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…

Background: Blended mathematical sensemaking in science ("MSS") involves deep conceptual understanding of quantitative relationships describing scientific phenomena. Previously we developed the cognitive framework describing proficiency in MSS across STEM disciplines, and specifically Physical Science. The framework was validated with…

This study explores how preservice secondary mathematics teachers comprehend and apply advanced mathematical concepts to the content they will teach in K-12 classrooms. Responding to student inquiries and guided by the "Mathematical Education of Teachers II" recommendations, an innovative capstone course was developed and integrated into…

Two problems, both from Gaspar Nicolas' "Tratado da Prática d'Arismética", published in 1519 are considered in this study. The tasks were carried out using pencil, paper and students from Portuguese schools. The aim was to explore the following students' performances: 1. The students were able to recognize the "error",…

As schools increasingly embrace embodied learning, there is a growing need to incorporate classroom teaching and learning activities that recognize the body's role as both an individual and collective resource for cognition and instruction. In response, we present a design for a classroom teaching sequence focused on early number learning,…