Background: In this cross-national study, Spanish, Finnish, and Swedish middle and high school students' procedural flexibility was examined, with the specific intent of determining whether and how students' equation-solving accuracy and flexibility varied by country, age, and/or academic track. The 791 student participants were asked to solve…

This study analysed the designs of algebraic problems in elementary mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This study employed a content-analysis method that focused on four dimensions: representational forms, cognitive demand levels (CDLs), contextual features, and types of responses. The result of the…

Quantitative reasoning is defined as reasoning about relationships between items, measurements of objects, and quantities rather than numbers. Both in the transition from arithmetic to algebra and in the problem-solving process, quantitative reasoning is seen as a critical instrument for the development of students' mathematical skills. In the…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing…

In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning…

This nation needs many more students to attend college and graduate, but several things are getting in the way, particularly for marginalized students. Among those who do get in, many are unable to finish. Children in this country need to be successful in school, graduate, and have options to either attend college or join the workforce. This…

This study explored the mathematics course placement process for incoming students in an all-boys Catholic high school. The sequential nature of mathematics significantly impacts students' opportunity to learn; moreover, the mathematics course taken by a student during ninth grade can have far-reaching effects. Previous studies have found that…

Generalisation is a skill that enables learners to acquire knowledge in general, and mathematical knowledge in particular. It is a core aspect of algebraic thinking and, in particular, of functional thinking, as a type of algebraic thinking. Introducing primary school children to functional thinking fosters their ability to generalise, explain and…

Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students' abstract thinking. However, in addition to research on cognitive processes, learners' affective characteristics have largely remained unexplored…

A series of course-specific MAP Growth Mathematics and Science subject tests were released successively starting in August 2017 to replace the older NWEA End-of-Course (EOC) tests. Different from the prior NWEA EOC tests taken only at the end of a course, these course-specific tests can be administered multiple times throughout the school year,…

Research studies have suggested that students who participate in daily physical activity and who are more physically fit may have improved academic achievement scores. However, pressures on school districts to improve students' academic achievement in core course areas such as math, science, and English have put less emphasis on courses such as…

To efficiently solve mathematical expressions and equations, students need to notice the systemic structure of mathematical expressions (e.g., inverse relation between 3 and 3 in 3 + 5 - 3). We examined how symbols--specifically variables versus numbers--and students' algebraic knowledge impacted seventh graders' problem-solving strategies and use…

The purpose of this study was to examine the impact and interactions of student-centered instructional techniques on College Algebra student engagement, mathematics attitudes, and achievement. At my place of practice, instructional shifts towards student-centered and social-efficiency models of instruction are taking place, supported by…

This preliminary study examined whether distinct student profiles (N = 760) emerged based on their behavioral patterns in an online algebraic learning game. We applied k-means clustering analysis to clickstream data collected in the game and then examined how students' behavioral patterns varied across the clusters using data visualization. The…