The September issue of Educational Studies in Mathematics is available. The issue contains five interesting articles:

• School mathematics and its everyday other? Revisiting Lave’s ‘Cognition in Practice’, by Christian Greiffenhagen and Wes Sharrock
• Beyond ‘blaming the victim’ and ‘standing in awe of noble savages’: a response to “Revisiting Lave’s ‘cognition in practice’”, by David W. Carraher
• The problem of the particular and its relation to the general in mathematics education, by Vicenç Font and Ángel Contreras
• Transitions among different symbolic generalizations by algebra beginners in a computer intensive environment, by Michal Tabach, Abraham Arcavi and Rina Hershkowitz
• Centenary birth anniversary of E. W. Beth (1908–1964), by Giorgio T. Bagni

Laura Jacobsen Spielman, Radford University, has written an article called Equity in mathematics education: unions and intersections of feminist and social justice literature. The article was published online in ZDM last week, and it takes up the discussion concerning gender equity. As a theoretical background, the author integrates theoretical perspectives from feminist and social justice literature. Here is the abstract of the article:

Traditional models of gender equity incorporating deficit frameworks and creating norms based on male experiences have been challenged by models emphasizing the social construction of gender and positing that women may come to know things in different ways from men. This paper draws on the latter form of feminist theory while treating gender equity in mathematics as intimately interconnected with equity issues by social class and ethnicity. I integrate feminist and social justice literature in mathematics education and argue that to secure a transformative, sustainable impact on equity, we must treat mathematics as an integral component of a larger system producing educated citizens. I argue the need for a mathematics education with tri-fold support for mathematical literacy, critical literacy, and community literacy. Respectively, emphases are on mathematics, social critique, and community relations and actions. Currently, the integration of these three literacies is extremely limited in mathematics.

Rina Zazkis and Roza Leikin have written an article that was published online in Educational Studies in Mathematics last week. The article is entitled Exemplifying definitions: a case of a square, and here is the abstract:

In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility and correctness, richness, and generality. Results shed light on participants’ understanding of what a mathematical definition should entail and, moreover, contrast their pedagogical preferences with mathematical considerations.

Bharath Sriraman, editor of The Montana Mathematics Enthusiast, has written an article that was published in ZDM last week. The article is entitled Mathematical paradoxes as pathways into beliefs and polymathy: an experimental inquiry. Here is the abstract of the article:

This paper addresses the role of mathematical paradoxes in fostering polymathy among pre-service elementary teachers. The results of a 3-year study with 120 students are reported with implications for mathematics pre-service education as well as interdisciplinary education. A hermeneutic-phenomenological approach is used to recreate the emotions, voices and struggles of students as they tried to unravel Russell’s paradox presented in its linguistic form. Based on the gathered evidence some arguments are made for the benefits and dangers in the use of paradoxes in mathematics pre-service education to foster polymathy, change beliefs, discover structures and open new avenues for interdisciplinary pedagogy.

International Electronic Journal of Mathematics Education has released Issue 2 of this year. The issue contains three research articles:

1. Critical Mathematics Education: Recognizing the Ethical Dimension of Problem Solving, by Elizabeth de Freitas, USA
2. Mathematics Teachers’ Interpretation of Higher-Order Thinking in Bloom’s Taxonomy, by Tony Thompson, USA
3. Development of a Computerized Number Sense Scale for 3-rd Graders: Reliability and Validity Analysis, by Der-Ching Yang, Mao-neng Fred Li and Wei-Jin Li, Taiwan

Kyeong Hah Roh has written an article that was recently published online in Educational Studies in Mathematics. The article is entitled Students’ images and their understanding of definitions of the limit of a sequence, and here is the abstract:

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students’ understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus students’ images of the limit of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews, students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on activity, called the ɛ–strip activity. This paper illustrates how these students’ understanding of definitions of the limit of a sequence was influenced by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching and learning the concept of limit, as well as on research in mathematics education, are also discussed.

One of my own articles have finally appeared in International Journal for Mathematics Teaching and Learning. The article is entitled “Real-life Connections in Japan and the Netherlands: National Teaching Patterns and Cultural Beliefs“. The article is freely available online, and here is the abstract:

The TIMSS 1999 Video Study revealed that Japan had the lowest (of the seven participating countries) amount of real-life connections in the eighth grade mathematics classrooms, whereas the Netherlands had the highest amount of connections with real life. This article examines more closely how these ideas were actually implemented by teachers in these two countries.

ZDM has published a number of new online first articles. Check them out!

Nicholas Emepue and Kola Soyibo have written an article that was recently published in International Journal of Science and Mathematics Education. The article is entitled Correlations Among Five Demographic Variables and the Performance of Selected Jamaican 11th-graders on Some Numerical Problems on Energy. Here is the abstract:

This study was designed to assess whether the level of performance of selected Jamaican 11th-grade physics students on some numerical problems on the energy concept was satisfactory and if there were significant differences in their performance linked to their gender, socioeconomic background (SEB), school location, English language and mathematical abilities. The 331 sampled students consisted of 213 boys and 118 girls; 197 students were from a high SEB and 134 students from a low SEB; 296 students were from seven urban schools and 35 students from three rural schools; 112, 153 and 66 of the students had high, average and low English language abilities, respectively, while 144, 81 and 106 of the students had high, average and low mathematical abilities, respectively. An Energy Concept Test (ECT) consisting of six structured numerical questions was employed for data collection. The results indicated that although the students’ level of performance was regarded as fairly satisfactory, there was a lot of room for improvement. There were statistically significant differences in the students’ performance on the ECT linked to SEB, and mathematical abilities in favour of students from a high SEB, and high mathematical abilities, respectively. There was a positive, statistically significant but weak correlation between the students’ (a) mathematical abilities, and (b) English language abilities and their performance on the ECT, while there were no correlations among their gender, school location, and SEB and their performance on the ECT.

Allen Leung (The University of Hong Kong) has written an article that was recently published in International Journal of Computers for Mathematical Learning. The article is entitled Dragging in a Dynamic Geometry Environment Through the Lens of Variation, and Leung draws upon Marton’s variation theory as a theoretical framework in the article. Here is the abstract of the article:

What makes Dynamic Geometry Environment (DGE) a powerful mathematical knowledge acquisition microworld is its ability to visually make explicit the implicit dynamism of thinking about mathematical geometrical concepts. One of DGE’s powers is to equip us with the ability to retain the background of a geometrical configuration while we can selectively bring to the fore dynamically those parts of the whole configuration that interest us. That is, we can visually study the variation of an aspect of a DGE figure while keeping other aspects constant, hence anticipating the emergence of invariant patterns. The aim of this paper is to expound the epistemic value of variation of the Dragging tool in DGE in mathematical discovery. Functions of variation (contrast, separation, generalization, fusion) proposed in Marton’s theory of learning and awareness will be used as a framework to develop a discernment structure which can act as a lens to organize and interpret dragging explorations in DGE. Such a lens focuses very strongly on mathematical aspects of dragging in DGE and is used to re-interpret known dragging modalities (e.g., Arzarello et al.) in a potentially more mathematically-relevant way. The exposition will centre about a specific geometrical problem in which two dragging trajectories are mapped out, consequently resulting in a DGE theorem and a visual theorem. In doing so, a new spectral dragging strategy will be introduced that literally allows one to see the drag mode in action. A model for the lens of variation in the form of a discernment nest structure is proposed as a meta-tool to interpret dragging experiences or as a meta-language to relate different dragging analyses which consequently might give rise to pedagogical and epistemological implications.