Visuospatial representations of numbers and their relationships are widely used in mathematics education. These include drawn images, models constructed with concrete manipulatives, enactive/embodied forms, computer graphics, and more. This paper addresses the analytical limitations and ethical implications of methodologies that use broad…

One of the greatest conceptual difficulties faced by middle level mathematics students is developing a rich understanding of irrational numbers that includes recognizing that irrational numbers are truly real numbers with an exact value and an exact place on the number line. Developing a deep conceptual understanding of irrational numbers is…

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…

Curriculum materials have a substantial influence on mathematics instruction and, consequently, students' learning opportunities. Many curriculum programs provide instructional notes for teachers and tasks for students as a means of accommodating particular student groups, such as those identified for English language learners. The presence of…

This study aims to elucidate a common professional learning opportunity in Japan, "instructional circles," which has not yet been studied systematically or described in detail. This study uses the mathematical knowledge for teaching (MKT) framework and research on features of professional learning opportunities that facilitate intended…

Mathematical literacy is a keystone of contemporary mathematics education research. We collectively, thoroughly explore this set of literacy practices from the perspectives of mathematical writing and mathematical discussion. Mathematical literacy practices, of course, include a third component--reading--which takes a number of forms. This…

In this study, it is aimed to determine the algebraic thinking habits of two eighth grade school students through the answers they gave in the process of solving mathematical problems. The algebraic habits of mind (ZCA) theoretical framework developed by Driscoll (1999) was used to reveal these thinking habits. The research design of this study is…

We examined how high school students use their cognitive and metacognitive skills in the geometry problem-solving process. This research employed a mixed-methods descriptive sequential design. Data were collected in the 2019-2020 academic year at secondary education institutions in the central districts of Adana, Türkiye. Using stratified…

In this article, we draw on teacher surveys and interviews to explore elementary teachers' perceived professional space, especially in relation to perceived autonomy, and what these perceptions reveal about the achieved agency of individual teachers. Our analyses revealed two distinct profiles for perceived professional space, and a positive…

The reality is that textbooks and state standards have more content than can reasonably be covered for proficiency in most classrooms. In years past, this typically meant cutting the last unit or two or moving along regardless of who was keeping up, in many cases resulting in cutting statistics from the curriculum. This article provides five…

One typical challenge in algebra education is that many students justify the equivalence of expressions only by referring to transformation rules that they perceive as arbitrary without being able to justify these rules. A good algebraic understanding involves connecting the transformation rules to other characterizations of equivalence of…

While classical studies have highlighted the many potential benefits of using original historical sources in the classroom, few studies have documented actual classroom practices outside of research contexts. In this case study, I aim to describe and explain how five French high school teachers autonomously designed and implemented classroom…

The objective of this study is to examine the characteristics of PSTs' selection of real-life examples for discussion, the aspects they attended to during the discussion, and their reflection on facilitating the discussion. A total of 46 elementary PSTs in the US joined in the study. We gathered data from a three-phase task using an online course…

This theoretical paper sets forth two "aspects of predication," which describe how students perceive the relationship between a property and an object. We argue these are consequential for how students make sense of discrete mathematics proofs related to the properties and how they construct a logical structure. These aspects of…

In recent decades, there has been considerable research that explores the teaching and learning of combinatorics. Such work has highlighted the fact that understanding and justifying combinatorial formulas can be challenging for students, and there is a need to identify ways to support students' combinatorial reasoning. In this paper, we…