Bulletin of the American Physical Society
APS April Meeting 2017
Volume 62, Number 1
Saturday–Tuesday, January 28–31, 2017; Washington, DC
Session Y2: Research on Conceptual Understanding |
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Sponsoring Units: GPER FED Chair: Ellie Sayre Room: Maryland B |
Tuesday, January 31, 2017 1:30PM - 1:42PM |
Y2.00001: Student construction of differential length elements in multivariable coordinate systems: A symbolic forms analysis John Thompson, Benjamin Schermerhorn Analysis of properties of physical quantities represented by vector fields often involves symmetries and spatial relationships best expressed in non-Cartesian coordinate systems. Many important quantities are determined by integrals that can involve multivariable vector differential quantities. Four pairs of students in junior-level Electricity and Magnetism (E&M) were interviewed to investigate their understanding of the structure of non-Cartesian coordinate systems and the associated differential elements. Pairs were asked to construct differential length elements for an unconventional spherical coordinate system. In order to explore how student conceptual understanding interacts with their understanding of the specific structures of these expressions, a symbolic forms framework was used. Analysis of student reasoning revealed both known and novel forms as well as the general progression of students’ use and combination of symbol templates during the construction process. Each group invoked and combined symbolic forms in a similar sequence. Difficulties with the construction of expressions seem to be related almost exclusively to the conceptual schema (e.g., neglecting the role of projection) rather than with symbol templates. [Preview Abstract] |
Tuesday, January 31, 2017 1:42PM - 1:54PM |
Y2.00002: Student understanding of balancing, mass distribution and center of mass Paula Heron Understanding the relationships between balancing, mass distribution and the center of mass is challenging for students. In particular there is a widespread tendency to attribute a balanced state to equal amounts of mass to both sides of the fulcrum if the mass distribution is continuous.(1) A number of explanations have been proposed, including a recent suggestion that perceptual difficulties in locating the center of mass are, at least in part, to blame.(2) Recent experiments suggest that it is unlikely that perceptual difficulties play a significant role. The results have implications for the interpretation of common student errors more broadly. (1) Ortiz, Heron and Shaffer, American Journal of Physics, 2005. (2) Sattizahn et. al., Mind, Brain and Education, 2015. [Preview Abstract] |
Tuesday, January 31, 2017 1:54PM - 2:06PM |
Y2.00003: Spin First vs. Position First instructional approaches to teaching introductory quantum mechanics Homeyra Sadaghiani As part of ongoing research in teaching and learning quantum mechanics, we are investigating student learning of basic introductory quantum concepts in two different paradigms. In one paradigm, students are introduced to the postulates of quantum mechanics by discrete bases of Spin-half (Spin First) before being introduced to Schrödinger's equation. In the second paradigm, continuous bases of position probability wave functions (Position First) are the context within which students first encounter quantum mechanical phenomena. In this paper, we compare student learning of basic introductory quantum ideas in two sections of a sophomore level modern physics course at Cal Poly Pomona that were taught using these two approaches by means of their performances on a research-based concept posttest. Based on our results, the students who were taught using Spin First outperformed their peers in Position First group with average score of {$53$ $ \pm $ {3}}\% vs. {$34$ $ \pm $ {5}}\% in Quantum Mechanics Concept Assessment (QMCA), suggesting that the Spin First approach might improve some aspects of student learning of quantum mechanics. [Preview Abstract] |
Tuesday, January 31, 2017 2:06PM - 2:18PM |
Y2.00004: Fostering Student Introspection through Guided Reflection Forms Laura Wood, Amanda Matheson, Scott Franklin Student self-reflection is an important metacognitive skill to developing expert-like habits of mind. This study focuses on student responses to Guided Reflection Forms (GRFs) and individualized instructor feedback to the submissions. Student and instructor entries were hand-coded by an emergent rubric and, separately, analyzed with LIWC (Linguistic Inquiry and Word Count), a computerized text analysis program that extracts affective sentiment. Sentiment analysis supports the development of a stable basis set (rubric) to describe responses that is robust across both introductory and advanced classes. The analysis also reveals the instructor's use of the ``praise sandwich,'' instinctively embedding critiques and suggestions between specific and general encouragements. The study demonstrates the utility of validated, automated, sentiment analysis as a method by which to analyze large corpuses of written text. [Preview Abstract] |
Tuesday, January 31, 2017 2:18PM - 2:30PM |
Y2.00005: What Physicist Mean By The Equals Sign In Undergraduate Education Dina Zohrabi Alaee, Kellianne Kornick, Eleanor C. Sayre, Scott V. Franklin Mathematical concepts and tools have an important role in physics. Faculties want students to think critically about mathematics and the underlying fundamental concepts, rather than simply memorizing a series of equations and answers. The equals sign -- ubiquitous in problem solving -- carries different conceptual meaning depending on how it is used; this meaning is deeply tied to cultural practices in problem solving in physics. We use symbolic forms to investigate the conceptual and cultural meanings of the equals sign across physics contexts. We built and validated a rubric to classify the ways that physics students use the equals sign in their written work. Our categories are causality, assignments, definitional, balancing, and just math. We analyze students’ use of the equals sign in their written homework and exam solutions in an upper-division electrostatics course. We correlate the kinds of equal signs within problem solutions with the difficulty of the problem. We compare they ways students use the equals sign to their course lectures and textbook. [Preview Abstract] |
Tuesday, January 31, 2017 2:30PM - 2:42PM |
Y2.00006: What Physicists Mean By the Equals Sign in Undergraduate Education Kellianne Kornick, Dina Alaee, Eleanor Sayre, Scott Franklin Mathematical syntax allows for the description of meaningful concepts in the physical sciences, and having nuanced proficiency in mathematical formalism is closely tied to communication and understanding of physical principles. The concept of equality is especially important, as it constrains and dictates the relationships between two equated expressions, and a student with detailed understanding of these relationships can derive physical meaning from syntactical expressions mediated by equals signs by knowing the “meaning” of equals signs. We delineate types of equals signs as used in undergraduate textbooks and develop a categorization scheme in order to investigate how equals signs are used paradigmatically and culturally in textbooks to convey physical meaning. We classify equals signs into general clusters (causal, definitional, assignment, balancing, and “just math”), each cluster containing more detailed types. We investigate differences across various topics and between introductory and upper-division textbooks. We found that upper division textbooks are more likely to use balancing, definitional, and more complex kinds of assignment forms, while introductory texts have much higher frequencies of simple assignment and “just math” types. [Preview Abstract] |
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