A spreadsheet plotting assignment of real-life data from a racecar is employed to help students master the relationships among speed, acceleration, and distance. The racecar application will capture the imagination and interest of the student. The data is obtained by reading speedometer values from a YouTube video for 40 s as a racecar accelerates…

In the same chapter of his book "Opera Geometrica," Torricelli published two discoveries: 1) initial velocity of a jet from a container increases with the square root of the depth of the hole; 2) he drew the pattern of jets from three openings at the wall of a container filled with water to constant level "H" and determined the…

Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.Motivated by the work of…

"Inequitable Opportunity to Learn: Access to Advanced Mathematics and Science Courses" is the second in a series of Learning Policy Institute reports analyzing data primarily from the U.S. Department of Education's Civil Rights Data Collection (CRDC). This report uses the most recent CRDC data from 2017-18. The CRDC includes data on a…

The 2015-16 Civil Rights Data Collection (CRDC) is a survey of all public schools and school districts in the United States. The CRDC measures student access to courses, programs, staff, and resources that impact education equity and opportunity for students. The CRDC has long provided critical information used by the Department of Education's…

By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we have previously found evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a…

Bertrand's paradox (Bertrand 1889 "Calcul des Probabilites" (Paris: Gauthier-Villars)) can be considered as a cautionary memento, to practitioners and students of probability calculus alike, of the possible ambiguous meaning of the term "at random" when the sample space of events is continuous. It deals with the existence of different possible…

The quantitative results of Sources of Self-Efficacy in Science Courses-Physics (SOSESC-P) are presented as a logistic regression predicting the passing of students in introductory Physics with Calculus I, overall as well as disaggregated by gender. Self-efficacy as a theory to explain human behavior change [Bandura [1977] "Psychological…

In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the…

The ability to categorize problems based upon underlying principles, rather than surface features or contexts, is considered one of several proxy predictors of expertise in problem solving. With inspiration from the classic study by Chi, Feltovich, and Glaser, we assess the distribution of expertise among introductory physics students by asking…

In this study, performance of a hydrogen-peroxide-driven car has been simulated using basic conservation laws and a few numbers of auxiliary equations. A numerical method was implemented to solve sets of highly non-linear ordinary differential equations. Transient pressure and the corresponding traveled distance for three different car weights are…

This study investigates how the beliefs and values of physics faculty influence their choice of physics problems for their students in an introductory physics course. The study identifies the goals these instructors have for their students, the problem features they believe facilitate those goals, and how those features correspond to problems they…

We examine an experimental apparatus that is used to motivate the connections between the basic properties of vectors, potential functions, systems of nonlinear equations, and Newton's method for nonlinear systems of equations. The apparatus is an adaptation of a force table where we remove the center-pin and allow the center-ring to move freely.…

Most students struggle when faced with complex and open-ended tasks because the strategies taught in schools and universities simply require finding and applying the correct formulae or strategy to answer well-structured, algorithmic problems. For students to develop their ability to solve ill-structured problems, they must first believe that…

The performance of over 2000 students in introductory calculus-based electromagnetism (E&M) courses at four large research universities was measured using the Brief Electricity and Magnetism Assessment (BEMA). Two different curricula were used at these universities: a traditional E&M curriculum and the Matter & Interactions (M&I)…