This study diagnoses and explores year eight students' misconceptions and mistakes in algebra. An in-depth exploration of students' misconceptions were carried out by conducting interviews based on the students' work as outlined in a cognitive map. Based on the cognitive maps, it can be seen that the students emphasize procedural knowledge rather…

Algebra is considered by many to be a gateway to higher-level mathematics and eventual economic success yet students with and without disabilities often struggle to develop algebra skills. This study builds on the limited understanding of how virtual manipulatives support students with disabilities in the area of algebra by investigating their use…

The authors discuss the status of college algebra and related offerings and their relationship to introductory statistics education. They also describe an innovative approach to college algebra that integrates a significant amount of statistical reasoning and concepts and statistical methods as natural applications of basic ideas that are part of…

We automate and randomize the building of linear systems with a parameter, appropriate for assigning to students. When the parameter takes on a specific value, the system has no solutions. When the parameter takes on a different value, the system has an infinite number of solutions.

In this work, we studied the use of open education resources (OER) in the form of online modules combined with an open textbook as it relates to student performance and perceptions in a Linear Algebra course. In this approach, we compared student performance and perceptions from three sections of this intermediate level mathematics course. One was…

In this paper we consider implications of the current world-wide inclusion of computational thinking in relation to children's development of algebraic thinking. Little is known about how newly developed visual programming environments such as Scratch could enhance early algebra learning. The study is based on examples of programming activities…

The overwhelming presence of a procedural meaning of equality and equations reported in previous research has led to a call for suitable pedagogical interventions to nurture a relational meaning of these concepts. This paper is a response to that call. Drawing on the theory of objectification, the first part deals with the configuration of a Grade…

The aim of the study was to investigate the validity level of Socrates-based linear algebra e-module, both material validity and design. This is a research and "development" (R&D) with ADDIE procedure: analysis, design, develop, implement, and evaluate. The participants were 30 students and 2 lecturers who supervised linear algebra…

The problem addressed by this study was that Title 1 high school Mathematics teachers are limiting technology integration in the classroom by using traditional teaching practices that decrease academic achievement, student engagement, and classroom climate. The purpose of this qualitative case study was to explore how Title 1 urban high school…

This paper describes Alkaline, a size-reduced version of Kyber, which has recently been announced as a prototype NIST standard for post-quantum public-key cryptography. While not as simple as RSA, I believe that Alkaline can be used in an undergraduate classroom to effectively teach the techniques and principles behind Kyber and post-quantum…

After nationwide school closures due to COVID-19, virtual learning environments (VLE) have seen tremendous increase in usage. The current study identified teacher activities for orchestration using an Algebra VLE during school closures, and whether these activities were related to student achievement. In May 2020, we collected survey data on how…

Mathematical aptitude in the United States has been a concern over the past few decades, not only from an international perspective but from a student proficiency perspective. This phenomenon is also further negatively impacted due to COVID-19 associated learning loss. Correspondingly, there are calls for students to develop entrepreneurial skills…

Research on dyscalculia has focused almost exclusively on elementary-aged students' deficits in speed and accuracy in arithmetic calculation. This case study expands our understanding of dyscalculia by documenting how one college student with dyscalculia understood algebra during a one-on-one design experiment. A detailed case study of 19 video…

Algebra 1 is a gatekeeper course with profound implications for students' academic and professional success. This study examines the implications of teaching Algebra 1 through a standardized, fully online, asynchronous course developed by one of the largest online course vendors in the United States in alignment with Common Core State Standards…

This study investigated the role of the bar model method, a significant aspect of the Singapore mathematics curriculum, in the remediation of seventh-grade students' errors on algebra word problems. To accomplish this purpose, we first assessed students' errors on a written test involving algebra problems and identified ten students based on the…