In this joint study, we try to uncover the common misconceptions amongst the educators that result from a lack of understanding of the underlying principles involved in the construction of mathematical and scientific concepts. We seek to raise awareness to the issue to provide support to mathematics and science educators in correcting their own misconceptions as well as strategies for identifying and correcting misconceptions held by their students. Research shows that teachers who understand their student’s common misconceptions are more likely to design instruction that will increase student understanding in the subject than teachers who do not. Additionally, teachers with misconceptions themselves unknowingly contribute to the reinforcement of student misconceptions during the teaching and learning cycle.

Data will be collected online and anonymously across the state and the country. The target participants include mathematics and science educators in universities, middle and high schools as well as pre-service Mathematics teacher candidates.

The Brief Electricity and Magnetism Assessment (BEMA) is a 31-question assessment designed to assess student understanding of basic principles of electricity and magnetism in an introductory, calculus-based physics course. This study develops a model of student knowledge measured by the BEMA. This is guided by a theoretical model of expert understanding of electricity and magnetism. Multidimensional Item Response Theory (MIRT) was used to investigate a large post-test dataset (N=9666) from a large, western public research university collected over the span of 15 years. An optimal model was found by exploring variations to the theoretical expert model and selecting the model with the optimal MIRT fit parameters.

Most research into educational augmented reality (AR) has centered around students’ attitudes toward the new technology, and not how effective AR is at increasing students understanding. This project compares improvements in student understanding between a three-dimensional AR visualization and the traditional two-dimensional visualization.  We included an interactive AR simulation in the magnetism unit in one section of a laboratory-based, algebra-based introductory physics class.  We selected a common exam problem that requires 3-D visualization of a magnetic field and compared the results of the treatment and control groups. We discuss the app, present results and present plans for future research.

Our investigation of introductory physics students' difficulties with pre-college mathematics has extended to five campuses at four universities, employing a 14-item diagnostic administered near the beginning of the semester.  More than 6000 students have taken the diagnostic over the past four years. We find (1) consistently high error rates (30-70%) on trigonometry, algebra, geometry, and graphing problems, (2) significant degradation of algebra performance when symbolic coefficients are substituted for numerical coefficients, and when Greek letters are substituted for Latin letters, and (3) high performance consistency among diverse question types, such that performance on a single test item can reliably predict overall diagnostic performance. A new online version of the diagnostic has been tested with small samples and seems to produce results that are largely consistent with the written version. Performance on non-mathematical conceptual physics questions, added to the online diagnostic, is significantly correlated with performance on the mathematics questions.

Over the past four years, we have administered over 6,000 mathematics diagnostics to introductory physics students at four large state universities. Previously, our hand-written diagnostic only included pure mathematics problems in graphing, trigonometry, geometry, and algebra. While these problems have shed light on the severity and nature of students’ mathematical difficulties, our new online diagnostic aims to also measure performance on conceptual physics problems (Newton’s second and third laws). We find the mathematics portion of our online diagnostic shares the same characteristics as older hand-written versions with similar correct-response rates, internal consistency, and performance predictability. Our analyses show that overall mathematics performance is correlated with performance on the newly added physics problems (r=0.35). Here, we present our most recent findings while examining the observed relationship between math and physics performance. 

Under NSF funding we have been developing and evaluating Interactive Video-Enhanced Tutorials (IVETs) which are designed to help students learn to use expert-like problem-solving strategies for college students in introductory physics. The tutorials involve web-based activities which lead students through a solution by providing guidance and feedback depending on the choices they make within the activities. This presentation will showcase one of our IVETs, namely Angular Momentum, and provide details about its design features, which involve multimedia principles of learning and research on human learning and memory, and subsequent impact on student problem-solving abilities.

*Work supported by the NSF IUSE Program (DUE #1821396)

As a part of our larger research on students’ conceptions on fluids, our group has been developing a taxonomy categorizing alternate conceptions about buoyancy and giving assessments in various introductory courses to determine the prevalence of selected taxonomy items.  This talk will focus on a few of those taxonomy items, discussing the populations in which they were identified and how they relate to the overall taxonomy construction. 

While the classic brachistochrone problem is too complicated to solve in an introductory course, students should be able to understand the qualitative features of the problem. We asked the students a number of questions about this problem. For this talk,  we will focus on the following question "Explain how it is possible for the mass to start from rest at different points along the cycloid and still reach the bottom at the same time."  Their answers display a wide variety of misconceptions and we will highlight some specific answers during this talk.