Humans have the remarkable ability to solve different tasks by simply reading textual instructions that define the tasks and looking at a few examples. Natural Language Processing (NLP) models built with the conventional machine learning paradigm, however, often struggle to generalize across tasks (e.g., a question-answering system cannot solve…

Learning transfer has been studied for over a century, though studies are primarily through the lens of the researcher or an expert. The purpose of this project was to better understand the student perspective in transfer by examining how they approached transfer tasks and how these approaches related to classroom instruction. The Actor-Oriented…

Optimization is introduced to teaching in secondary school, focussing on functions of one variable with the first derivative criterion for critical points and monotonicity of functions. The second derivative criterion is also used to determine the nature of the critical points. Similarly, in university-level teaching, algebraic work using criteria…

In this article, the authors focus on five instructional approaches with a strong evidence base for the teaching and learning of math: (a) plan, model, and practice: systematic and explicit instruction; (b) focus on the language of math; (c) use multiple representations, including number lines; (d) build fluency; and (e) provide word problem…

This study used a qualitative, holistic case study to explore obstacles tutors faced when implementing high cognitive demand (HCD) tasks and the possibility of using embedded educative curricular supports to overcome them. Much prior research has explored using educative supports in classrooms with teachers (Davis et al., 2017), but more research…

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…

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…

The basic notions of combinatorics, including systematic listing and permutations, are important topics of mathematics that are recommended to be learned eventually from elementary schools. However, there is little research in mathematics education regarding elementary students' combinatorial strategies. The purpose of this research is to…

In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of…

This study considered a preservice teacher's (PST's) attention to multilingual learner core practices within her approximations of practice of mathematics language routines during a secondary mathematics methods course. We used a framework of approximations of practice to understand how a PST enacted and developed an understanding of multilingual…

The most common challenges students face in solving first-order ordinary differential equations (ODEs) can be overcome by identifying the types of errors, understanding the factors that cause difficulties, and finding appropriate solutions. Therefore, this research aimed to adopt a descriptive qualitative approach, including nine sixth-semester…

The study reported in this paper is motivated by an article published on a financial portal that presented loan repayments with a continuous approach, as opposed to the discrete approach of addressing loan repayments applied in mathematics courses for economists. Using the Anthropological Theory of the Didactic, we analyse the current didactic…

Technological mediation has gained relevance in teaching mathematics. Its usefulness and impact depend, to a great extent, on how students approach the learning of the discipline. Two independent instrumental studies were conducted to analyze the psychometric properties of the Spanish version of the Mathematics and Technology Attitudes Scale…

Knowing functions and functional thinking have recently moved from just knowledge for older students to incorporating younger students, and functional thinking has been identified as one of the core competencies for algebra. Although it is significant for mathematical understanding, there is no unified view of functional thinking and how different…

This study aimed to conduct a comprehensive investigation into the Mathematics Writing (MW) of Chinese students. We conducted a comparison between MW and general writing on organizational features. The analysis was based on a sample of 138 sixth-grade students. Our findings revealed: (a) students demonstrated significantly higher performance in…