Early education is replete with debates about "academic" versus "play" approaches. We evaluated 2 interventions, the "Building Blocks" (BB) mathematics curriculum and the BB synthesized with scaffolding of play to promote executive function (BBSEF), compared to a business-as-usual (BAU) control using a 3-armed cluster…

Computer programming and mathematical algorithms are natural partners in the development of programming skills, logical thought, and a deeper understanding of mathematical concepts. We present the details of a course which blends the two at the sophomore level. This course is required of our mathematics majors, but attracts mathematics minors from…

In this article, a theoretically derived grid is presented combining Pólya's phases of the problem-solving process with the way in which teachers emphasize their students' strategic diversity in problem solving. It is used to categorize previous results from the literature. In an empirical part, the grid is also used to describe mathematics…

A major challenge in the field of spatial reasoning is the translation of decades of accumulated research findings from the domain of psychology and mathematics education into the school mathematics curriculum. This study aimed to operationalise a heuristic termed visualise-predict-check (VPC) for the teaching of spatial visualisation and explore…

Arithmetic problem solving is a crucial part of mathematics education. However, existing problem solving theories do not fully account for the semantic constraints partaking in the encoding and recoding of arithmetic word problems. In this respect, the limitations of the main existing models in the literature are discussed. We then introduce the…

While participating as a mentor teacher in a professional development project, Alison Vickery, a middle school teacher, developed a strategy: claim-rule-connection (CRC). The "claim" was the answer or response to the question; the "rule" was the theorem, fact, or proof; and the "connection" was an explanation of how…

The translation of evidence-based practices (EBPs) to improve students' social, emotional, behavioral, and academic outcomes into authentic school settings has posed significant challenges for both researchers and practitioners. Among the many barriers to the adoption and use of EBPs are their associated costs. This study presents a framework for…

Students are typically introduced to probability through calculating simple events like flipping a coin. While these calculations can be done by hand, more complex probabilistic events, both in class and in the real world, require the use of computers. In this paper, we introduce a new tool--an R shiny web app and associated CRAN package based on…

Within a study of student reasoning in abstract algebra, we encountered the claim "division and multiplication are the same operation." What might prompt a student to make this claim? What kind of influence might believing it have on their mathematical development? We explored the philosophical roots of "sameness" claims to…

In this qualitative study, we investigated teachers' use of proportional knowledge resources while being asked to appropriately identify if a given situation was proportional or not using clinical interview data from a large grant funded project. We found that knowledge resources related to the mathematical structure of the situation were most…

We use Taylor's formula with Lagrange remainder to make a modern adaptation of Poisson's proof of a version of the fundamental theorem of calculus in the case when the integral is defined by Euler sums, that is Riemann sums with left endpoints which are equally spaced. We discuss potential benefits for such an approach in basic calculus courses.

This paper substantiates the notion of inclusive materialism by illustrating the role of signs and micro-perception in the learning process of multiplication. Inclusive materialism, offered by de Freitas and Sinclair, considers mathematical learning a process of becoming a learning assemblage, which embodies various materials in a Deleuzian sense.…

Mathematization is critical in providing students with challenges for solving modelling tasks. Inadequate assumptions in a modelling task lead to an inadequate situational model, and to an inadequate mathematical model for the problem situation. However, the role of assumptions in solving modelling problems has been investigated only rarely. In…

Binary operations are one of the fundamental structures underlying our number and algebraic systems. Yet, researchers have often left their role implicit as they model student understanding of abstract structures. In this paper, we directly analyze students' perceptions of the general binary operation via a two-phase study consisting of task-based…

The use of cartoons, songs, and quotes can be a useful way to engage students in discussion and learning key concepts about quantifying the uncertainty in statistical estimates.