In most mathematics textbooks, each lesson is followed by a set of homework problems in one of two ways -- blocked practice and mixed practice. Additionally, most mathematics textbooks rely on a common learning strategy called overlearning, that is, mastering a skill and continuing to practice this same skill. This study investigated the effects…

For students to advance beyond arithmetic, they must learn how to attend to the structure of math notation. This process can be challenging due to students' left-to-right computing tendencies. Brackets are used in mathematics to indicate precedence but can also be used as superfluous cues and perceptual grouping mechanisms in instructional…

Learning curves have proven to be a useful tool for understanding how a student learns a given skill as they progress through a curriculum. A learning curve for a given Knowledge Component (KC) is a plot of some measure of competence as a function of the number of opportunities the student has had to apply that KC. Consider the case where each…

The flipped classroom is a teaching methodology that has gained recognition in primary, secondary and higher education settings. The flipped classroom inverts traditional teaching methods, delivering lecture instruction outside class, and devoting class time to problem solving, with the teacher's role becoming that of a learning coach and…

E-Learning brings access to a powerful but often overlooked teaching tool: random number generation. Using random number generation, a practically infinite number of quantitative problem-solution sets can be created. In addition, within the e-learning context, in the spirit of the mastery of learning, it is possible to assign online quantitative…

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…

Intelligent tutors have become increasingly accurate at detecting whether a student knows a skill, or knowledge component (KC), at a given time. However, current student models do not tell us exactly at which point a KC is learned. In this paper, we present a machine-learned model that assesses the probability that a student learned a KC at a…