It is commonly accepted that repeatedly using mental procedures results in a transition to memory retrieval, but the determinant of this process is still unclear. In a 3-week experiment, we compared two different learning situations involving basic additions, one based on counting and the other based on arithmetic fact memorization. Two groups of…

Perceptual learning theory suggests that perceptual grouping in mathematical expressions can direct students' attention toward specific parts of problems, thus impacting their mathematical reasoning. Using in-lab eye tracking and a sample of 85 undergraduates from a STEM-focused university, we investigated how higher-order operator position (HOO;…

Symbolic and situational mathematics are the two major representations of mathematical knowledge. Although previous literature has studied the relationship between the two from the perspective of teaching practice, learning effectiveness and behavioural performance, there is still a lack of empirical psychological research on cognitive mechanisms…

The authors have found that having students learn accessible standard algorithms by explaining them using mathematics drawings increases students' sense of place--value numbers and enables students to articulate their understanding of what is actually happening with the numbers and why. In this article, they will discuss three standard algorithms…

For schools implementing Response-to-Intervention, it is important to understand how to efficiently intensify interventions. Treatment intensity, or intervention design, is a critical yet overlooked and understudied aspect in math. More frequent dosage results in greater student gains. However, questions remain regarding how teaching episodes…

Background: Recent research showed that cross-notation magnitude knowledge of fractions and decimals was related to better performance in fraction arithmetic, but it remains unclear whether it made an independent contribution to fraction arithmetic longitudinally when other cognitive variables are considered. Aims: To examine the extent to which…

Within the research on bilingual learning, first studies have revealed that content learned in one language is retrieved more slowly when participants have to switch language from instruction to testing (i.e., language-switching costs, LSC). These costs are attributed to language-dependent knowledge representations. However, the cognitive…

As AI increasingly enters classrooms, educational designers have begun investigating students' learning processes vis-à-vis simultaneous feedback from active sources--AI and the teacher. Nevertheless, there is a need to delve into a more comprehensive understanding of the orchestration of interactions between teachers and AI systems in educational…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…