In this survey paper, we describe the state of the field on linear algebra research. We synthesize themes, questions, results, and perspectives emphasized in the papers that appear in this issue, as well as a selection of those published between 2008 and 2017. We highlight the extensive base of empirical research detailing how students reason…

The aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…

In this study, the author examined student attempts to translate a verbal problem into an algebraic statement relating two variables, after they had solved an arithmetic question from the same problem. A total of 645 students from New England (U.S.A.) answered the problem on a mathematics assessment administered at the beginning of the school…

This Data Point uses data from the High School Longitudinal Study of 2009 (HSLS:09), a nationally representative, longitudinal study of more than 23,000 ninth-graders in 2009, to examine the association between the timing of Algebra I coursetaking and enrollment in postsecondary education. HSLS:09 cohort members were asked when they last took…

"Wheel spinning" is the phenomenon in which a student fails to master a Knowledge Component (KC), despite significant practice. Ideally, an intelligent tutoring system would detect this phenomenon early, so that the system or a teacher could try alternative instructional strategies. Prior work has put forward several criteria for wheel…

This autobiographical study of teaching and learning Algebra 1 was developed to examine classroom experiences through the lens of the researcher and to explore the perceptions of teachers and students involved in the study. The goal was to identify the quality, meaningful educational experiences in the classroom which led to the development of…

The present study explored the learning challenges that African American female students experience in their algebra or biology courses. Existing literature does not fully explore this subject, as studies are often inclusive of all races (i.e., all girls in science, technology, engineering, or math [STEM] fields) or all genders (i.e., all Black…

In this paper we review selected significant developments in the use of digital technology in the teaching and learning of mathematics over the last five years. We focus on a number of important topics in this field, including the evolvement of STEAM and critical making as well as the process of redefining learning spaces in the transformation of…

Precalculus and calculus are considered gatekeeper courses because of their academic challenge and status as requirements for STEM (science, technology, engineering, and mathematics) and non-STEM majors alike. Despite college mathematics often being seen as a neutral space, the field has identified ways that expectations, interactions, and…

Algebraic thinking is a method of solving math problems that stresses the significance of general connections. Excellent algebraic thinking necessitates strong symbolization and generalization ability. Students aged 7 to 15 are at the Piaget thinking stage's formal operational stage. Teachers, especially those working with secondary school…

For quite some time, research on the use of the History of Mathematics in the classroom has confirmed a lot of academic benefits for students. However, the History of Mathematics can also be used as an inclusion tool in classrooms where there are foreign students because it allows working with the specific contexts of other cultures. This article…

The purpose of this quantitative, quasi-experimental study was to determine if, and to what extent, technology-enhanced problem-based formative assessment instruction would have an impact on college students' algebra learning and development of critical thinking skills, when compared to traditional classroom instruction in a first-year college…

The current study examines both student self-regulated learning (SRL) and teacher orchestration in a virtual learning environment (VLE), with respect to student achievement. The study used SRL indicators derived from the log data on how students used the VLE system, survey data on how teachers made use of the VLE for Algebra instruction, as well…

There have been recent pushes for more active learning in mathematics classrooms, especially at the undergraduate level. To incorporate more active learning, there is a need for tasks that explicitly support this type of instruction, attention to student reasoning and whose ideas are publicly acknowledged, and awareness of differences in students'…

This report uses Spring 2022 data from nationally representative surveys of principals and math teachers in kindergarten through grade 12 (K-12) to explore students' opportunities to prepare for and take advanced math. The authors found that small high schools, high schools in rural areas, and high schools that predominantly serve students from…