Much of the education research on implicit differentiation and related rates treats the topic of differentiating equations as an unproblematic application of the chain rule. This paper instead problematizes the legitimacy of this procedure. It develops a conceptual analysis aimed at exploring how a student might come to understand when and why one…

The ability to choose the larger between two numbers reflects a mature understanding of the magnitude associated with numerical symbols. The present study explores how the knowledge of the number sequence and memory capacity (verbal and visuospatial) relate to number comparison skills while controlling for cardinal knowledge. Preschool children's…

The use of written or graphic representations is essential in mathematics. Graphic representations are mainly used and researched as instruments for problem solving. There is a gap in research for interventions that use learner-generated graphic representations as documents for reflection processes for promoting the development of children's…

Subitizing, a quick apprehension of the numerosity of a small set of items, has been found to explain students' number understanding when counting. We utilized a constructivist teaching experiment methodology to investigate how the counting and subitizing activity of one student, Diego, related to his number understanding (described by his…

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…

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…

In this review, findings from studies investigating gender differences in spatial ability, math anxiety, and math achievement, the relationship between spatial ability and math anxiety, between spatial ability and math achievement, and between math anxiety and math achievement are synthesized. As a result of this synthesis, a sequential mediation…

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…

Research findings and reform-oriented standards emphasise the importance of mathematical connections in support of students' conceptual development. Previous research on teachers attending to mathematical connections has tended to focus on expert teachers' practice. Complementing previous research, this study describes how a cohort of twelve…

When Katrina Lindo taught Integrated Mathematics 1 to ninth- and tenth-grade students, she encountered some students who appeared initially resistant to doing mathematics. Lindo wanted her students to see themselves as capable of making sense of mathematics. Lindo said that being a mathematician is "the process of taking what you know and…

Thirty-seven preservice teachers engaged in a self-regulated learning experience proposed to increase their algebra content knowledge and to examine their use of data to make instructional decisions. Using weekly algebra curriculum-based measures, preservice special education teachers set learning goals and objectives, individually selected and…