Capitalizing on cognitive load theory and learning by analogy, we propose two instructional methods to learn a complex linear equation (e.g. two-step equation) by building on prior knowledge of a simpler linear equation (e.g. one-step equation). We will examine the proposal theoretically in this paper. In line with the design principles of…

Because deficits in executive functions (EFs) characterize most neurodevelopmental disorders, it is appropriate to question the value of EFs for understanding learning disabilities. Two types of studies--those testing whether EFs moderate treatment effects and those testing the direction of effects between EFs and academic skills--are presented to…

This study strived to determine the effectiveness of integrative teaching of reading strategies and working memory on basic math and problem-solving skills. It is a quasi-experimental pretest-posttest study carried out on 50 second-graders from Chahashk Shandiz village in the academic year of 2020-2021 who were randomly selected by cluster…

Cognitive load theory (CLT) uses working memory resources depletion to explain the superiority of spaced learning, predicting that working memory resources will be less taxed if there are resting/spacing periods inserted between learning tasks, in comparison to learning from the same tasks in a single session. This article uses the working memory…

Young children can quickly and intuitively represent the number of objects in a visual scene through the Approximate Number System (ANS). The precision of the ANS--indexed as the most difficult ratio of two numbers that children can reliably discriminate--is well known to improve with development: whereas infants require relatively large ratios to…

This study's purpose was to investigate effects of 3 intervention approaches for building working memory (WM) and improving word-problem solving (WPS). Children with mathematics difficulties (n = 240; 7.51 years [SD = 0.33]) were randomized to 4 conditions: a control group, general WM training with contiguous math practice, WPS intervention…

This study's purpose was to investigate effects of 3 intervention approaches for building working memory (WM) and improving word-problem solving (WPS). Children with mathematics difficulties (n = 240; 7.51 years [SD = 0.33]) were randomized to 4 conditions: a control group, general WM training with contiguous math practice, WPS intervention…

The outcomes of a longitudinal randomized number sense intervention including pre-, post- and follow-up tests are reported. The intervention was conducted in Grade 0 when children were six years old. Using Concrete-Representational-Abstract principles, a structured explicit 10-week program focusing on numbers and collective reasoning about…

Children start preschool with large individual differences in their early numerical abilities. Little is known about the importance of heterogeneous patterns that exist within these individual differences. A person-centered analytic approach might be helpful to unravel these patterns and the cognitive and environmental factors that are associated…

This study assessed the relation between long-term memory retrieval and mathematics calculation and mathematics problem solving achievement among elementary, middle, and high school students in nationally representative sample of US students, when controlling for fluid and crystallized intelligence, short-term memory, and processing speed. As…

Influenced by COVID-19, online learning has become one of the most important forms of education in the world. In the era of intelligent education, knowledge tracing (KT) can provide excellent technical support for individualized teaching. For online learning, we come up with a new knowledge tracing method that integrates mathematical exercise…

Research has highlighted the role of working memory and inhibition on the performance of pupils in mathematics. This study was an attempt to look into the relationship between executive function including working memory capacity and inhibition on the one hand and mathematical abilities on the other. 30 primary school students were selected from…

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…

The effectiveness of an experimental middle school fraction intervention was evaluated. The intervention was centered on the number line and incorporated key principles from the science of learning. Sixth graders (N = 51) who struggled with fraction concepts were randomly assigned at the student level to the experimental intervention (n = 28) or…

In the present chapter, we review the evidence for several principles that are especially promising for improving mathematics instruction. Using the classification scheme proposed by Koedinger et al. (2013), we begin with principles that focus on improving memory and fluency: scaffolding, distributed practice, and feedback. We then move to worked…