Following psychologist Langer's theory, this study aimed to examine the influence of conditional tasks containing inherent uncertainty on the cultivation of mindfulness. It used preceding research to develop conditional mathematics tasks corresponding to integers and rational numbers, within a 10-lesson curriculum. It divided a total of 182 middle…

This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…

Productive struggle is an effective mathematics teaching practice that provides students opportunities to grapple with challenging mathematical concepts, connect prior knowledge, discover new ideas, and develop their critical thinking skills. Research has documented the benefits of secondary mathematics students engaging in productive struggle.…

Prompting learners to generate examples has been proposed as an effective way of developing understanding of a new concept. However, empirical support for this approach is lacking. This article presents two empirical studies on the use of example-generation tasks in an online course in introductory university mathematics. The first study compares…

In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the…

This study examined repeating and growing pattern knowledge and their associations with procedural and conceptual arithmetic knowledge in a sample of U.S. children (N = 185; M[subscript age] = 79.5 months; 55% female; 88% White) and adults (N = 93; M[subscript age] = 19.5 years; 62% female; 66% White) from 2019 to 2020. Three key findings emerged:…

This study is aimed to understand the connections between didacticians' meta-didactical praxeologies for the design and implementation of a teacher professional development program and their documentation work for the program itself. Didacticians are mathematics education researchers with the role of teacher educators. Data presents a case study,…

This article provides an analysis of a data set coming from a two-phase qualitative study that focused on fostering primary students' abstraction of interrelations among quadrilaterals (squares, rectangles, parallelograms, rhombuses, trapezoids). The pilot study consisted of work with eight primary students operating at van Hiele level 2 (e.g.,…

The current study highlights the importance of inhibitory ability in facilitating performance in mathematics. To understand the role of inhibition in mathematical knowledge, this study tested 102 college students on a series of standardized complex math exercises. Inhibition tasks varied by task and stimuli (letters, numbers, and arrows). The…

This study sought to explore whether access to definitions and general representations influences the construction of general direct arguments. Data was collected in college mathematics courses for prospective elementary school teachers. Participant arguments were analyzed along two variables: the generality of the representations and the…

Previous research has investigated the Spatial Numerical Associations of Response Codes (SNARC) effect as a measure of spatial number coding in relation to mathematics (Cipora et al., 2020, https://doi-org.bibliotheek.ehb.be/10.1111/nyas.14355). An issue that arises if one wants to correlate mathematical performance with the SNARC effect, is how individual…

Teachers' ability to accurately judge difficulties of mathematical tasks is an essential aspect of their diagnostic competencies. Although research has suggested that pedagogical content knowledge (PCK) is positively correlated with the accuracy of diagnostic judgments, experimental studies have not been conducted to investigate how PCK affects…

This exploratory study reports on characteristics of proof production and proof writing observed in the work of first-year university students who took part in workshops on the theorem prover LEAN (https://leanprover.github.io). These workshops were voluntary and offered alongside a transition to proof module in a UK university. Through…

An extended (and probably unnecessary) parallel is drawn between engagement in mathematics and engagement in musical performance. Key facets of engagement are described and a model of how mathematics engagement plays out in task-level activities is discussed in light of new findings related to its social and emotional facets. Implications for…

Understanding how physicists solve problems can guide the development of methods that help students learn and improve at solving complex problems. Leveraging the framework of cognitive task analysis, we conducted semistructured interviews with theoretical physicists (N=11) to gain insight into the cognitive processes and skills that they use in…