Productive learning of algebra is supported when students reflect on multiple strategies, compare them and discuss the rationale behind and relative merits of particular strategies. Comparison and Discussion of Multiple Strategies (CDMS) is an instructional approach designed to support these processes in math classrooms. In the current study, 16…

A first-year algebra student's curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics. In this article, the authors, math teachers in Massachusetts, examine how to solve for factorials of negative numbers and discuss how they taught…

Massive open online courses (MOOCs) describe platforms where users with completely different backgrounds subscribe to various courses on offer. MOOC forums and discussion boards offer learners a medium to communicate with each other and maximize their learning outcomes. However, oftentimes learners are hesitant to approach each other for different…

Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…

Cooking is a tangible, familiar, and delicious tool for teaching physics, which is easy to implement in a university setting. Through our courses at Harvard and UCLA, each year we are engaging hundreds of undergraduate students, primarily non-science majors, in science concepts and the scientific research process. We find that weekly lectures by…

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into…

Although it is difficult to find any current literature that does not encourage use of multiple representations in mathematics classrooms, there has been very limited research that compared such practice to student achievement level on standardized tests. This study examined the associations between students' achievement levels and their (a)…

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…

Although an understanding of radiometric dating is central to the preparation of every geologist, many students struggle with the concepts and mathematics of radioactive decay. Physical demonstrations and hands-on experiments can be used to good effect in addressing this teaching conundrum. Water, heat, and electrons all move or flow in response…