External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to…

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

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…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

A logit model predicting student outcomes for a gateway course, Math for Liberal Arts, was successfully developed which fits the data well. Two variables, ACT math score and high school GPA, were found to be significant predictors of achieving a C or better in Math for Liberal Arts. A practical implication of the study suggests that with just two…

In this report, we establish benchmarks of readiness for four common first-year college courses: English Composition, College Algebra, Social Science, and Biology. Using grade data from a large sample of colleges, we modeled the probability of success in these courses as a function of ACT test scores. Success was defined as a course grade of B or…

Reviewed are 11 studies reported in Dissertation Abstracts International for Social Sciences in 1989. Topics include problem solving, mathematics education, LOGO computer language, implementation of instructional computing, algebra, effects of differential grouping on learning science skills, simulations, and graphing as they relate to the use of…