savoy081

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...