How should we expect growing understandings of the nature of mathematical practice to inform classroom mathematical practice? We address this question from a perspective that takes seriously the notion that mathematics education, as a societal enterprise, is accountable to multiple sets of stakeholders, with the discipline of mathematics being…

Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

In many discussions of the ways in which abstraction is applied in computer science (CS), researchers and advocates of CS education argue that CS students should be taught to consciously and explicitly move among levels of abstraction (Armoni "Journal of Computers in Mathematics and Science Teaching," 32(3), 265-284, 2013; Kramer…

This article is the first in a series about teaching statistics. The authors discuss the role of statistics and the difference between mathematics and statistics.

This article is the first in a series of activities that discusses some interesting relationships with triangles. Brian Sherman shows how to find five centres for a triangle--the circumcentre, the incentre, the orthocentre, the centroid and the nine-point centre, with four of the five to be found on the Euler line. With these centres, he shows…

Recently, Christopher C. Tisdell questions some claims and results that appear in our article [Rivera-Figueroa A, Rivera-Rebolledo JM. A new method to solve the second-order linear difference equations with constant coefficients. Int J Math Educ Sci Technol. 2016;47(4):636-649.] regarding the novelty and simplicity of a method to solve…

The goal of our research program is to explicate the learning of mathematical concepts in ways that are useful for instructional design and to develop design principles based on those explications. I review one type of concept and our elaboration of reflective abstraction, coordination of actions (COA) that accounts for its construction. I then…

The aim of this article is to advise readers that natural numbers may be introduced as ordinal numbers or cardinal numbers and that there is an ongoing discussion about which come first. In addition, through several examples, the authors demonstrate that in the process of answering the question "How many?" one may, if convenient, use…

This study describes the initial psychometric evaluation of an Understanding Procedures observation rubric. The instrument is intended to provide feedback to teachers working in mathematics intervention settings. The rubric translates the research base from mathematics education and special education into practice in the form of specific items and…

Covariation and covariational reasoning are key themes in mathematics education research. Recently, these ideas have been expanded to include cases where more than two variables relate to each other, in what is termed multivariation. Building on the theoretical work that has identified different types of multivariation structures, this study…

This study describes the initial psychometric evaluation of the Understanding Procedures observation rubric for use as an instrument for feedback to teachers working in mathematics intervention settings. The rubric translates the research base from mathematics education and special education into practice in the form of specific items and…

The present study is a systematic meta-analytic study of 38 primary sources investigating the effectiveness of algebra interventions for students who are struggling. We systematically searched and screened over 1,300 records for studies to include. We computed summary effect sizes for each of the 12 interventions included. We conducted 4 separate…

We explore how relational trust was evidenced within the leadership activity of one mathematics leader using cultural-historical activity theory as a theoretical perspective. We use data from interview and observation sources to suggest that relational trust was a motive object of that mathematics leader's activity. Findings contribute knowledge…

This paper reports on 73 Grades 3 to 6 students' written responses to equal groups, arrays, multiplicative comparison and Cartesian product word problems. It is part of a larger study relating to students' development of multiplicative thinking (MT). The potential of using multiplicative word problems as a diagnostic assessment to reveal students'…

This article describes the research design and findings from a use-inspired study of online text-based mathematics resources. We sought to understand whether and how existing mathematics interest, together with the learner characteristics of prior coursework in mathematics and proof scheme, influenced comprehension of mathematical argumentation…