This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in…

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/10.1111/nyas.14355). An issue that arises if one wants to correlate mathematical performance with the SNARC effect, is how individual…

We explored the multi-dimensionality of mathematics and working memory (WM) by examining the differential relationships between different areas of mathematics with visual, spatial, and verbal WM. Previous research proposed that visuospatial WM is a unique predictor of mathematics, but neuroimaging and cognitive research suggest divisions within…

This study examined the role of student generated drawings to offload cognitive demands of a mathematical problem. We used Unit Transformation Graphs to compare students' thought processes when they had to solve the problem mentally, and when they were allowed to use pen and paper. The results indicated that the possibility to rely on drawings…

Retrieving information from memory increases the likelihood the information will be remembered later. The strategic use of retrieval to enhance memory is known as retrieval practice. Teachers can exert considerable control over students' retrieval practice, dictating when and how much students practice. Laboratory research has shown that retention…

Mathematics faculty created a model for intermediate algebra integrating principles from the science of learning. The redesigned curriculum revolved around two big ideas (solving and graphing) and provided students with information about the formation of long-term memories, the benefits of distributed practice, the impact of physiological aspects…

A major challenge college students face is retaining the knowledge they acquire in their classes, especially in cumulative disciplines such as engineering, where ultimate success depends on long-term retention of foundational content. Cognitive psychologists have recently recommended various techniques educators might use to increase retention.…

Pre-service early childhood teachers' beliefs about mathematics are significant because those beliefs will affect many factors involved in their future teaching. This research explored pre-service teachers' unforgettable mathematics experiences and how these experiences were related to their beliefs about preparing an unforgettable mathematics…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

Purpose: Drawing on semi-structured and focused-group interviews performed with various pre-service mathematics teachers and in-service mathematics teachers, the present study benefits from the frame of teacher identity to make the meaning of heterogeneity among their experiences and perceptions of mathematics teaching anxiety. The current study…

Within-class ability grouping (WCAG) is widely used in elementary mathematics instruction in the United States, yet it has drawn criticism on the grounds that it can inequitably limit the learning opportunities of some students, not least because of its connection to between-class ability grouping (BCAG) that is more common in middle or secondary…

Prospective middle school pre-service teachers' knowledge and affect in Australia has had little empirical research. In this study, 108 graduate entry pre-service teachers were surveyed for their knowledge of middle years' mathematics, confidence, and self efficacy at the commencement of a mathematics curriculum course. It was found that their…

Instructors of postsecondary classes in statistics rely heavily on visuals in their teaching, both within the classroom and in resources like textbooks, handouts, and software, but this information is often inaccessible to students who are blind or visually impaired (BVI). The unique challenges involved in adapting both pedagogy and course…

The sequence in which problems of different concepts are studied during instruction impacts concept learning. For example, several problems of a given concept can be studied together (blocking) or several problems of different concepts can be studied together (interleaving). In the current study, we demonstrate that the 2 sequences impact concept…

This study investigates the effects of Digital Learning Material (DLM) including instructional clips, online guidance, structuring of content, and a collaboration tool on students' mathematics learning in Dutch vocational education. A pretest-posttest design was used. Apprenticeship students were asked to complete assignments and to discuss them…