When it comes to choosing tasks, values can have a significant impact. This study explores teachers' values as they choose one task from among three that they believe will have the most potential to occasion mathematical creativity in the classroom. Participants' analyses of each task, as well as their reasons for choosing one task as most…

Teachers' ability to accurately judge difficulties of mathematical tasks is an essential aspect of their diagnostic competencies. Although research has suggested that pedagogical content knowledge (PCK) is positively correlated with the accuracy of diagnostic judgments, experimental studies have not been conducted to investigate how PCK affects…

It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing…

Feedback provided by mathematics teachers usually addresses procedural skills and, to a much lesser extent, other competencies such as conceptual understanding or engagement in mathematical practices. As most previous literature has studied feedback provided on homework or video prompts, how teachers provide such feedback in the classroom is…

In this paper, we network five frameworks (cognitive demand, lesson cohesion, cognitive engagement, collective argumentation, and student contribution) for an analytic approach that allows us to present a more holistic picture of classrooms which engage students in justifying. We network these frameworks around the edges of the instructional…

Students' issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students' outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads…

This paper presents the findings from a survey used to investigate how mathematicians perceive the genre of mathematical proof writing at the undergraduate level. Mathematicians were asked whether various proof excerpts highlighted in four partial proofs were unconventional in each one of three pedagogical contexts: undergraduate mathematics…

Educational literature indicates that solving open mathematical tasks (OTs) is a powerful creativity-directed activity. However, the use of these tasks with school students on an everyday basis is extremely limited. To promote implementation of OTs in middle school, we manage a large-scale R&D project, Math-Key, which makes open mathematical…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

The aim of this study is to better understand the notion of early algebraic thinking by describing differences in grade 4-7 students' thinking about basic algebraic concepts. To achieve this goal, one test that involved generalized arithmetic, functional thinking, and modeling tasks, was administered to 684 students from these grades. Quantitative…

Middle school students have been pervasively described in the research literature as exhibiting disaffection, disengagement, and a lack of interest in mathematics classrooms. This study investigated this notion empirically using students' own voice on their wishes for mathematics learning to see if they characterise themselves in this way in their…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. ("Journal for Research in Mathematics Education"…

In this paper, we consider theories about processes of visual perception and perception-based knowledge representation (VPR) in order to explain difficulties encountered in figural processing in junior high school geometry tasks. In order to analyze such difficulties, we take advantage of the following perspectives of VPR: (1) Perceptual…

An attempt is made to establish a link between ordinary arithmetical situations and relevant mathematical concepts by the analyzing of complexity of concepts. (MP)