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Maria Trigueros and Rafael Martinez-Planell have written an article entitled Geometrical representations in the learning of two-variable functions . The article was published online in Educational Studies in Mathematics on Wednesday. Here is the abstract of their article: This study is part of a project concerned with the analysis of how students work with two-variable functions. This is of fundamental importance given the role of multivariable functions in mathematics and its applications. The portion of the project we report here concentrates on investigating the relationship between students’ notion of subsets of Cartesian three-dimensional space and the understanding of graphs of two-variable functions. APOS theory and Duval’s theory of semiotic representations are used as theoretical framework. Nine students, who had taken a multivariable calculus course, were interviewed. Results show that students’ understanding can be related to the structure of their schema for R³ and to thei...

Nadia Hardy has written an article called Students’ perceptions of institutional practices: the case of limits of functions in college level Calculus courses . The article has recently been published online in Educational Studies in Mathematics . Here is the abstract of her article: This paper presents a study of instructors’ and students’ perceptions of the knowledge to be learned about limits of functions in a college level Calculus course, taught in a North American college institution. I modeled these perceptions using a theoretical framework that combines elements of the Anthropological Theory of the Didactic, developed in mathematics education, with a framework for the study of institutions developed in political science. While a model of the instructors’ perceptions could be formulated mostly in mathematical terms, a model of the students’ perceptions included an eclectic mixture of mathematical, social, cognitive, and didactic norms. I describe the models and illustrate them wi...

The British Society for the HIstory of Mathematics has published issue 2 of their bulletin this year. This issue contains four interesting articles: Mathematics of currency and exchange: arithmetic at the end of the thirteenth century , by Norman Biggs  Formulating figurate numbers , by Janet L. Beery  Mathematics goes ballistic: Benjamin Robins, Leonhard Euler, and the mathematical education of military engineers , by Janet Heine Barnett  Bernt Michael Holmboe (1795–1850) and his mathematics textbooks , by Andreas Christiansen

Yesterday, I presented an article by three Swedish scholars about mathematical reasoning when using digital tools in the mathematics classroom, and today I follow up with an article about the Potential scenarios for Internet use in the mathematics classroom . The article is written by Marcelo C. Borba, and it was published online in ZDM on Friday. Here is the abstract of Borba's article: Research on the influence of multiple representations in mathematics education gained new momentum when personal computers and software started to become available in the mid-1980s. It became much easier for students who were not fond of algebraic representations to work with concepts such as function using graphs or tables. Research on how students use such software showed that they shaped the tools to their own needs, resulting in an intershaping relationship in which tools shape the way students know at the same time the students shape the tools and influence the design of the next generation o...

I came across an interesting post about a project related to mathematics in early childhood education today. This project is described as "an innovative, district-wide early childhood education initiative", and it is conducted in Bremerton, Washington (U.S.). Apparently, the project was initially focused on early literacy skills, but they have now started to focus on mathematical skills as well. A goal is to "decrease the number of children (...) with learning disabilities". An interesting interview with the director of the program: Linda Sullivan-Dudzic has been postend on the Public School Insigths website. They have also written about this program earlier , and the story was originally published on the website of The Center for Public Education . Thanks to Alexander G. Rivadeneira for pointing me to this story :-)

Mark Boyland at Sheffield Hallam University (UK) has written an article about Engaging with issues of emotionality in mathematics teacher education for social justice . The article was recently published online in Journal of Mathematics Teacher Education . In the article, Boyland reports on a study where student teachers are encouraged to reflect on relationships and practices in the classroom that can promote social justice. In the article he relates to affective issues like emotions, beliefs and values, and he refers to some interesting literature on this. The interventions that were used in the study are referred to as "creative action methods", and they were originally developed by psychotherapist Jacob Moreno . This is a very interesting approach to research on affective issues, and to me it is a new approach that I hadn't heard of before. Here is the abstract of Boyland's article: This article focuses on the relationship between social justice, emotionality and ...

A new issue of Instructional Science has been published, and it contains an interesting article by Annika Lantz-Andersson, Jonas Linderoth and Roger Säljö: What’s the problem? Meaning making and learning to do mathematical word problems in the context of digital tools . A major presumption in their article is that problems which are given in a mathematics classroom will be interpreted differently by the students than problems which are given in social studies class, or outside of school. Theoretically, they thereby build upon the theories of Lave, Wenger and others concerning the situated nature of learning and human reasoning. In this article, their focus is on the mathematical reasoning of students when using digital tools in a mathematics classroom context. Here is the abstract of their article: The general background of this study is an interest in how digital tools contribute to structuring learning activities. The specific interest is to explore how such tools co-determine stud...

Three articles were published online in Journal of Mathematics Teacher Education on Monday : Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions , by Ji-Won Son and Sandra Crespo. Abstract: Recognizing meaning in students’ mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary and secondary teachers to a student’s non-traditional strategy for dividing fractions. Six categories of reasoning were constructed, making a distinction between deep and surface layers. The connections between the participants’ reasoning, their teaching response, and their beliefs about mathematics teaching were investigated. We found that there were not only differences but also similarities between the prospective elementary and secondary teachers’ reasoning and responses. We also found that those ...

In 2007, Rosella Santagata, Claudia Zannoni and James W. (Jim) Stigler wrote an article that was published in Journal of Mathematics Teacher Education . The article was entitled The role of lesson analysis in pre-service teacher education: an empirical investigation of teacher learning from a virtual video-based field experience , and the authors raised some very important questions in that article, questions that are still highly relevant. I rediscovered this article today, and I am going to share some of my discoveries with you now. In most teacher-preparation programs, the preservice students are faced with some sort of field experiences (in Norway we call this "practice", or "praksis" in Norwegian). A focus on the quality of field experiences received a lot of attention when U.S. teacher education was reformed in the 1980s, and there were several recommendations indicating that preservice teachers should have more "authentic experiences to prepare them to h...

Jo Boaler is a well known scholar within the field of mathematics education research, and she has written several books and articles related to the teaching and learning of mathematics. On June 30, a book called " What's Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject " will be released. I have read previous books and articles that Boaler has written, and I have even had the privilege of attending one of her lectures (at ICME-10 in Copenhagen), so I am sure this book will also be worth reading! Here is a copy of the product description from Amazon: A recent assessment of mathematics performance around the world ranked the United States twenty-eighth out of forty countries in the study. When the level of spending was taken into account, we sank to the very bottom of the list. We are falling rapidly behind the rest of the developed world when it comes to math education—and the consequences are dire. In this ...

The July issue of The Montana Mathematics Enthusiast will soon be published. Editor Bharath Sriraman has provided me with a preview of what appears to be a very interesting issue: THE MONTANA MATHEMATICS ENTHUSIAST ISSN 1551-3440 Vol.6, No.3, July 2009 TABLE OF CONTENTS Editorial Information 0. THE JOURNAL (WHEEL) KEEPS ON TURNING Bharath Sriraman (USA) FEATURE ARTICLES 1. TWO APPLICATIONS OF ART TO GEOMETRY Viktor Blåsjö (Sweden/USA) 2. INTUITIONS OF "INFINITE NUMBERS": INFINITE MAGNITUDE VS. INFINITE REPRESENTATION Ami Mamolo (Canada) 3. ON THE USE OF REALISTIC FERMI PROBLEMS FOR INTRODUCING MATHEMATICAL MODELLING IN SCHOOL Jonas Bergman Ärlebäck (Sweden) 4. MATHEMATICAL BEAUTY AND ITS CHARACTERISTICS- A STUDY ON THE STUDENT'S POINT OF VIEW Astrid Brinkmann (Germany) 5. AN APPLICATION OF GRÖBNER BASES Shengxiang Xia and Gaoxiang Xia (China) 6. SMALL CHANGE - BIG DIFFERENCE Ilana Lavy and Atara Shriki (Israel) 7. MATHEMATICAL CURI...

My university - University of Stavanger , Norway - has now announced a vacant position/stipend for a PhD student in mathematics education. The position is related to our project "Teachers' knowledge of mathematics" (which represents an attempt to adapt and use the MKT measures in Norway). For more information (the website is in Norwegian only) you can contact me (reidar.mosvold_AT_uis.no) or my colleague Raymond Bjuland (raymond.bjuland_AT_uis.no). Please note that the deadline for application is June 29, 2009!

Doug M. Clarke and Anne Roche have written an article entitled Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction . The article was published online in Educational Studies in Mathematics on Friday. Here is a copy of the article's abstract: As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that predicted, with the exception of fractions with the same numerators and different denominators, which proved surprisingly difficult. Students who demonstrated the greatest success were likely to use benchmark (transitive) and residual thinking. It is hypothesised that the methods of these successful students could form the basis of instr...

Amy J. Hackenberga and Erik S. Tillema have written an article entitled Students’ whole number multiplicative concepts: A critical constructive resource for fraction composition schemes . The article was published online in The Journal of Mathematical Behavior on Thursday. Here is the abstract of their article: This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students’ construction of fraction composition schemes. A fraction composition scheme consists of the operations and concepts used to determine, for example, the size of 1/3 of 1/5 of a whole in relation to the whole. Students’ whole number multiplicative concepts were found to be critical constructive resources for students’ fraction composition schemes. Specifically, the interiorization of two levels of units, a particular multiplicative concept, was found to be necessary for the construction of a unit fraction composition scheme, ...