One of the foundational topics in first-year algebra concerns the concept of factoring. This article discusses an alternative strategy for factoring quadratics of the form ax[superscript 2] + bx + c, known as "factoring for roots." This strategy enables students to extend the knowledge they used when the leading coefficient was 1 and…

A broad categorisation of different reading styles for mathematics text is generated in this research. The styles derive from those found in literature around academic reading skills. These styles are inductively refined using video transcripts of five specially chosen students studying out loud from a prescribed mathematics textbook. The context…

We present an embodied theory of transfer as applied to mathematical ideas. Project-based learning (PBL) offers important sites for investigating transfer because students and teachers must track mathematical invariant relations that are embedded in complex settings where knowledge and information is distributed and extended across various…

The current quantitative study, a naturalistic field experiment, was conducted in a public primary school in Soweto, Johannesburg, with the objective to examine how children's achievement on four assessments at the beginning of Grade R, namely their numeracy, their mathematics-specific vocabulary, their executive functions, and their logical…

We examined whether students were accurate in predicting their test performance in both low-stakes and high-stakes testing contexts. The sample comprised U.S. high school students enrolled in an advanced placement (AP) statistics course during the 2017-2018 academic year (N = 209; M[subscript age] = 16.6 years). We found that even two months…

This project describes a way to help students recognise that the expressions on both sides of the equals sign are the same. It was developed to support teachers in disadvantaged communities to help their students make sense of mathematics.

Digital math apps on touch-screen devices have become popular as effective tools to support mathematics learning. Many apps incorporate gaming elements such as points, stars, coins, or storylines to increase student interest and motivation. However, there is limited research regarding the balance of gaming and mathematics elements and how it…

We report on mixed methods research that explored pre-service teachers' pedagogical content knowledge in basic musical methods for teaching and learning of basic fractions within the framework of Vygotsky's Theory of Scaffolding. Vygotsky's use of scaffolding opines that knowledge, skills and prior experiences, create the foundation for potential…

We report on mixed methods research that explored pre-service teachers' pedagogical content knowledge in basic musical methods for teaching and learning of basic fractions within the framework of Vygotsky's Theory of Scaffolding. Vygotsky's use of scaffolding opines that knowledge, skills and prior experiences, create the foundation for potential…

The variability effect occurs when learners' exposure to highly variable tasks results in better learning. It was hypothesised that learners who studied high variability worked examples would obtain higher post-test scores compared to learners who studied low variability examples, and learners who self-generated problem solutions for the same high…

Prior research shows that self-explanation promotes understanding by helping learners connect new knowledge with prior knowledge. However, despite ample evidence supporting the effectiveness of self-explanation, an instructional design challenge emerges in how best to scaffold self-explanation. In particular, it is an open challenge to design…

Decades of scholarly work continue to document the marginalization of children from nondominant backgrounds in mathematics classrooms. Learning to equitably teach children from linguistically, ethnically, racially, and culturally diverse backgrounds remains a priority. This dissertation approaches this broader problem in society by understanding…

Psychologists and mathematics educators have long viewed flexibility as critical to students' mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified…

This chapter focuses on the interaction of two first graders as they attempt to make sense of a particular instructional context for learning negative numbers. The context is one where they move an elevator to a building's floors above and below ground in order to model integer addition and subtraction problems. In particular, the focus of the…

Given growing interest in K-12 data and data science education, new approaches are needed to help students develop robust understandings of and familiarity with data. The model of the "quantified self"--in which data about one's own activities are collected and made into objects of study--provides inspiration for one such approach. By…