Takeshi Miyakawa and Carl Winsløw have written an article called Didactical designs for students’ proportional reasoning: an “open approach” lesson and a “fundamental situation”. The article was published online in Educational Studies in Mathematics on Saturday. Here is their abstrac:

In this paper, we analyze and compare two didactical designs for introducing primary school pupils to proportional reasoning in the context of plane polygons. One of them is well-documented in the literature; the other one is based on our own data and is accordingly presented and discussed in more detail in this paper. The two designs come from different cultural and intellectual environments: lesson study in Japan (implicitly based on the “open approach method”) and “didactical engineering” in France (based on the theory of didactical situations). The general aim of our paper is to compare these two environments and their approaches to didactical design, basing our discussion on the concrete designs mentioned above. Clear differences among them are presented, while we also identify links which hold potential for integrating research and practice.

Sean Kelly has written an article about The Black-White Gap in Mathematics Course Taking. This article has been published in a recent issue of the journal Sociology of Education. Here is the abstract of Kelly’s article:

Using data from the National Education Longitudinal Study, this study investigated differences in the mathematics course taking of white and black students. Because of lower levels of achievement, prior course taking, and lower socioeconomic status, black students are much more likely than are white students to be enrolled in low-track mathematics courses by the 10th grade. Using multilevel models for categorical outcomes, the study found that the black-white gap in mathematics course taking is the greatest in integrated schools where black students are in the minority and cannot be entirely accounted for by individual-level differences in the course-taking qualifications or family backgrounds of white and black students. This finding was obscured in prior research by the failure to model course taking adequately between and within schools. Course placement policies and enrollment patterns should be monitored to ensure effective schooling for all students.

The December issue (2008) of International Journal of Computers for Mathematical Learning has recently been made available – obviously a bit late. These are the five articles included:

• Playing with Representations: How Do Kids Make Use of Quantitative Representations in Video Games? by Tom Satwicz and Reed Stevens
• Graphic Calculators and Micro-Straightness: Analysis of a Didactic Engineering, by Michela Maschietto
• An ‘Emergent Model’ for Rate of Change, by Sandra Herbert and Robyn Pierce
• Using Dynamic Geometry Software to Gain Insight into a Proof, by Bulent Guven
• Computational Diversions: Julia Variations, by Michael Eisenberg

Laetitia Bueno-Ravel and Ghislaine Gueudet have written an article that was recently published in International Journal of Computers for Mathematical Learning. The article provides some interesting perspectives on issues that should be relevant to most mathematics teachers: Online Resources in Mathematics, Teachers’ Geneses and Didactical Techniques. The examples provided in their article is related to a particular electronic resource called (in French) “Mathenpoche” (or “Maths in the pocket”). Here is the abstract of their article:

The study we present here concerns the consequences of integrating online resources into the teaching of mathematics. We focus on the interaction between teachers and specific online resources they draw on: e-exercise bases. We propose a theoretical approach to study the associated phenomena, combining instrumental and anthropological perspectives. For given didactical tasks, we observe teachers’ instrumental geneses, and the didactical techniques they develop. We exemplify our approach with the analysis of a case study of trigonometry in grade 9.

Núria Gorgorió and Guida de Abreu have written an article that was published in Educational Studies in Mathematics on Tuesday. The article is entitled Social representations as mediators of practice in mathematics classrooms with immigrant students. Here is a copy of their abstract:

This article suggests that a critical perspective of the notion of social representations can offer useful insights into understanding practices of teaching and learning in mathematics classrooms with immigrant students. Drawing on literature using social representations, previous empirical studies are revisited to examine three specific questions: what are the dominant social representations that permeate the mathematics classroom with immigrant students? What impact do these social representations have on classroom practices? What are the spaces for changing these practices through becoming reflective and critically aware of these representations? These questions are addressed mostly in relation to teachers’ representations, though the article also draws on data from research with students and parents to illustrate the diversity of representations and to argue for a critical and reflective perspective.