United States

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.

AAPT WM 21

A Study on Misconceptions of Mathematics and Science Teachers

misconceptions stem

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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.

Multidimensional Item Response Theory and the BEMA

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.&nbsp;&nbsp;More than&nbsp;6000 students have taken the diagnostic&nbsp;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&nbsp;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&nbsp;to the online diagnostic, is significantly correlated with performance on the mathematics questions.

Consistency of Students' Mathematical Difficulties May Allow Reliable Performance Predictability

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.&nbsp;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.&nbsp;

Introductory Physics Students’ Mathematical Preparedness and Conceptual Understanding of Force

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)

Impact of an Angular Momentum Problem-solving Tutorial on Student Performance

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.&nbsp; 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.&nbsp;

Discussion of Selected Alternate Conceptions about Buoyancy in College Populations

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.&nbsp; This talk will focus on the results of selected assessment questions given to multiple introductory physics courses at Grove City College; some questions were also given to students at the University of Washington.&nbsp; The prevalence of each alternate conception probed will be discussed, along with similarities and differences between the populations.&nbsp;

Prevalence of Selected Alternate Conceptions about Buoyancy in College Populations

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,&nbsp; 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."&nbsp; Their answers display a wide variety of misconceptions and we will highlight some specific answers during this talk.

Introductory Students' Qualitative Analysis of the Brachistochrone

We will present our experience assigning specific roles to each member of student groups to assist them with group dynamics when working through cooperative laboratory tasks. The initial implementation was inspired by an introductory POGIL seminar given to science faculty. Connections will be made to the work done by the Hellers from the University of Minnesota on Group Problem Solving Strategies in introductory physics classes. We will also present results of informal polling of our Faculty Online Learning Community (FOLC) on techniques for forming effective groups. This is part of a series of talks stemming from the NextGen PET FOLC project. This work was supported by the National Science Foundation grant NSF DUE-1626496.

POGIL-inspired Roles for Small Groups and Other Group Management Techniques

Argument-Driven Inquiry (ADI) is an instructional model which originated in Chemistry education and provides students opportunities to develop and carry out their own experimental designs while engaging in argumentation and peer review. In 2019, we adopted a modified ADI instructional model into our Introductory Physics Labs for Life Sciences (IPL 2 S) courses to include a more formal structure for student engagement in scientific practices as part of three-dimensional learning. In this talk, we introduce the ADI instructional model, discuss integration of the ADI instructional model into our reformed lab course, and describe recent impacts it has had on our course. Specifically, we present how our modified ADI model has: 1) enhanced student engagement in scientific practices, specifically experimental design planning and scientific argumentation; 2) aided in the shift to online instruction while maintaining course learning outcomes; and 3) provided pedagogical consistency in a course with rotating instructional faculty.

Bringing Argument-Driven Inquiry into IPLS labs

Students reflect all rays parallel with the main axis in a spherical concave mirror to draw with a focal&nbsp;point that called real focal. In this paper we prove that the geometric method with a primary focus of rays parallel with&nbsp;the main axis of a spherical surface, is not a point.

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A Study on Misconceptions of Mathematics and Science Teachers

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