Proof and proving play a fundamental role in mathematics education and have the potential to serve as a vehicle for developing a deeper conceptual understanding. However, engaging students in proving activities presents challenges, and mathematics teacher educators thus are responsible for supporting preservice teachers, providing opportunities to…

Inequities in student access to trigonometry and calculus are often associated with racial and socioeconomic privilege, and often influence introductory physics course performance. To mitigate these disparities in student preparedness, we developed a two-pronged intervention consisting of (1) incentivized supplemental math assignments and (2)…

Zearn Math is a popular software platform for K-8 mathematics learning, designed to enable all students to successfully access grade-level content. RAND researchers collaborated with Zearn, the product's developer, to design this evaluation. Then RAND conducted the study independently, randomly assigning 64 schools in an urban Texas district to…

In this paper, we discuss mathematical modeling opportunities that can be included in an introductory Differential Equations course. In particular, we focus on the development of and extensions to the single salty tank model. Typically, salty tank models are included in course materials with matter-of-fact explanations. These explanations miss the…

Background: While students possess procedural knowledge associated with engineering calculations and calculus, they often exhibit a disconnect between the conceptual meaning of mathematics and the problem being solved. This conceptual understanding of what mathematics "says" is defined by the theoretical framework of numeracy. Many…

Poor math and numeracy skills are associated with a range of adverse outcomes, including reduced employability and poorer physical and mental health. Research has increasingly focused on understanding factors associated with the improvement of math skills in school. This systematic literature review and meta-analysis investigated the association…

This meditation on subjectivity draws on mundane and explicitly political contexts to argue for mathematics education practices that help us understand how people use mathematics to shape our world. I use two contexts to consider how to develop citizens who understand how we are subjugated by mathematical systems (designed and sustained by…

This paper explores how different schools of thought in mathematics education think and speak about preparing mathematics for teaching by introducing and proposing certain metaphors. Among the metaphors under consideration here are the unpacking metaphor, which finds its origin in the Anglo-American school of thought of pedagogical reduction of…

Academic and practice-based research constructs specific learning difficulties as a collection of lifelong, within-person conditions that negatively affect learning and daily functioning. Investigation has historically adopted a medical model, specifically a neurodeficit perspective. Conversely, neurodiversity has emerged as a concept that seeks…

This paper contains interesting facts regarding the powers of odd ordered special circulant magic squares along with their magic constants. It is shown that we always obtain circulant semi-magic square and special circulant magic square in the case of even and odd positive integer powers of these magic squares respectively. These magic squares…

Discrete mathematics brings interesting problems for teaching and learning proof, with accessible objects such as integers (arithmetic), graphs (modeling, order) or polyominoes (geometry). Many problems that are still open can be explained to a large public. The objects can be manipulated by simple dynamic operations (removing, adding, 'gluing',…

While helping proofread a book during my doctoral studies, I came across a chapter that included (among other things) a discussion of a set of problems and tasks involving the building of towers using only two (or three) colours of cubes (Maher & Ahluwali, 2014). Later that year, as I started my tenure track position at the University of…

Accountability pressures and the Common Core State Standards for Mathematics have created complex demands for educators, especially early-career teachers (ECTs). Analyzing longitudinal data, including the social networks of 119 ECTs, we find that ECTs increase their ambitious mathematics instruction when their network members positively interpret…

We posit a dual approach to digital task design: to engineer opportunities for students to conceive of graphs as representing relationships between quantities and to foreground students' reasoning and exploration, rather than their answer-finding. Locally integrating Ference Marton's variation theory and Patrick Thompson's theory of quantitative…

This article explores the approaches used to plan mathematical reasoning tasks by two peer learning teams, one based in regional Victoria and the other in Vancouver, Canada. The results revealed that planning and peer observation support teachers' knowledge of mathematical reasoning and the pedagogy required to promote it.