Students' understanding of mathematical expressions in physical chemistry contexts: An analysis using Sherin’s symbolic forms

Becker, Nicole; Towns, Marcy H.

doi:10.1039/c2rp00003b

Cited by 86 publications

(80 citation statements)

References 23 publications

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“…One of these is the transference of mathematical skills from the context of mathematics courses into applied subjects such as thermodynamics (Jasien and Oberem, 2002;Greenbowe and Meltzer, 2003;Thompson et al, 2006;Bucy et al, 2007;Hadfield and Wieman, 2010;Becker and Towns, 2012). One of these is the transference of mathematical skills from the context of mathematics courses into applied subjects such as thermodynamics (Jasien and Oberem, 2002;Greenbowe and Meltzer, 2003;Thompson et al, 2006;Bucy et al, 2007;Hadfield and Wieman, 2010;Becker and Towns, 2012).…”

Section: Main Challenges In the Teaching Of Thermodynamicsmentioning

confidence: 99%

Student oriented approaches in the teaching of thermodynamics at universities – developing an effective course structure

Partanen

2016

Chem. Educ. Res. Pract.

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The aim of this study was to apply current pedagogical research in order to develop an effective course and exercise structure for a physical chemistry thermodynamics course intended for second or third year university students of chemistry. A mixed-method approach was used to measure the impact the changes had on student learning. In its final form in 2014, the course consisted of lectures following a broken lecture structure that incorporated different kinds of activating learning tasks, and a three-tiered exercise structure including qualitative and quantitative tasks with a large emphasis on collaborative problem-solving. The new lecture and exercise structures improved student learning as measured by students' exercise points, exam results, and, between 2013 and 2014, the results of a conceptual thermodynamics test the students took at the beginning and end of the course. Even though the new exercise structure increased students' motivation, positive affect and satisfaction with the course, in both 2013 and 2014, it was the interactive lecture structure that students reported to be the most beneficial part of the course. In light of these results, this study demonstrates the advantages on student learning of adopting a multifaceted approach to both lectures and exercises.

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Section: Main Challenges In the Teaching Of Thermodynamicsmentioning

confidence: 99%

Student oriented approaches in the teaching of thermodynamics at universities – developing an effective course structure

Partanen

2016

Chem. Educ. Res. Pract.

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“…However, there is growing evidence that mathematical proficiency is perhaps necessary, but not sufficient for understanding thermodynamics topics. Even students who are successful according to course metrics and are well-prepared in terms of their mathematical background may use algorithmic approaches to successfully solve problems and may not grasp what those expressions mean at a fundamental level (Hadfield and Wieman, 2010;Becker and Towns, 2012). Even students who are successful according to course metrics and are well-prepared in terms of their mathematical background may use algorithmic approaches to successfully solve problems and may not grasp what those expressions mean at a fundamental level (Hadfield and Wieman, 2010;Becker and Towns, 2012).…”

Section: Introductionmentioning

confidence: 99%

Translating across macroscopic, submicroscopic, and symbolic levels: the role of instructor facilitation in an inquiry-oriented physical chemistry class

Becker

Stanford

Towns³

et al. 2015

Chem. Educ. Res. Pract.

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In physical chemistry classrooms, mathematical and graphical representations are critical tools for reasoning about chemical phenomena. However, there is abundant evidence that to be successful in understanding complex thermodynamics topics, students must go beyond rote mathematical problem solving in order to connect their understanding of mathematical and graphical representations to the macroscopic and submicroscopic phenomena they represent. Though traditional curricular materials such as textbooks may provide little support for coordinating information across macroscopic, submicroscopic, and symbolic levels, instructor facilitation of classroom discussions offers a promising route towards supporting students' reasoning. Here, we report a case study of classroom reasoning in a POGIL (process-oriented guided inquiry learning) instructional context that examines how the class coordinated macroscopic, submicroscopic, and symbolic ideas through classroom discourse. Using an analytical approach based on Toulmin's model of argumentation and the inquiry-oriented discursive moves framework, we discuss the prevalence of macroscopic, submicroscopic and symbolic-level ideas in classroom reasoning and we discuss how instructor facilitation strategies promoted reasoning with macroscopic, submicroscopic, and symbolic levels of representation. We describe one sequence of instructor facilitation moves that we believe promoted translation across levels in whole class discussion.

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“…When constructing vector differential lengths, students attended to the need for multiple components and connected differentials to unit vectors of the same variable. In cases where students had difficulty, recall mediated the construction of their expressions, as seen with partial derivative expressions [13]. In our study, however, recall often led students to incorrect expressions (e.g., both groups AB and CD included a term [15]).…”

Section: Discussionmentioning

confidence: 78%

“…They identified dependence, the reliance on a particular quantity, and parts-of-a-whole as major cues for integration. Symbolic forms have been used to describe physical chemistry students' sense-making of partial derivatives in thermodynamics [13]. The ideas of symbolic forms were used to address students' conceptual schemata when making sense of various integrals, which was often mediated by a graphical representation [14].…”

Section: Symbolic Formsmentioning

confidence: 99%

Students’ use of symbolic forms when constructing differential length elements

Schermerhorn¹,

Thompson²

2016

2016 Physics Education Research Conference Proceedings

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As part of an effort to examine students' understanding of the structure of non-Cartesian coordinate systems and the differential vector elements associated with these systems, students in junior-level electricity and magnetism (E&M) were interviewed in pairs. Students constructed differential length and volume elements for an unconventional spherical coordinate system. A symbolic forms analysis found that students invoked known as well as novel symbolic forms when building these vector expressions. Further analysis suggests that student difficulties were primarily conceptual rather than symbolic.

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Students' understanding of mathematical expressions in physical chemistry contexts: An analysis using Sherin’s symbolic forms

Cited by 86 publications

References 23 publications

Student oriented approaches in the teaching of thermodynamics at universities – developing an effective course structure

Student oriented approaches in the teaching of thermodynamics at universities – developing an effective course structure

Translating across macroscopic, submicroscopic, and symbolic levels: the role of instructor facilitation in an inquiry-oriented physical chemistry class

Students’ use of symbolic forms when constructing differential length elements

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