Supporting students' in-the-moment perseverance is a vital objective in mathematics education because it promotes learning with understanding. Yet, little is written about if and how student perseverance can improve over time. I examine the specific ways in which secondary students improved their perseverance as they engaged with challenging…

This study compared area lessons from Korean textbooks and US standards-based textbooks to understand differences and similarities among these textbooks, as well as how these textbooks address known learning challenges in area measurement. Several well-known challenges have been identified in previous studies, such as covering, array structure,…

In this article, we report how a geometric task based on the ACODESA methodology (collaborative learning, scientific debate and self-reflection) promotes the reformulation of the students' validations and allows revealing the students' aims in each of the stages of the methodology. To do so, we present the case of a team and, particularly, one of…

In this exploratory study, our goal was to engage students in dynamic experiences of area as a continuous quantity that can be measured by multiplicatively composing two linear measures (lengths), an approach we refer to as 'dynamic measurement,' or DYME. In this paper, we present the learning trajectory constructed from two cycles of teaching…

Teachers' efforts to support students, both academically and socially, can play a role in how high school students productively engage with mathematics in the moment. To examine the connection between teacher support and student engagement, we conducted an exploratory mixed-methods study combining data from 20 high school classroom observations…

Low achievement in mathematics education has been an increasing problem in the recent years in some countries. According to a 2010 study from the U.S. Department of Education, blended learning classes produce statistically better results than their face-to-face. There is also an increasing number of students using smartphones and tablets in…

In this theoretical paper, I consider reversibility as a defining characteristic of mathematics. Inverse pairs of formalized operations, such as multiplication and division, provide obvious examples of this reversibility. However, there are exceptions, such as multiplying by 0. If we are to follow Piaget's lead in defining mathematics as the…

Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

This paper uses multimodal discourse analysis to show that discursive form, in addition to words, gestures and sound dimensions of speech, is an important linguistic resource for expressing mathematical meaning. During a collaborative task, a student spoke an insight about an algebraic property five times over a few minutes, in slightly different…

This paper reports on a study into pre-school children's self-regulated learning. Analysis is provided through findings taken from a larger study, the core aim of which was to contribute to developing and strengthening self-regulated learning competencies through merging Traditional African music and mathematics. An…

This paper aims to revisit and clarify the term problem context and to develop a theoretical classification of the construct of levels of context use (LCU) to analyse how the context of a problem is used to formulate a problem in mathematical terms and to interpret the answer in relation to the context of a given problem. Two criteria and six…

Studies on cognition have capitalized on the role of contexts and experience in shaping our cognitive competence. In the past few decades, the mathematical education research field has begun to pay increased attention to the mathematics practices of both adults and children that take place in non-academic settings. As a result, theoretical fields…

The [National Council of Teachers of Mathematics] NCTM research committee made a recent, urgent call for mathematics education researchers to "examine and deeply reflect on our research practices through an equity lens." With this in mind, we use this paper to reflect on the ways in which Steffe's work has contributed to three facets of…

Despite the importance of teachers' conception of effective problem-solving instruction, limited attention is given to this area in the current literature. In this study we examined 96 preservice teachers' (PSTs) views on effective problem-solving instruction and how their conceptions are related and reflected in their views on problem solving and…

This case study of a third grade classroom details the ways that competence was jointly constructed by students and the teacher in relation to students' efforts to engage with each other's mathematical ideas. By creating consistent opportunities for students to share and make sense of others' ideas, and by supporting students to take up these…