Blog tips: "Wild about math!"

Sol Lederman has a very nice blog about mathematics, and the focus is on "making math fun and accessible". The blog itself is called "Wild About Math!", and it is definitely worth checking out!

Sol has written much about learning mathematics by doing mathematics, and he appears to have a special interest in solving mathematical problems. One of the things Sol often writes about is the so called Monday Math Madness problem from the Blinkdagger blog. Lots of people already subscribe to the blog, and you can too! It's easy!

A good idea for starters would be to read some of Sol's featured articles. The first five are:


TMME, No 1/2 2009 is here!

I gave a pre-announcement of this two days ago, but now the first number of The Montana Mathematics Enthusiast for 2009 is ready for everyone to read. The feature themes in this double-issue is statistics education, and mathematics education research in the southern hemisphere. The first section of the issue has a number on articles on this:
Other feature articles in this double-issue include:

IJSME, February 2009

International Journal of Science and Mathematics Education has already released the February issue (Number 1) of 2009. The issue contains the following articles:

ESM, January 2009


TMME, No 1/2, 2009

The Montana Mathematics Enthusiast is about to publish issues 1 and 2 of 2009. You can find them in print or in electronic format quite soon. Before they arrive at these web sites, you can take a look at the table of contents, or you can read the editorial below:

TMME 2 Article 0 Editorial Pp.1 2


Mathematics in everyday life - a PhD thesis lives on!

Normally, a PhD thesis is seldom read by many people, and years of work often end up in a drawer. My own thesis was published in a very limited number, and most of these disappeared during the day of my defense. About a year ago, I decided to publish my PhD thesis on Scribd, because - well mainly because I wanted more people to read it, of course!

Since then, my thesis - a 300 page long thesis in mathematics education - has been viewed 2779 times (as of writing), downloaded 4 times, liked by 4 people and 18 people have added the thesis to their favorites. It has also been awarded to the hot-list on Scribd. Although these numbers are not fantastic, I think it is pretty good for such a thesis. If you are interested in taking a look for yourself, you can either click on the link above, or you can read the embedded document below. If you rather want to read in fullscreen, click here. If you want to download it, click here (pdf).

Mathematics in everyday life - A study of beliefs and actions

Holidays are approaching...

The holidays are approaching, and the Christmas bells have almost started ringing in my house. In that connection, I am going to inform the readers of Mathematics Education Research Blog that the next two weeks are probably going to be a bit slower than usual here. Most of the main journals have also entered a slow period it seems, so this might work out fine.

I am planning to write something during Christmas break, but the pace will be slower. If you want to make sure that you don't miss all the important new articles that appear in the next two weeks, you might want to take a look at this page! This is a shared page from my Google Reader account, which is automatically updated with news from most of the journals I follow (those that have an RSS feed). No matter how slow my own pace is, this page will always be updated.

If you still need something more to read during Christmas break, you might want to take a look at the 630+ references that I have stored in my CiteULike account, or the 275+ bookmarks related to mathematics in my Delicious account. You might also be interested in taking a look at the list of academic journals in mathematics education, that I created over at Wikipedia the other day (and possibly contributing to the expansion of the list)!

Merry Christmas to all!


NCTM E-workshops

If you would like to learn more about teaching mathematics, a good idea might be to participate in an e-workshop! NCTM are going to organize several such workshops in 2009. If you want to learn more you might want to check out their website.


Reading tips: Branford (1908)

Many great books have been written, and an increasing number are becoming part of the public domain. One of them, which I would like to point your attention to, is a classical book written by Benchara Branford in 1908! The title of the book is: "A Study of Mathematical Education, including The Teaching of Arithmetic". Besides being an important book in the history of mathematics education, it also provides a nice insight into the teaching of mathematics as it was 100 years ago!

Personally, I think his very direct connection between the historical development of mathematics and the child's development of mathematical thinking (often referred to as "the genetic approach" in mathematics education) is interesting.

A Study of Mathematical Education

If you want to read the book in fullscreen format, click here. For download (pdf), click here.


ATM eNews

ATM Conference 2009ATM eNews is available, and it was published yesterday. Those who subscribe to the newsletter have probably got an email about it already, and those who don't can read the entire newsletter online. The eNews contains lots of useful information about new publications, conferences, etc. If you don't know, ATM is the Association of Teachers of Mathematics (in UK), and it has about 4000 members. ATM has an annual conference, which might be worth paying attention to. Online registration is now open.

Working for learning

Pat Drake has written an article that was recently published online in Journal of Mathematics Teacher Education. The article is entitled Working for learning: teaching assistants developing mathematics for teaching. Here is the abstract of the article:

This article derives from a case study of 10 secondary school teaching assistants (TAs) who did not have conventional pre-qualifications in mathematics but who undertook an honours degree in mathematics education studies at a Higher Education Institution in England whilst continuing to work as TAs in school. Work-based learning was thus undertaken in parallel with advancement through the hierarchical undergraduate mathematics curriculum. Lave and Wenger’s work on communities of practice is used as a framework to explore the TAs’ learning of mathematics alongside their professional work in schools. This case illustrates how and where institution-based undergraduate teaching relates to work in school, and where it does not, thus signalling the importance of the TAs’ informal learning strategies in bringing together these experiences.


ZDM, No 1-2, 2009

A new issue of ZDM was published on Friday. It is a double issue, with the following theme: Interdisciplinarity in Mathematics Education: Psychology, Philosophy, Aesthetics, Modelling and Curriculum. Guest editor of this issue is Bharath Sriraman, the editor of The Montana Mathematics Enthusiast. The issue contains not less than 22 articles:

If you don't have full access to Springer (so that you can read these articles), you might want to pay attention to the article by Doorman and Gravemeijer, which is an Open Access article (i.e. freely available for all to read). 

A brief history of mathematics (book)

For those of you who haven't already discover it, here is a tip for Christmas: Scribd! You can find lots of interesting books and papers here, and some are true gems. Here is one of them: A brief history of mathematics, by Karl Fink. This official translation was published in 1900, and therefore is in the public domain. You can read the book in its entirety here:

A brief history of mathematics

If you want to read the book in fullscreen, you can go here. To download the book as pdf, click on this link.

A comparison of curricular effect

The new issue of Instructional Science (January, 2009) has an article related to mathematics education: A comparison of curricular effects on the integration of arithmetic and algebraic schemata in pre-algebra students, by Bryan Moseley and Mary E. ("Betsy") Brenner. Here is their article abstract:
This research examines students’ ability to integrate algebraic variables with arithmetic operations and symbols as a result of the type of instruction they received, and places their work on scales that illustrate its location on the continuum from arithmetic to algebraic reasoning. It presents data from pre and post instruction clinical interviews administered to a sample of middle school students experiencing their first exposure to formal pre-algebra. Roughly half of the sample (n = 15) was taught with a standards-based curriculum emphasizing representation skills, while a comparable group (n = 12) of students received traditional instruction. Analysis of the pre and post interviews indicated that participants receiving a standards-based curriculum demonstrated more frequent and sophisticated usage of variables when writing equations to model word problems of varying complexity. This advantage was attenuated on problems that provided more representational support in which a diagram with a variable was presented with the request that an expression be written to represent the perimeter and area. Differences in strategies used by the two groups suggest that the traditional curriculum encouraged students to continue using arithmetic conventions, such as focusing on finding specific values, when asked to model relations with algebraic notation.


A cultural-historical approach to teaching geometry

Stuart Rowlands has recently written an article called A Pilot Study of a Cultural-Historical Approach to Teaching Geometry, which was published in Science & Education on Wednesday. Here is the abstract of the 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.

The development of beliefs and practice

Despina Potari  and Barbara Georgiadou–Kabouridis have written an article called A primary teacher’s mathematics teaching: the development of beliefs and practice in different “supportive” contexts. The article was recently published online in Journal of Mathematics Teacher Education. Here is the article abstract:

This article refers to a longitudinal case study of a primary school teacher over a period of 4 years. The focus is on the development of the teacher’s beliefs regarding mathematics teaching and learning from the last year of her university studies up to the third year of teaching mathematics in school. This development has been investigated within three different contexts, which have been distinguished in terms of the kind of support provided to this teacher. Two dominant beliefs emerged which have been traced through the period of the study from both the teacher’s reflections and actions. The first belief drew on the idea that what was considered an easy mathematical task by an adult could also be easily understood by children, while the second was that children learn mathematics through their actual involvement in a variety of teaching activities. The results indicate the way that teacher’s experiences from her university studies, actual classroom practice and inservice education interact and influence her beliefs and professional development.

Using history of mathematics

Charalambos Y. Charalambous, Areti Panaoura and George Philippou have written an article called Using the history of mathematics to induce changes in preservice teachers’ beliefs and attitudes: insights from evaluating a teacher education program. The article was published online in Educational Studies in Mathematics on Tuesday. Here is the abstract of their article:

Scholars and teacher educators alike agree that teachers’ beliefs and attitudes toward mathematics are key informants of teachers’ instructional approaches. Therefore, it has become clear that, in addition to enriching preservice teachers’ (PSTs) knowledge, teacher education programs should also create opportunities for prospective teachers to develop productive beliefs and attitudes toward teaching and learning mathematics. This study explored the effectiveness of a mathematics preparatory program based on the history of mathematics that aimed at enhancing PSTs’ epistemological and efficacy beliefs and their attitudes toward mathematics. Using data from a questionnaire administered four times, the study traced the development of 94 PSTs’ beliefs and attitudes over a period of 2 years. The analysis of these data showed changes in certain dimensions of the PSTs’ beliefs and attitudes; however, other dimensions were found to change in the opposite direction to that expected. Differences were also found in the development of the PSTs’ beliefs and attitudes according to their mathematical background. The data yielded from semi-structured follow-up interviews conducted with a convenience sample of PSTs largely corroborated the quantitative data and helped explain some of these changes. We discuss the effectiveness of the program considered herein and draw implications for the design of teacher education programs grounded in the history of mathematics.


Reasons for change in enrolments

Derek Holton, Eric Muller, Juha Oikkonen, Oscar Adolfo Sanches Valenzuela, and Ren Zizhao have written an article called Some reasons for change in undergraduate mathematics enrolments. This article article was published online in International Journal of Mathematical Education in Science and Technology yesterday. Here is the abstract of their article:
Here, we look at the enrolments of students in undergraduate mathematics courses in a number of countries. The data show various increases and decreases and we suggest some common reasons for the fluctuations. These include students' goals of a secure and well-paid job, government actions and the state of the economy in the country concerned. We consider several ways in which departments have successfully approached downturns in numbers by their interactions with students by introducing new teaching approaches, using technology and establishing mathematics centres.


The professional education of mathematics teachers

Springer has recently published a new book on mathematics education. The book is entitled The Professional Education and Development of Teachers of Mathematics, and it is edited by Ruhama Even and Deborah Loewenberg Ball. Here are some of the highlights of the book, as presented by the publisher:

  • Focuses specifically on mathematics teacher education development
  • Provides practical strategies for learning
  • Addresses the balance between pedagogy and mathematical content
  • Edited by the world's leading scholars on mathematics teacher education, teacher knowledge, and teacher education

Educational Researcher, December 2008

The December issue of Educational Researcher has been published, and it is a special issue on Foundations for Success: The Final Report of the National Mathematics Advisory Panel. The issue contains 13 interesting articles with a focus on the Math Panel Report:


TIMSS 2007

The results from TIMSS 2007 were released today, and the media appears to be full of reports about how the students in each of our countries are doing. Overall, countries from Asia are on top as usual. If you want to learn more, there is a webcast to watch (.rm and .mov formats), international reports to read as well as a Technical Report and a very interesting set of Encyclopedias, which offer a nice overview of the mathematics (and science) teaching in each of the participating countries. That means: lots of interesting reading to do!


Conference calendar updated

I have now updated the conference calendar to include relevant conferences in 2009. If there are any conferences that I have missed, please let me know by sending me an e-mail or writing in the comment field below this message! 

You can always find a quick link to the conference calendar in the column to the right.

Terence Tao in Norway

Terence Tao is by many said to be the best mathematician in the world today, and for two days this week (today and tomorrow) he is visiting Trondheim, Norway. Unfortunately, I don't have the opportunity to travel to Trondheim and listen to him, but it sure would have been interesting.

Tao - born in 1975 (like myself) - is professor of mathematics at UCLA, winner of the Fields medal and lots of other prizes. He is working within many different fields of mathematics, and he frequently reports his work on his web page and his blog. Below is a small video presenting Tao:

Science & Education, January 2009

Science & Education

Science & Education is a journal that is devoted to publishing articles related to improving the teaching and learning of science and mathematics. The January issue of 2009 has recently been published. None of the articles in this issue are directly related to mathematics education, but if you are interested in science education in general, you might want to have a closer look at the issue anyway!

Building intellectual infrastructure

James Kaput wrote an article that was published online in Educational Studies in Mathematics on Friday. The article is entitled: Building intellectual infrastructure to expose and understand ever-increasing complexity. Here is the abstract of the article:
This paper comments on the expanded repertoire of techniques, conceptual frameworks, and perspectives developed to study the phenomena of gesture, bodily action and other modalities as related to thinking, learning, acting, and speaking. Certain broad issues are considered, including (1) the distinction between “contextual” generalization of instances across context (of virtually any kind—numeric, situational, etc.) and the generalization of structured actions on symbols, (2) fundamental distinctions between the use of semiotic means to describe specific situations versus semiosis serving the process of generalization, and (3) the challenges of building generalizable research findings at such an early stage in infrastructure building.


IEJME, October issue revisited

I have written about the October issue of International Electronic Journal of Mathematics Education in an earlier post. For some reason, the full-text version of the articles in this journal don't appear as a new issue of the journal appears - at least for me they don't! The articles are available now however, and you can freely download them in PDF format. This provides a nice occasion of referring to the articles again, and writing more about one of them:
In this collection, I found the article by Chamberlin, Powers and Novak particularly interesting, so I will provide you with some more details about it. The study reported in this article is related to the No Child Left Behind initiative in the U.S. In relation to this initiative, several professional development courses in the U.S. are required to assess the teachers' content knowledge. This article reports on the evaluation of the impact of these assessments. Although the article does not provide a very thorough theoretical background, it gives a good overview of the survey that were made to investigate the teachers' perceptions about these assessments.

One of the results of this survey was that the teachers appeared to learn more because of the assessments. They explain it like this:
We surmise that these positive effects may be due to an important aspect of theassessment process in these PD courses – the assessment and learning of mathematical topics and material was on-going and demonstrating mastery of those ideas was expected.
Many teachers appear to be reluctant to be tested, and this study apparently describes a study which had positive experiences with assessing the teachers after a course, and this might be interesting for other teacher educators or providers of in-service courses to take a closer look at.

Where am I, and where do I want to go?

I have started the countdown to Christmas, and 2008 is approaching the end. Since the major journals in mathematics education are having a few slow days at the moment, I found it useful to start reflecting about the year that is soon behind us, and the one which lies ahead.

I started this blog in February this year, and in the welcome post on February 5, I wrote:
There are so many journals, so many conferences, so many web-sites that cover research in mathematics education. This blog will be my humble attempt to cover the most important ones. In the sidebar, you can find feeds from the most important scientific journals in mathematics education research. In this blog, I will comment on new and interesting (to me at least) articles in these and other journals. I will also try to follow some of the most important conferences in mathematics education, as well as sharing interesting bookmarks regarding mathematics education.
Now, ten months later, I think it's appropriate to look back and see where I have come. The blog started out as a personal wish to get to know my own field of research better, and I personally feel that I have been extremely successful in this realm! I never advertised much for this blog, but when I started tracking the statistics with Google Analytics in late June, I realized that lots of people from all over the world actually read the blog!

Between July 1 and December 1, the blog had 5423 unique visitors, from 114 countries. I know this doesn't sound like a lot, but for a niche blog like this, I think it is actually quite good. For me, it is also interesting to note that my own country - Norway - is only in the third spot when it comes to number of visitors.

Most of my time has been spent on covering articles from peer-reviewed journals in mathematics education, and I have also covered some conferences. This is something I intend to continue doing, but I have been thinking about different possible ways of doing this. First, I have thought about the possibility of writing more about some main articles in a way that people who are not researchers can relate to. I think it is important for researchers to communicate their results not only to fellow researchers. Unfortunately, but understandably, most teachers do not read our research journals! So, I have started thinking about writing some abstracts or impressions of research articles that teachers, parents and others who are interested but not researchers might relate to. I have also started thinking about making a stronger effort into providing an even better overview of the field (indexing journal articles, updating the conference calendar more, etc.). These are some of my own thoughts. But I am also interested in learning about your ideas! So, if you read this blog frequently, or if this is the first time you drop by ... What do you think? What would be more useful to you? Please write comments to this post, or send me an e-mail to let me know!

I already know what an incredible learning experience this blog has been for me, but now I want to know how I can make it a better experience for you - the readers - as well!


Elementary prospective teachers' mathematical beliefs

Susan L. Swars, Stephanie Z. Smith, Marvin E. Smith and Lynn C. Hart have written an article called A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs. The article was published online in Journal of Mathematics Teacher Education on Thursday. Here is the abstract of their article:
The universal emphasis in mathematics education on teaching and learning for understanding can require substantial paradigmatic shifts for many elementary school teachers. Consequently, a pressing goal of teacher preparation programs should be the facilitation of these changes during program experiences. This longitudinal, mixed methods study presents a thorough investigation of the effects of a distinctive teacher preparation program on important constructs related to prospective teacher preparedness to teach mathematics for understanding, including mathematics pedagogical and teaching efficacy beliefs, mathematics anxiety, and specialized content knowledge for teaching mathematics. The results indicate that the programmatic features experienced by the prospective teachers in this study, including a developmental two-course mathematics methods sequence and coordinated developmental field placements, provided a context supporting teacher change. These shifts are interpreted through the nature and timing of the experiences in the program and a model of teacher change processes. The findings provide insights for mathematics educators as to the outcomes of these programmatic features.

Belief enactment

Danish colleague Jeppe Skott has written an interesting article about research concerning teachers' beliefs. The article is entitled Contextualising the notion of ‘belief enactment’, and it was published online in Journal of Mathematics Teacher Education on Wednesday. Skott is a prominent researcher within the field of mathematics education research in the Nordic countries, and he has a critical view on the notion of research on teachers' beliefs, as well as the approach to this area of research. Here is the abstract of his article:
For more than 20 years, belief research has been based on the premise that teachers’ beliefs may serve as an explanatory principle for classroom practice. This is a highly individual perspective on belief–practice relationships, one that does not seem to have been influenced by the increasingly social emphases in other parts of mathematics education research. In this article, I use the notions of context and practice to develop a locally social approach to understanding the belief–practice relationships. It is a corollary of the approach taken that the high hopes for belief research with regard to its potential impact on mathematics instruction need to be modified.

Method, certainty and trust

David Pimm has written an article called Method, certainty and trust across disciplinary boundaries. This article was published online in ZDM earlier this week. Here is the abstract of his article:
This paper starts from some observations about Presmeg’s paper ‘Mathematics education research embracing arts and sciences’ also published in this issue. The main topics discussed here are disciplinary boundaries, method and, briefly, certainty and trust. Specific interdisciplinary examples of work come from the history of mathematics (Diophantus’s Arithmetica), from linguistics (hedging, in relation to Toulmin’s argumentation scheme and Peirce’s notion of abduction) and from contemporary poetry and poetics.


New IJMTL articles

Five new articles were published in International Journal for Mathematics Teaching and Learning on Tuesday:

How Does the Problem Based Learning Approach Compare to the Model-Eliciting Activity Approach in Mathematics? by Scott A. Chamberlin and Sidney M. Moon. Abstract: The purpose of this article is to discuss the similarities and differences in the two approaches referred to in the article title with an emphasis on implementation and outcomes.

Seeds of Professional Growth Nurture Students’ Deeper Mathematical Understanding, by Ji-Eun Lee and Dyanne Tracy. Abstract: This manuscript describes a group of middle school age students' exploration of virtual mathematics manipulatives and the authors' professional development process. In the manuscript, the authors share the experiences they had with middle school students and the process that they, as mathematics teachers, used to refine their own learning and teaching alongside the middle school students.

The State of Balance Between Procedural Knowledge and Conceptual Understanding in Mathematics Teacher Education, By Michael J. Bossé and Damon L. Bahr. Abstract: In this paper, we present the results of a survey-based study of the perspectives of mathematics teacher educators in the United States regarding the effects of the conceptual/procedural balance upon four concerns: the type of mathematics that should be learned in school, preservice teacher preparation, instructional conceptualization and design, and assessment.

An Exploration of the Effects of a Practicum-Based Mathematics Methods Course on the Beliefs of Elementary Preservice Teachers, by Damon L. Bahr and Eula Ewing Monroe. Abstract: Effects of a practicum-based elementary mathematics methods course on the beliefs of preservice teachers regarding conceptual knowledge in school mathematics were explored using a pre-post design. The intensity of those beliefs was assessed before and after the methods course using the IMAP Web-Based Beliefs Survey, an instrument constructed by the “Integrating Mathematics and Pedagogy” (IMAP) research group at San Diego State University.

What is Good College Mathematics Teaching? by Carmen M. Latterell. Abstract: This article attempts to answer the question “What is good college mathematics teaching?” by examining three sources of information: research, student course evaluations, and responses on the website RateMyProfessors.com.

This is the journal where I published my own article about Real-life Connections in Japan and the Netherlands: National Teaching Patterns and Cultural Beliefs, in July, and as always, all articles are freely available in pdf format.


Pearson's correlation between three variables

Pauline Vos has written an article called Pearson's correlation between three variables; using students' basic knowledge of geometry for an exercise in mathematical statistics. The article was recently published in International Journal of Mathematical Education in Science and Technology. Here is a copy of the article abstract:
When studying correlations, how do the three bivariate correlation coefficients between three variables relate? After transforming Pearson's correlation coefficient r into a Euclidean distance, undergraduate students can tackle this problem using their secondary school knowledge of geometry (Pythagoras' theorem and similarity of triangles). Through a geometric interpretation, we start from two correlation coefficients rAB and rBC and then estimate a range for the third correlation rAC. In the case of three records (n = 3), the third correlation rAC can only attain two possible values. Crossing borders between mathematical disciplines, such as statistics and geometry, can assist students in deepening their conceptual knowledge.


Book review: "Algebra in the Early Grades"

The latest issue of Teachers College Record includes a book review of "Algebra in the Early Grades". This important book was edited by late James J. Kaput together with David W. Carraher and Maria L. Blanton, and it was published by Lawrence Erlbaum Associates in 2007. David Slavit provides a thorough review, which gives a nice insight into the main parts of the book.

If you are interested, you might want to check out the information about the book in Google Books (which includes links to where you can buy the book), and you might also be interested in taking a look at this page about Early Algebra.

Activating mathematical competencies

César Sáenz from the Autonomous University of Madrid, Spain, has written an article called The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA). This article describes and analyzes the difficulties that Spanish student teachers had when attempting to solve the released items from PISA 2003. The student teachers (n=140) were first-year students, and they had not taken any mathematics courses in their teacher training at the time of the study. They didn't have any experience with the PISA tests, and they had no more than secondary-level mathematics studies before they started their teacher education. The test they took was made from a collection of 39 released items from PISA 2003.

The article was published in Educational Studies in Mathematics on Sunday. Here is the article abstract:
This paper analyses the difficulties which Spanish student teachers have in solving the PISA 2003 released items. It studies the role played by the type and organisation of mathematical knowledge in the activation of competencies identified by PISA with particular attention to the function of contextual knowledge. The results of the research lead us to conclude that the assessment of the participant’s mathematical competencies must include an assessment of the extent to which they have school mathematical knowledge (contextual, conceptual and procedural) that can be productively applied to problem situations. In this way, the school knowledge variable becomes a variable associated with the PISA competence variable.

Prospective elementary teachers' motivation

Amanda Jansen has written an article entitled Prospective elementary teachers’ motivation to participate in whole-class discussions during mathematics content courses for teachers. This article was published on Sunday in Educational Studies in Mathematics. Here is the abstract of her article:
Prospective elementary teachers’ (N = 148) motivation to participate in whole-class discussions during mathematics content courses for teachers, as expressed in their own words on an open-ended questionnaire, were studied. Results indicated that prospective teachers were motivated by positive utility values for participating (to achieve a short-term goal of learning mathematics or a long-term goal of becoming a teacher), to demonstrate competence (to achieve performance-approach goals), or to help others (to achieve social goals). Negative utility values for participating were expressed by those who preferred to learn through actively listening. Five motivational profiles, as composed of interactions among motivational values, beliefs, goals and self-reported participation practices, were prevalent in this sample. Self-reported variations among participants’ utility values and participation practices suggested that prospective teachers engaged differentially in opportunities to learn to communicate mathematically. Results provide pedagogical learner knowledge for mathematics teacher educators.

Gestures as semiotic resources

Ferdinando Arzarello, Domingo Paola, Ornella Robutti and Cristina Sabena have written an article called Gestures as semiotic resources in the mathematics classroom. The article was published online in Educational Studies in Mathematics a while ago. Here is the abstract of their paper:
In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such, gestures are seen as one of the semiotic tools used by students and teacher in mathematics teaching–learning. To analyze them, we introduce a suitable model, the semiotic bundle. It allows focusing on the relationships of gestures with the other semiotic resources within a multimodal approach. It also enables framing the mediating action of the teacher in the classroom: in this respect, we introduce the notion of semiotic game where gestures are one of the major ingredients.


Research fellow at University of Agder!

University of Agder, Norway, arguably has one of the strongest research groups in mathematics education. They have a strong Master programme, a PhD programme, and five international professors in mathematics education. Now, they have announced a free position/appointment as research fellow for a period of three years. So, if you want to become a PhD student in Norway, this might be your lucky day :-)

Some of the research areas within the field of mathematics education in Agder include:

  • Developmental research in the teaching and learning of mathematics (from day-care centres to the university level)
  • Mathematics classroom research
  • Pupils' and students' understanding, attitudes and motivation for mathematics
  • Problem solving and modelling in mathematics
  • History of mathematics
  • Mathematics teacher education and professional development
If you are interested, you can read the entire announcement from the link above, or you can contact Professor Simon Goodchild (simon.goodchild@uia.no).

ZDM, No 5, 2008

For some reason, ZDM has published two December issues this year. I have already covered one of them, which is actually No 6, but I have not covered No 5 (both are December issues). ZDM, No 5 has a focus on Empirical Research on Mathematics Teachers and their Education, and it is a very interesting issue (for me at least), with 14 articles:
So, if you (like me) you are interested in research related to mathematics teachers and/or mathematics teacher education, this would certainly be an issue to take a closer look at!

A large part of the articles in this issue are related to the international comparative study: "Mathematics Teaching in the 21st Century (MT21)". This study, according to the editorial, is the first study that has a focus on "how teachers are trained and how they perform at the end of their education".


NOMAD, No 3, 2008

Mathematics teachers' observable learning objectives

Paul Andrews has written an article entitled Comparative studies of mathematics teachers’ observable learning objectives: validating low inference codes. The article was published online in Educational Studies in Mathematics on Wednesday. Here is a copy of the article abstract:
Videotape is an increasingly used tool in cross-national studies of mathematics teaching. However, the means by which videotaped lessons are coded and analysed remains an underdeveloped area with scholars adopting substantially different approaches to the task. In this paper we present an approach based on generic descriptors of mathematics learning objectives. Exploiting live observations in five European countries, the descriptors were developed in a bottom-up recursive manner for application to videotaped lessons from four of these countries, Belgium (Flanders), England, Hungary and Spain. The analyses showed not only that the descriptors were consistently operationalised but also that they facilitated the identification of both similarities and differences in the ways in which teachers conceptualise and present mathematics that resonated with the available literature. In so doing we make both methodological and theoretical contributions to comparative mathematics research in general and debates concerning the national mathematics teaching script in particular.

Mathematical enculturation

Jacob Perrenet and Ruurd Taconis have written an article called Mathematical enculturation from the students’ perspective: shifts in problem-solving beliefs and behaviour during the bachelor programme. The article was published online in Educational Studies in Mathematics on Tuesday, and it is an Open Access article, so it is freely available to anyone! Here is the article abstract:
This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill in the questionnaire. As an educational exercise in academic reflection, they have to explain their individual shifts in beliefs, if any. Significant shifts for the group as a whole are reported, such as the growth of attention to metacognitive aspects in problem-solving or the growth of the belief that problem-solving is not only routine but has many productive aspects. On the one hand, the changes in beliefs and behaviour are mostly towards their teachers’ beliefs and behaviour, which were measured using the same questionnaire. On the other hand, students show aspects of the development of an individual problem-solving style. The students explain the shifts mainly by the specific nature of the mathematics problems encountered at university compared to secondary school mathematics problems. This study was carried out in the theoretical framework of learning as enculturation. Apparently, secondary mathematics education does not quite succeed in showing an authentic image of the culture of mathematics concerning problem-solving. This aspect partly explains the low number of students choosing to study mathematics.


ZDM, December 2008

The December issue of ZDM is out, and it contains 12 interesting articles. The theme of the issue is "An Asia Pacific focus on Mathematics Classrooms:

Embodied multi-modal communication

Julian Williams from University of Manchester (UK) has written an article entitled Embodied multi-modal communication from the perspective of activity theory. This article was published online in Educational Studies in Mathematics last week. Here is the abstract of the article:
I begin by appreciating the contributions in the volume that indirectly and directly address the questions: Why do gestures and embodiment matter to mathematics education, what has understanding of these achieved and what might they achieve? I argue, however, that understanding gestures can in general only play an important role in ‘grasping’ the meaning of mathematics if the whole object-orientated ‘activity’ is taken into account in our perspective, and give examples from my own work and from this Special Issue. Finally, I put forward the notion of a ‘threshold’ moment, where seeing and grasping at the nexus of two or more activities often seem to be critical to breakthroughs in learning.


IJSME, December 2008

The December issue of International Journal of Science and Mathematics Education has been published. This peer-reviewed journal is sponsored by the National Science Council in Taiwan, and has a particular emphasis on articles "that explore science and mathematics education from different cultural perspectives". The journal also encourages articles written by authors who do not have English as their first language. This is, in my opinion, a very nice focus from a scientific journal! The issue contains the following articles:


Playing with representations

Tom Satwicz and Reed Stevens have written an article called Playing with Representations: How Do Kids Make Use of Quantitative Representations in Video Games? The article was published online in International Journal of Computers for Mathematical Learning on Tuesday. Here is a copy of the abstract of their article:
This paper describes the use of quantities in video games by young people as part of a broader effort to understand thinking and learning across naturally occurring contexts of activity. Our approach to investigating the use of quantities in game play is ethnographic; we have followed eight children over a six-month period as they play their own games at home. The data set is composed of video recordings and artifact-based interviews. The concept of disciplined perception is used to understand how quantities are coordinated during game play. The current study shows young people using quantities in games to make predictions and organize their actions based on those predictions. Some ideas based on the study’s findings for using video games in school are discussed.


New journal: Educational Designer

A new journal for educational research has seen the light of day: Educational Designer! The journal is an online journal, and it was established by the International Society for Design and Development in Education. One of the articles in the first issue is written by Malcolm Swan, mathematics education researcher from the University of Nottingham. The article is concerned with Designing a Multiple Representation Learning Experience in Secondary Algebra. Here is the abstract of Swan's article (but the entire article is available online!):
This paper describes some of the research-based principles that I use when designing learning experiences to foster conceptual understanding. These principles are illustrated through the discussion of one type of experience: that of sorting multiple representations. I refer to learning experiences rather than tasks, because tasks are only one component of the design. Close attention is also paid to the role of the teacher in creating an appropriate climate for learning to take place.

After a brief excursion into my own theoretical framework, I describe the educational objectives behind my design and provide a detailed explanation of it in one topic, that of algebraic notation.  This is followed with an explanation of the principles that informed the design and the evolution of the task. Finally, I briefly indicate how the design might be generalised to include other topics.

ICMI newsletter, No 6, 2008

The October version of the ICMI newsletter has been sent to the subscribers' mailboxes. If you do not subscribe to the newsletter, you can find a complete archive here. Here is a copy of the table of contents:
1. Editorial: About the ICMI Studies --- and a Call For Proposals
2. Symposium Celebrating the Centennial of the ICMI
3. Proceedings of the Symposium Celebrating the Centennial of the ICMI
4. ICTMA 14
5. New e-journal: Educational Designer
6. Calendar of Events of Interest to the ICMI Community
7. Subscribing to ICMI News