The rise of digital resources has had profound effects on mathematics curricula and there has been a concurrent increase in teachers flipping their instruction--that is, assigning instructional videos or multimedia for students to watch as homework and completing problem or exercise sets in class rather than vice versa. These changes have created…

Research suggests that people use a variety of strategies for comparing the numerical values of two fractions. They use holistic strategies that rely on the fraction magnitudes, componential strategies that rely on the fraction numerators or denominators, or a combination of both. We investigated how mathematically skilled adults adapt their…

Higher-level mathematics requires a connection between literal symbols (e.g., "x") and their mental representations. The current study probes the nature of mental representations for literal symbols using both the priming distance effect, in which ease of comparing a target number to a fixed standard is a function of prime-target…

It is not yet understood how children acquire the meaning of numerical symbols and most existing research has focused on the role of approximate non-symbolic representations of number in this process (see Piazza, ("Trends in Cognitive" 14(12):542-551, 2010). However, numerical symbols necessitate an understanding of both order and…

Mathematical processing associated with solving short geometry problems requiring logical inference was examined among students who differ in their levels of general giftedness (G) and excellence in mathematics (EM) using ERP research methodology. Sixty-seven male adolescents formed four major research groups designed according to various…

Students' difficulties in mathematics and science may stem from interference of irrelevant salient variables. We focus on the comparison of perimeters task, in which area is the irrelevant salient variable. A previous fMRI brain-imaging study related to the comparison of perimeters task suggested that increasing the level of salience of the…

We asked: "What are the similarities and differences in mathematical processing associated with solving learning-based and insight-based problems?" To answer this question, the ERP research procedure was employed with 69 male adolescent subjects who solved specially designed insight-based and learning-based tests. Solutions of…

Due to the need for measurement instruments that allow an investigation of teachers' situational cognition and thus go beyond the limited scope of classical paper-and-pencil-tests, we ask how a specific video-based measurement of teachers' classroom management expertise can provide additional information when compared with an established…

Originating in Asia, lesson study is gradually spreading around the globe. As evident from the papers in this issue, we have much to learn as it is implemented in a variety of cultural contexts. In this article we reflect on the goals of lesson study, the organizational supports required to sustain the practice in various contexts, and the…

There is no doubt that a lesson plan is a necessary product of Lesson Study. However, the collaborative work among teachers that goes into creating that lesson plan is largely under-appreciated by non-Japanese adopters of Lesson Study, possibly because the effort involved is invisible to outsiders, with our attention going to its most visible…

Our article aims to show how illuminating mathematical work as a concept from didactics of mathematics is useful in understanding issues relating to proving and learning of proof, with or without technology. After posing our hypotheses on the relationship of proof with mathematical work, the pedagogical intent of historical elements of geometry…

This study investigates students' conceptions of absolute value (AV), their performance in various items on AV, their errors in these items and the relationships between students' conceptions and their performance and errors. The Mathematical Working Space (MWS) is used as a framework for studying students' mathematical work on AV and the…

Univocal discourse, characterized by its function of conveying information from one person to another, is common in mathematics classrooms but dialogic teaching aims at students coming to participate in dialogic discourse, that is, discourse functioning to generate new meaning within a community. Many mathematical practices are directed at the…

Even in the resource-rich, more ideal conditions of many design-based classroom interventions, unexpected events can lead to disappointing results in student learning. However, if later iterations in a design research study are more successful, the previous failures can provide opportunities for comparisons to reveal subtle differences in…

Students' difficulties in mathematics and science may stem from interference of the task's salient irrelevant variables. Here, we focus on a comparison of perimeters task, in which the area is the irrelevant salient variable. In congruent trials (no interference), accuracy is higher and reaction time is shorter than in incongruent trials (area…