• 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

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.

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.

• Language and Student Performance in Junior Secondary Science Examinations: The Case of Second Language Learners in Botswana, by Robert B. Prophet and Nandkishor B. Badede
• The system of coordinates as an obstacle in understanding the concept of dimension, by Constantine Skordoulis, Theodore Vitsas, Vassilis Dafermos and Eugenia Koleza
• Misconceptions of Turkish Pre-Service Teachers about Force and Motion, by Sule Bayraktar
• Variable Relationships among Different Science Learners in Elementary Science-Methods Courses, by Robert E. Bleicher
• Efficacy of Two Different Instructional Methods Involving Complex Ecological Content, by Christoph Randler and Franz X. Bogner
• Correlations Among Five Demographic Variables and the Performance of Selected Jamaican 11th-graders on Some Numerical Problems on Energy, by Nicholas Emepue and Kola Soyibo
• From “exploring the middle zone” to “constructing a bridge”: Experimenting in the Spiral Bianshi mathematics curriculum, by Ngai-Ying Wong, Chi-Chung Lam, XuHua Sun and Anna Mei Yan Chan
• Number Sense Strategies Used by Pre-Service Teachers in Taiwan, by Der-Ching Yang, Robert E. Reys and Barbara J. Reys
• Listen to the silence: The left-behind phenomenon as seen through classroom videos and teachers’ reflections, by Hagar Gal, Fou-Lai Lin and Jia-Ming Ying

The present study explores students’ abilities in conversions between geometric and algebraic representations, in problem- solving situations involving the concept of “limit” and the interrelation of these abilities with students’ constructed understanding of this concept. An attempt is also made to examine the impact of the “didactic contract” on students’ performance through the processes they employ in tackling specific tasks on the concept of limit. Data were collected from 222 12th-grade high school students in Greece. The results indicated that students who had constructed a conceptual understanding of limit were the ones most probable to accomplish the conversions of limits from the algebraic to the geometric representations and the reverse. The findings revealed the compartmentalized way of students’ thinking in non-routine problems by means of their performance in simpler conversion tasks. Students who did not perform under the conditions of the didactic contract were found to be more consistent in their responses for various conversion tasks and complex problems on limits, compared to students who, as a consequence of the didactic contract, used only algorithmic processes.

Many studies have reported on the economical, social, and educational difficulties encountered by Ethiopian Jews since their immigration to Israel. Furthermore, the overall academic underachievement and poor representation of students of Ethiopian origin (SEO) in the advanced mathematics and science classes were highlighted and described. Yet, studies focusing on differential achievements within SEO and on students who succeed against all odds are scarce. In this study, we explored success stories of five SEO studying in a pre-academic program at a prestigious technological university in Israel. Our goal was to understand how these students frame and interpret their success in mathematics and to identify elements perceived as fostering their mathematics and academic trajectories. Using qualitative methodology, we identified perceived personal motivational variables, effective learning and coping strategies, and students’ immediate environment as key elements contributing to achieving and maintaining success. We discuss possible theoretical contributions and practical implications of the findings.