit but did not have any experience with rigorous proofs using the ε–N definition. This study suggested two statements, each of which is written by using a relationship between ε and N, similar to the ε–N definition. By analyzing the students’ responses to the validity of the statements as definitions of the limit of a sequence, students’ understanding of such a relationship was classified into five major categories. This paper discusses some essential components that students must conceptualize in order properly to understand the relationship between ε and N in defining the limit of a sequence.

Working like real mathematicians

2009-09-10T07:54:00.000+02:00

Atara Shriki has written an interesting article called Working like real mathematicians: developing prospective teachers’ awareness of mathematical creativity through generating new concepts. This article was recently published online in Educational Studies in Mathematics. The author reports from a study related to a methods course, where a strong focus is on creativity in mathematics. The article has a particular focus on prospective teachers' awarenes of creativity in mathematics.

Here is the abstract of Shriki's article.

This paper describes the experience of a group of 17 prospective mathematics teachers who were engaged in a series of activities aimed at developing their awareness of creativity in mathematics. This experience was initiated on the basis of ideas proposed by the participants regarding ways creativity of school students might be developed. Over a period of 6 weeks, they were engaged in inventing geometrical concepts and in the examination of their properties. The prospective teachers’ reflections upon the process they underwent indicate that they developed awareness of various aspects of creativity while deepening their mathematical and didactical knowledge.

Exploration of technologies

2009-09-09T07:45:00.000+02:00

Paulus Gerdes has written an article called Exploration of technologies, emerging from African cultural practices, in mathematics (teacher) education. This article was recently published online in ZDM. In this article, Gerdes provides an interesting overview of how the cultural practices of African mathematics (teacher) education has developed, and he makes a seemingly (to me) impossible connection between traditional basket weaving and exploration of technologies.

Here is the abstract of the article:

The study at teacher education institutions in Africa of mathematical ideas, from African history and cultures, may broaden the horizon of (future) mathematics teachers and increase their socio-cultural self-confidence and awareness. Exploring educationally mathematical ideas embedded in, and derived from, technologies of various African cultural practices may contribute to bridge the gap between ‘home’ and ‘school’ culture. Examples of the study and exploration of these technologies and cultural practices will be presented. The examples come from cultural practices as varied as story telling, basket making, salt production, and mat, trap and hat weaving.

Theories of Mathematics Education

2009-09-09T07:14:00.001+02:00

A new book, entitled Theories of Mathematics Education, is about to be published by Springer (due October 2009). One of the editors, Bharath Sriraman (also editor of The Montana Mathematics Enthusiast) has been kind enough to give me permission to post the book cover and the table of contents here on my blog. Thanks, Bharath!

Looking at the table of contents is enough to make me believe that this is definitely going to be an important book, and it will make an impact on our field of research! If you won't take my word for it, please take the time to read through the table of contents yourself:

Theories of Mathematics Education - TOC

I especially like the way it is built up, with introductions and commentaries to all the parts of the book. This will give the reader a feeling of how the field has evolved, and how it is still in a process of evolving.

The publisher has given the following description of the book:

This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors at the 29th Annual PME meeting in Melbourne and using the unique style of preface-chapter-commentary, this volume consist of contributions from leading thinkers in mathematics education who have worked on theory building.

This book is as much summative and synthetic as well as forward-looking by highlighting theories from psychology, philosophy and social sciences that continue to influence theory building. In addition a significant portion of the book includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory, feminist theory, social justice theory and networking theories. The 19 parts, 17 prefaces and 23 commentaries synergize the efforts of over 50 contributing authors scattered across the globe that are active in the ongoing work on theory development in mathematics education.

You might also be interested in taking a look at the cover of the book

Theories of Mathematics Education - Cover

To me, at least, this is definitely a book I am looking forward to read. And after all, October is not that far away :-)

IJSME, August 2009

2009-09-08T07:41:00.000+02:00

The August issue (Volume 7, Number 4) of International Journal of Science and Mathematics Education has been published. This issue contains 9 articles:

INVESTIGATING THE EFFECTIVENESS OF AN ANALOGY ACTIVITY IN IMPROVING STUDENTS’ CONCEPTUAL CHANGE FOR SOLUTION CHEMISTRY CONCEPTS, by Muammer Çalik, Alipaşa Ayas and Richard K. Coll
INSTRUCTIONAL ACTIVITIES AND GROUP WORK IN THE US INCLUSIVE HIGH SCHOOL CO-TAUGHT SCIENCE CLASS, by Laura J. Moin, Kathleen Magiera and Naomi Zigmond
DESIGNING AND EVALUATING RESEARCH-BASED INSTRUCTIONAL SEQUENCES FOR INTRODUCING MAGNETIC FIELDS, by Jenaro Guisasola, Jose Manuel Almudi, Mikel Ceberio and Jose Luis Zubimendi
ENGINEERING IN CHILDREN’S FICTION - NOT A GOOD STORY? by Allyson Holbrook, Lisa Panozza and Elena Prieto
RELATIONS BETWEEN TEACHING AND RESEARCH IN PHYSICAL GEOGRAPHY AND MATHEMATICS AT RESEARCH-INTENSIVE UNIVERSITIES, by Lene Møller Madsen and Carl Winsløw
GEOMETRIC AND ALGEBRAIC APPROACHES IN THE CONCEPT OF “LIMIT” AND THE IMPACT OF THE “DIDACTIC CONTRACT”, by Iliada Elia, Athanasios Gagatsis, Areti Panaoura, Theodosis Zachariades and Fotini Zoulinaki
IDENTIFYING SENIOR HIGH SCHOOL STUDENTS’ MISCONCEPTIONS ABOUT STATISTICAL CORRELATION, AND THEIR POSSIBLE CAUSES: AN EXPLORATORY STUDY USING CONCEPT MAPPING WITH INTERVIEWS, by Tzu-Chien Liu, Yi-Chun Lin and Chin-Chung Tsai
PROMOTING EFFECTIVE SCIENCE TEACHER EDUCATION AND SCIENCE TEACHING: A FRAMEWORK FOR TEACHER DECISION-MAKING, by Michael P. Clough, Craig A. Berg and Joanne K. Olson
VARIABLE RELATIONSHIPS AMONG DIFFERENT SCIENCE LEARNERS IN ELEMENTARY SCIENCE-METHODS COURSES, by Robert E. Bleicher and Joan S. Lindgren

School mathematics curriculum materials for teachers’

2009-09-07T10:06:00.000+02:00

Gwendolyn M. Lloyd has written an article that was recently published online in ZDM. The article is entitled School mathematics curriculum materials for teachers’ learning: future elementary teachers’ interactions with curriculum materials in a mathematics course in the United States. Here is the abstract of her article:

This report describes ways that five preservice teachers in the United States viewed and interacted with the rhetorical components (Valverde et al. in According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks, Kluwer, 2002) of the innovative school mathematics curriculum materials used in a mathematics course for future elementary teachers. The preservice teachers’ comments reflected general agreement that the innovative curriculum materials contained fewer narrative elements and worked examples, as well as more (and different) exercises and question sets and activity elements, than the mathematics textbooks to which the teachers were accustomed. However, variation emerged when considering the ways in which the teachers interacted with the materials for their learning of mathematics. Whereas some teachers accepted and even embraced changes to the teaching–learning process that accompanied use of the curriculum materials, other teachers experienced discomfort and frustration at times. Nonetheless, each teacher considered that use of the curriculum materials improved her mathematical understandings in significant ways. Implications of these results for mathematics teacher education are discussed.

ICMI News

2009-09-04T09:48:00.000+02:00

A new newsletter has been published from ICMI, and, as usual, it contains lots of interesting information. I would have liked to post the entire newsletter here, but since it is freely available online, I am only going to point to the table of contents:

Editorial: Continuing Professional Development and Effective integration of Digital Technologies in Teaching and Learning Mathematics: Two Challenges for ICMI
A XXIst century Felix Klein's follow up workshop
Deadline Extended: ICMI / ICIAM STUDY
EARCOME5: First Announcement
Chilean Journal of Statistics (ChJS)
Calendar of Events of Interest to the ICMI Community
ICMI encounters: Hassler Whitney, Laurence C. Young and Dirk J. Struik: Personal recollections
Subscribing to ICMI News

You can also check out the archive for a complete listing of previous (and current) newsletters!

Algebra - the birthplace and graveyard for many

2009-09-04T08:13:00.000+02:00

Eleanor Chute has written an interesting article about the importance of algebra in school mathematics. It is not a scientific article, but I think it is worth reading even though! (It was published on September 1st in the Pittsburgh Post-Gazette.) The article is part of a series related to school mathematics, and the two previous articles in the series raise interesting questions about early math and fractions.

Although algebra to many represents a hurdle, or even the graveyard in their mathematical careers, the article claims that:

Algebraic thinking is done even by people who don't realize they're using algebra.

After a series of examples, Chute goes on to quote Michele Burgess, who claims that students should not be confronted with algebra for the first time in the Algebra 1 course. This leads me to think about the debate (and research) concerning early algebra, although this is not referred to in this article in particular. If you are interested, I recommend the chapter on early algebra by David Carraher and Analucia Schliemann in NCTM's Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007), or even Carolyn Kieran's chapter on algebra in the same handbook.

Reference:

Lester, F. K. (Ed.) (2007). Second handbook of research on mathematics teaching and learning. Charlotte, NC: Information Age Pub.

Understanding the complexities of student motivations

2009-09-01T10:03:00.000+02:00

Janet G. Walter and Janelle Hart have written an article about the interesting issue of Understanding the complexities of student motivations in mathematics learning. The article was recently published in The Journal of Mathematical Behavior. Here is the abstract of their article:

Student motivation has long been a concern of mathematics educators. However, commonly held distinctions between intrinsic and extrinsic motivations may be insufficient to inform our understandings of student motivations in learning mathematics or to appropriately shape pedagogical decisions. Here, motivation is defined, in general, as an individual's desire, power, and tendency to act in particular ways. We characterize details of motivation in mathematical learning through qualitative analysis of honors calculus students’ extended, collaborative problem solving efforts within a longitudinal research project in learning and teaching. Contextual Motivation Theory emerges as an interpretive means for understanding the complexities of student motivations. Students chose to act upon intellectual-mathematical motivations and social-personal motivations that manifested simultaneously. Students exhibited intellectual passion in persisting beyond obtaining correct answers to build understandings of mathematical ideas. Conceptually driven conditions that encourage mathematical necessity are shown to support the growth of intellectual passion in mathematics learning.

How to develop mathematics for teaching and understanding

2009-09-01T07:35:00.001+02:00

Susanne Prediger has written an article about How to develop mathematics-for-teaching and for understanding: the case of meanings of the equal sign. The article was published online in Journal of Mathematics Teacher Education on Thursday last week. Point of departure in her article is the very important question about what mathematical (content) knowledge prospective teachers need. A main claim which is raised already in the introduction is: "Listen to your students!" In the theoretical background, Prediger takes Shulman's classic conceptualization of three main categories of content knowledge in teaching as point of departure:

Subject-matter knowledge
Pedagogical-content knowledge
Curricular knowledge

She continues to build heavily on the work done by Hyman Bass and Deborah Ball (e.g. Ball & Bass, 2004), and she goes on to place her own study in relation to the work of Bass and Ball:

Whereas Bass and Ball (2004) concentrate on the first part of their program, namely, identifying important competences, this article deals with both parts, the analytical study of identifying, and the developmental study of constructing a sequence for teacher education, exemplified by a sequence in the course entitled school algebra and its teaching and learning for second-year, prospective middle-school teachers.

Here is the abstract of Prediger's article:

What kind of mathematical knowledge do prospective teachers need for teaching and for understanding student thinking? And how can its construction be enhanced? This article contributes to the ongoing discussion on mathematics-for-teaching by investigating the case of understanding students’ perspectives on equations and equalities and on meanings of the equal sign. It is shown that diagnostic competence comprises didactically sensitive mathematical knowledge, especially about different meanings of mathematical objects. The theoretical claims are substantiated by a report on a teacher education course, which draws on the analysis of student thinking as an opportunity to construct didactically sensitive mathematical knowledge for teaching for pre-service middle-school mathematics teachers.

References:
Bass, H., & Ball, D. L. (2004). A practice-based theory of mathematical knowledge for teaching: The case of mathematical reasoning. In W. Jianpan & X. Binyan (Eds.), Trends and challenges in mathematics education (pp. 107–123). Shanghai: East China Normal University Press.

"The conference was awesome"

2009-09-01T07:26:00.000+02:00

Tamsin Meaney, Tony Trinick and Uenuku Fairhall have written an article with an interesting focus on professional development and mathematics teacher conferences. The title of their article is ‘The conference was awesome’: social justice and a mathematics teacher conference. The article was recently published online in Journal of Mathematics Teacher Education. Here is the abstract of their article:

Professional development comes in many forms, some of which are deemed more useful than others. However, when groups of teachers are excluded, or exclude themselves, from professional development opportunities, then there is an issue of social justice. This article examines the experiences of a group of teachers from a Māori-medium school who attended a mathematics teacher conference. By analysing the teachers’ sense of belonging through their ideas about engagement, alignment and imagination, we are able to describe how different kinds of relationships influence the inclusion/exclusion process. This leads to a discussion about what can be done by the teachers as well as conference organisers to increase these teachers’ likelihood of attending further conferences in the future.

Alignment, cohesion, and change

2009-08-31T13:53:00.001+02:00

Dionne I. Cross has written an article called Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices. This article was recently published online in Journal of Mathematics Teacher Education. Here is the abstract of the article:

This collective case study reports on an investigation into the relationship between mathematics teachers’ beliefs and their classroom practices, namely, how they organized their classroom activities, interacted with their students, and assessed their students’ learning. Additionally, the study examined the pervasiveness of their beliefs in the face of efforts to incorporate reform-oriented classroom materials and instructional strategies. The participants were five high school teachers of ninth-grade algebra at different stages in their teaching career. The qualitative analysis of the data revealed that in general beliefs were very influential on the teachers’ daily pedagogical decisions and that their beliefs about the nature of mathematics served as a primary source of their beliefs about pedagogy and student learning. Findings from the analysis concur with previous studies in this area that reveal a clear relationship between these constructs. In addition, the results provide useful insights for the mathematics education community as it shows the diversity among the inservice teachers’ beliefs (presented as hypothesized belief models), the role and influence of beliefs about the nature of mathematics on the belief structure and how the teachers designed their instructional practices to reflect these beliefs. The article concludes with a discussion of implications of teacher education.

Blog reading tips - Poincaré's prize

2009-08-27T08:04:00.001+02:00

Peter Ash has a nice blog about mathematics and education, and he has given a nice review of what appears to be an interesting book in a blog post about "Poincare's Prize". Here is the intro of his post, to tickle your interest:

I recently read Poincaré's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles by George C. Szpiro. I recommend it highly. Some time back I recommended another book on the same topic, The Poincaré Conjecture: In Search of the Shape of the Universe by Donal O'Shea. If you can only read one book on the topic, I recommend the Szpiro book.

Tutored problem solving

2009-08-24T09:41:00.000+02:00

Ron J.C.M. Salden, Vincent Aleven, Rolf Schwonke and Alexander Renki have written an article entitled The expertise reversal effect and worked examples in tutored problem solving. The article was printed online in Instructional Science on Thursday. Here is the abstract of their article:

Prior research has shown that tutored problem solving with intelligent software tutors is an effective instructional method, and that worked examples are an effective complement to this kind of tutored problem solving. The work on the expertise reversal effect suggests that it is desirable to tailor the fading of worked examples to individual students’ growing expertise levels. One lab and one classroom experiment were conducted to investigate whether adaptively fading worked examples in a tutored problem-solving environment can lead to higher learning gains. Both studies compared a standard Cognitive Tutor with two example-enhanced versions, in which the fading of worked examples occurred either in a fixed manner or in a manner adaptive to individual students’ understanding of the examples. Both experiments provide evidence of improved learning results from adaptive fading over fixed fading over problem solving. We discuss how to further optimize the fading procedure matching each individual student’s changing knowledge level.

An integrative learning experience

2009-08-21T08:09:00.000+02:00

Barbra Melendez, Silas Bowman, Keith Erickson and Edward Swim have written an article called An integrative learning experience within a mathematics curriculum. The article was recently published online in Teaching Mathematics and its Applications. Here is the abstract of their article:

We developed four separate scenarios focusing on the connections between mathematics, biology, and social sciences. This structure facilitated the coordination of faculty from seven academic departments on campus. Each scenario had students from different majors build mathematical models, gather information from their respective disciplines, and develop a final presentation that included a committee consensus on how to approach the problem in a practical way. As a result, students learned how mathematics plays a role in other disciplines and how insight from different points of view affects the approach taken to a complex problem.

Interdisciplinary mathematics-physics approaches

2009-08-21T08:06:00.000+02:00

Valérie Munier and Helene Merle have written an article that was published in the September issue of International Journal of Science Education. The article is entitled Interdisciplinary Mathematics-Physics Approaches to Teaching the Concept of Angle in Elementary School. Unfortunately, I don't have access to this article, but I find the topic interesting! Here is a copy of the abstract of their article:

The present study takes an interdisciplinary mathematics-physics approach to the acquisition of the concept of angle by children in Grades 3-5. This paper first presents the theoretical framework we developed, then we analyse the concept of angle and the difficulties pupils have with it. Finally, we report three experimental physics-based teaching sequences tested in three classrooms. We showed that at the end of each teaching sequence the pupils had a good grasp of the concept of angle, they had truly appropriated the physics knowledge at play, and many pupils are enable to successfully grasp new physics situations in which the angle plays a highly meaningful role. Using a physics framework to introduce angles in problem situations is then pertinent: by interrelating different spaces, pupils were able to acquire skills in the domains of mathematics, physics, and modelling. In conclusion, we discuss the respective merits of each problem situation proposed.

International Handbook of Research on Teachers and Teaching

2009-08-20T11:43:00.000+02:00

Springer has published a new and interesting book: International Handbook of Research on Teachers and Teaching. This handbook has been edited by Lawrence J. Saha and A. Gary Dworkin, and it is a huge book of 1200 pages. Although the book is concerned with research on teachers and teaching in general, it should be interesting to researchers within the field of mathematics education as well. It also contains a chapter that is concerned with mathematics teaching in particular. Here is a copy of the publisher's info about the book:

This book takes into account new research on both teachers and the nature of teaching
Includes over 70 completely new and original articles covering many aspects of what we know about the teaching profession and about classroom teaching
Treats teachers and teaching from a comparative perspective, highlighting similarities and differences across countries
Addresses the role of culture in understanding variations in teaching practices
Discusses both the changing levels of accountability for teachers and its effects

The International Handbook of Research on Teachers and Teaching provides a fresh look at the ever changing nature of the teaching profession throughout the world. This collection of over 70 original articles addresses a wide range of issues that are relevant for understanding the present educational climate in which the accountability of teachers and the standardized testing of students have become dominant.

The international collection of authors brings to the handbook a breadth of knowledge and experience about the teaching profession and a wealth of material across a number of comparative dimensions, such as between developed and developing countries and between Eastern and Western cultures. In addition, many articles address the emerging challenges to education and to the lives of teachers which are brought about by the globalization trends of the 21st Century.