Active learning techniques, such as peer instruction and group work, have been gaining a lot of traction in universities. Taking a natural next step in re-evaluating current practices, many institutions recently started experimenting student-centred group exams. In order to assess the feasibility and effectiveness of collaborative assessments, we…

Students with autism spectrum disorders (ASD) are included more frequently in general education, and are increasingly expected to access and master core curricular content, including mathematics. However, mathematics often presents challenges to students with ASD. Studies on instructional interventions in mathematics for students with ASD are also…

The paper describes one problem solving strategy -- the Use of false assumption. The objective of the paper is to show, in accordance with Phylogenesis and Ontogenesis Theory, that it is worthwhile to reiterate the process of development of the concept of a variable and thus provide to pupils one of the ways helping them to eliminate usual…

We present a new learning activity that enables students to apply eigenvalue theory to investigate a practical modeling problem. We demonstrate how to build a spring-coupled pair of pendula and describe how students can measure the movements of these pendula using open-source image processing software. We then illustrate how to analyze this…

This study embarks on the question in the title with the construct of epistemological status, which pertains to the solver's satisfaction with the way and the degree to which their solution had fulfilled their intellectual and psychological needs in a particular problem situation. The construct is used to hypothesize that a solver's decision to…

Although often considered a more advanced area of mathematics, principles of algebra are taught throughout different mathematical concepts, and algebra is often considered gateway mathematical knowledge for more advanced mathematical concepts. For this reason, attention is needed toward making algebraic instruction more accessible to all types of…

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are…

An impediment to conducting high-quality quantitative research studies in education is the paucity of valid measures of learning gains. Studies often seek to investigate students' deep, conceptual understanding yet many measures assess only surface, procedural understanding. One reason is that the development of validated measures of conceptual…

Despite repeated discussions and practice, algebra students continue to make variable errors, in many ways, year after year. This same problem appeared thirty years ago in a list of common errors that math teachers today would immediately recognize, many involving exponents and distribution (Marquis 1988). Similar complaints even appeared in the…

An exploratory study was conducted to investigate the use of magic activities in a math course for prospective middle-school math teachers. This research report focuses on a lesson using two versions of math magic: (1) the "5-4-3-2-1-½ Magic" involves having students choose a secret number and apply six arithmetic operations in sequence…

The purpose of this study was to examine the effects of Google Classroom on the outcomes of students with learning disabilities in the mathematics classroom. Specifically, the study evaluated students' organizational skills, student achievement, and student satisfaction. The study included 7 high school students, 4 males and 3 females, in an…

This research focuses on the retention of students' algebraic understandings one year following a Grades 3-5 early algebra intervention. Participants included 1455 Grade 6 students who had participated in a cluster randomized trial. Approximately half of these students received an early algebra intervention as part of their regular instruction in…

The purpose of this article is to share a new approach for introducing students to the definition and standard examples of Abelian groups. The definition of an Abelian group is revised to include six axioms. A bullseye provides a way to visualize elementary examples and non-examples of Abelian groups. An activity based on the game of Jenga is used…

This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based…

Research in this study investigates teachers' perceptions of professional development (PD), funding and end-of course testing in Algebra I and Geometry. The research explores strategies to raise awareness of the significance of PD using information that is grounded in data and research. Teachers are surveyed to gain insight into the perceptions…