The aim of the study is to examine how lesson study activities affect primary school preservice teachers' noticing of students' misconceptions. A qualitative research approach was adopted and action research method was used. The study was conducted with 9 primary school preservice teachers. The data were obtained from the observation form, video…

This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…

Creativity and problem solving are considered to be twenty-first-century competencies, therefore promoting mathematical creativity should be an important part of school mathematics. The study presented in this paper is inspired by the notion of mathematical creativity and the utilization of multiple solution tasks (MSTs) to investigate students'…

We have expanded Stein's "Sweetness of Aspartame" laboratory project (Stein, P. J. "J. Chem. Educ." 1997, 74, 1112, DOI: 10.1021/ed074p1112) to include extensive use of statistical testing. Students test the statistical significance of a nonzero intercept in a linear regression, bias in comparison to a true value, and…

The concept of derivative is used in many areas including applied problems and requiring mathematical modelling in different disciplines. One of the most important approaches for teaching the derivative is to support students in visualizing the concept. Also, it is necessary to shift researchers and teachers' focuses to students' dynamic mental…

In this study, we present a mathematical analysis distinguishing two conceptions of equivalence: "proportional equivalence" and "unit equivalence." These two conceptions have distinct meanings in relation to equivalent fractions: one is grounded in proportionality, while the other is grounded in equal wholes. We argue that (a)…

This article elaborates a theoretical, methodological, and analytical approach intended to highlight the materiality and reciprocity of noticing in mathematics classrooms. Drawing from highly resonant concepts from materialism and Indigenous Knowledges--two perspectives that researchers rarely bring into dialogue--this alternative approach…

On the basis of a substantial, robust, and well-replicated cognitive science research literature, interleaving has been recommended across a range of professional pedagogical works as an evidence-based strategy for mathematics teachers. This report first notes the conflation of interleaving and spacing effects underpinning those recommendations…

Research has shown there are algebra concepts elementary teachers can introduce that help prepare elementary students for the eventual transition to algebra (e.g., the relational interpretation of the equal sign). "Early algebra" refers to the use of informal approaches to introduce such concepts to elementary students. "Strip…

Research indicates that investigating phenomena, rather than reproducing facts, should be a core experience in the education of prospective mathematics teachers. Corresponding with its centrality to quality teacher education, there are multiple existing methodologies for analyzing the effects of investigation tasks on teachers' mathematical…

Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to…

Competence with rational numbers is essential for mathematics proficiency in secondary mathematics. However, many students struggle with rational number concepts, and students with mathematics difficulties struggle even more. The purpose of this study was to examine the effects of an intervention that incorporated the use of explicit instruction…

In this study, the 8th grade secondary school mathematics textbook approved by the ministry in Turkey was compared with the mathematics textbooks in France and the USA in terms of the use of the multiple representation method in the probability learning domain. Document analysis, one of the qualitative research methods, was used in the study, and…

This study explores ASD (Autism Spectrum Disorder) students' early algebraic thinking abilities by comparing them to their non-ASD peers. The first aim was to examine whether possible significant differences between ASD and non-ASD students in arithmetic also extend to early algebra. The second aim focused further on early algebraic thinking,…

Early understanding of base-10 concept has been shown to be associated with superior mathematical achievement among East Asian children. In addition to their base-10 structured number system, teacher support in kindergarten is also crucial to children's development of this complex mathematical concept. Therefore, this study examined how Japanese…