Build collective teacher efficacy and students' mathematical thinking using the Mathematics in a PLC at Work™ lesson-design process. This second edition of the popular "Mathematics Instruction and Tasks" book guides preK-12 teacher teams in ensuring improved mathematics achievement. Gain new and enhanced understanding of…

Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research…

The virtual-representational-abstract (VRA) instructional sequence presents as a viable mathematics intervention for students with disabilities, including students with autism spectrum disorder (ASD). Yet, to date, all research has been conducted face-to-face with students. However, virtual manipulatives provide an opportunity for educators to…

Representation is widely viewed as central to mathematical problem solving, while online scaffolding is considered helpful in supporting learners' progress from actual to potential developmental levels of mathematics understanding. Therefore, this study investigated the effectiveness of employing online single vs. multiple representational…

Traditionally, various meanings of "10" are systematically ignored in early childhood curriculum and children's understanding of numbers is restricted within the solitary mapping between the symbol "10" and quantity concept of "ten." This may be problematic for other ways that mathematics is used, both in modern life…

This paper reports on data obtained during semi-structured interviews with students who had recently experienced a guided inquiry approach to learning ordinary differential equations (ODEs) in a service-taught module. Previous research identified the strengths and weaknesses of similar cohorts of students. The results from that research informed…

Purpose: The purpose of this study is to develop a game-based mobile application to help learners practice mathematical patterns and structures. Method: The study followed a mixed-method research design and prototyping methodology to guide the study in developing the mobile application. An instrument based on the Octalysis framework was developed…

The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.

In this age of easy access to the internet and to spreadsheets, easy-to-apply numerical methods exist that are vastly superior to Simpson's rule and the (corrected) trapezoidal rule. Gaussian quadrature (GQ) is such a method. What follows tells how enthusiastic Year 9 students with a physics problem provoked a science teacher into re-discovering a…

Kitcher's idea of 'explanatory unification', while originally proposed in the philosophy of science, may also be relevant to mathematics education, as a way of enhancing student thinking and achieving classroom activity that is closer to authentic mathematical practice. There is, however, no mathematics education research treating explanatory…

A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course.

Recently, people prefer learning information operationally rather than conceptually. In this context, this study was carried out to uncover how preservice math teachers construct in their minds the conceptual definition of limit within the scope of the Calculus Course. The participants of this study consisted of 62 (30 female, 32 male) sophomore…

Ratio and proportion have been part of school mathematics since the earliest manifestations of anything like school math in the Middle Ages. In this paper, I compile and comment on statements from primary sources of the last 2300 years to exhibit ideas that appear to have influenced the treatment of these topics in schoolbooks today. Historical…

Students who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of…