A growing literature reports significant associations between children's executive functioning skills and their mathematics achievement. The purpose of this study was to examine if specific early number skills, such as quantity discrimination, number line estimation, number sets identification, fast counting, and number word comprehension, mediate…

The synergistic potential of cognitive neuroscience and education for efficient learning has attracted considerable interest from the general public, teachers, parents, academics and policymakers alike. This review is aimed at providing 1) an accessible and general overview of the research progress made in cognitive neuroscience research in…

This paper focuses on children's number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including…

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…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

These are the appendixes for the report, "What Grade 7 Foundational Knowledge and Skills Are Associated with Missouri Students' Algebra I Achievement in Grade 8?" To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

Current curriculum initiatives (e.g., National Governors Association Center for Best Practices and Council of Chief State School Officers 2010) advocate that models be used in the mathematics classroom. However, despite their apparent promise, there comes a point when models break, a point in the mathematical problem space where the model cannot,…

How do children map number words to the numerical magnitudes they represent? Recent work in adults has shown that two distinct mechanisms--structure mapping and associative mapping--connect number words to nonlinguistic numerical representations (Sullivan, J., 2012). This study investigated the development of number word mappings, and the roles of…

Ideas about temporal (and spatial) scale impact students' understanding across science disciplines. Learners have difficulty comprehending the long time periods associated with natural processes because they have no referent for the magnitudes involved. When people have a good "feel" for quantity, they estimate cardinal number magnitude…

"Embodied trainings" allowing children to move their whole body in space have recently been shown to foster the acquisition of basic numerical competencies (e.g. magnitude understanding, addition performance). Following a brief summary of recent embodied training studies, we integrate the different results into a unified model framework…

A lack of numerical knowledge early on can impede a child's academic development. In past research, playing linear board games improved children's understanding of numerical relations, which the authors theorised could extend to children with autism spectrum disorder. For this pilot study, 10 children played a board game where they moved tokens…

This paper outlines an approach to definitively find the general term in a number pattern, of either a linear or quadratic form, by using the general equation of a linear or quadratic function. This approach is governed by four principles: (1) identifying the position of the term (input) and the term itself (output); (2) recognising that each…

The number and algebra strand of the "Australian Curriculum: Mathematics" (2015) advocates for holding together the study of number and algebra across years K-8--a position that mathematics educators have endorsed in many countries. This recommendation along with the report "Shape of the Australian Curriculum: Mathematics"…

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…