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Our investigation of introductory physics students&#39; 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.&amp;nbsp;&amp;nbsp;More than&amp;nbsp;6000 students have taken the diagnostic&amp;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&amp;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&amp;nbsp;to the online diagnostic, is significantly correlated with performance on the mathematics questions.

AAPT WM 21

Consistency of Students&#39; Mathematical Difficulties May Allow Reliable Performance Predictability

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university

diagnostic

mathematics

introductory

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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

technical paper

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.

Association of Concave Spherical Mirrors

In our algebra-based introductory physics sequence, we have had exams consisting of multiple choice questions and traditional math problems. The multiple choice questions were more conceptual in nature and would come at the beginning of our exams. Then we would have all of the math problems. Unfortunately, a single multiple choice question that potentially covers a number of topics at an arbitrary level of difficulty doesn’t allow an instructor to determine a student’s level of understanding of any single topic. To better assess students’ levels of understanding, we designed sets of questions and problems with increasing difficulty, as defined by Bloom’s Taxonomy. This new way of structuring exams benefited the instructor in documenting levels of student understanding. It also allowed weaker students to show mastery at some level and possibly boost their confidence with the more challenging questions. In general, the students have rated this new assessment positively.

Using Bloom’s Taxonomy to Develop New Assessments

One of two complementary panels dedicated to raising awareness about improving the accessibility of undergraduate physics laboratory courses. In this panel, former physical science students talk about their previous experiences in physics and other science labs, and they make suggestions for improving accessibility of labs.] Physics labs are an exciting opportunity to teach and learn about physics by collaboratively planning, building, and carrying out experiments and interacting with advanced phenomena, apparatus, and software. Students, staff, and faculty with disabilities deserve full access to these learning environments, and it is everyone’s responsibility to recognize and mitigate the specific barriers to participation posed by space, technology, and pedagogical constraints that are unique to labs. To that end (and with support from an AAPT Special Projects Grant), the AAPT Committee on Laboratories assembled a task force whose charge is to issue an open call for increased investment in accessible physics labs.

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