Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among…

Fractions are highly important. Therefore, it is crucial to understand the developmental trajectory of fraction knowledge and its main predictors and consequences. Our research team has proposed that we have a neurocognitive architecture dedicated to processing nonsymbolic ratios, which serves as a startup tool for fractions: the Ratio Processing…

This study focuses on students' reflections on their prior learning, action plans generated by them, and the corrective instructional design process. The concern that initiates the beginning of this action research is two folds: on the side of students, to maximize students benefit from corrective instruction and on the teacher's side, being more…

This study investigated personalization as an innovation that can be used to impact college mathematics achievement. In the reported study, similar tasks using personalized data and teacher-selected data were implemented in courses in both 4-year and 2-year colleges. Pre- and posttests and student work were analyzed to examine the impact of…

This study aims to investigate the similarities and differences between prospective mathematics teachers' creative thinking skills in paper-pencil test and on a GeoGebra-supported environment in terms of problem-posing. This case study used purposive sampling method for determining the participants. Findings revealed that the activities carried…

We present the results of a research project on arithmetic-algebraic thinking that was carried out jointly by a team in Mexico and another in Quebec. The project deals with the concepts of variable and covariation between variables in the sixth grade at the elementary level and the first, second, and third years of secondary school--namely,…

The quality of mathematics assignments from teachers to students is one important element that determines whether learning is effective or not. To make quality math assignments requires knowledge from the teacher about content and students, who are subdomains of mathematical knowledge to teach. This knowledge needs to be developed in prospective…

The goal of this study was to design and implement curricula in the Adult Basic Education classroom that aligned to the Critical Mathematics Pedagogical Framework. Specifically, this study assessed if ABE students' mathematics anxiety and mathematics self-efficacy ware affected by curricula that aligns to the Critical Mathematics Pedagogical…

Families are a crucial element of children's overall learning (Castro et al. 2015), and their involvement can directly influence children's overall math achievement (Sheldon 2009). School events that foster math among families, such as family math nights, have the potential of improving student math performance (Lopez and Donovan 2009). Latino…

A synthesis of reasons for the production of this monograph is presented with a focus on contemporary research in the context of the Ninth Congress of the European Society for Research in Mathematics Education. Within the domain of mathematics and language, three lines of concern are addressed: (1) classroom discourse, (2) language diversity, and…

Traditionally, many undergraduate mathematics courses have been defined in terms of mathematical content and the techniques in which students should become proficient or theorems they should be able to prove. This can result in a reliance on shallow or rote learning by students, despite the fact that the main goal of a mathematics lecturer is…

Children and animals of all kinds are said to develop some degree of number sense. The search for "number neurons" and neural correlates of computational thinking aims to identify biological primitives to explain the emergence of number sense. This work typically looks for the sources of number sense in organisms, but one might extend…

This paper reports on combining semiotic and discursive approaches to reification in classroom interactions. It focuses on the discursive characteristics and semiotic processes involved in the teaching and learning of square roots in a ninth grade classroom in Japan. The purpose of this study is to characterize the development of mathematical…

This article presents a new method for introductory teaching of the sample mean, median and mode(s) from a univariate dataset. These basic statistical concepts are taught at various levels of education from elementary school curriculums to courses at the tertiary level. These descriptive measures of location can be taught as optimized solutions to…

The purpose of this study was to investigate the flow of thought of the pre-service mathematics teachers through the answers of a function limit evaluation by formal definition. This study used a qualitative approach with descriptive method. The research subjects were the students of mathematics education department of Universitas Serang Raya,…