I have moved!!!

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:

1. Wordpress is a very flexible blogging platform (even more so than Blogger)!
2. 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

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

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

"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

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

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

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

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

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

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.