Cognitive Framework for Blended Math-Science Sensemaking for Vectors, Vector Operations, and Integrals
Abstract/Contents
- Abstract
- Blended mathematical sensemaking in science (blended MSS) involves developing a conceptual understanding of quantitative relationships and the scientific meaning of equations describing phenomena. In recent work, Kaldaras & Wieman developed and provided initial validity evidence for a unified cognitive framework (the framework) for blended MSS across various scientific disciplines, including Physics and Chemistry. The framework describes increasingly sophisticated ways of engaging in blended MSS as students develop an equation describing the scientific phenomenon or build a deeper understanding of the known equation describing the phenomenon. Kaldaras and Wieman validated the framework for simple mathematical relationships describing scientific phenomena involving multiplication, division, subtraction, and addition. In my senior thesis, I am extending the framework by Kaldaras & Wieman to include mathematical relationships describing phenomena that include vectors, vector operations, and integrals. I will present initial validity evidence for my framework grounded in analysis of student interviews. I use my cognitive framework to investigate whether taking vector calculus and intro electricity and magnetism (E&M) in separate contexts or courses that do not support blended MSS is effective in helping students build an integrated understanding of physics phenomena involving vectors, vector operations, and integrals. The interview analysis showed evidence for the validity of most of the levels of my framework for vectors, vector operations, and integrals. Interview analysis results showed no significant difference in the ability to engage in blended MSS between students who took intro E&M and students who did not. This finding suggests that intro E&M does not sufficiently prepare students to engage in higher levels of blended MSS for physics phenomena involving vectors, vector operations, and integrals.
Description
| Type of resource | text |
|---|---|
| Publication date | June 12, 2023; May 12, 2023 |
Creators/Contributors
| Author | Murillo Gonzalez, Gabriel |
https://orcid.org/0000-0002-7802-0509
(unverified)
|
|---|---|---|
| Thesis advisor | Wieman, Carl | |
| Thesis advisor | Kaldaras, Leonora | |
| Degree granting institution | Stanford University | |
| Department | Department of Physics |
Subjects
| Subject | Cognitive Framework |
|---|---|
| Subject | Blended Math-Science Sensemaking |
| Subject | Vectors |
| Subject | Vector Operations |
| Subject | Integrals |
| Subject | Electricity and Magnetism (E&M) |
| Genre | Text |
| Genre | Thesis |
Bibliographic information
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- User agrees that, where applicable, content will not be used to identify or to otherwise infringe the privacy or confidentiality rights of individuals. Content distributed via the Stanford Digital Repository may be subject to additional license and use restrictions applied by the depositor.
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 4.0 International license (CC BY-NC).
Preferred citation
- Preferred citation
- Murillo Gonzalez, G. (2023). Cognitive Framework for Blended Math-Science Sensemaking for Vectors, Vector Operations, and Integrals. Stanford Digital Repository. Available at https://purl.stanford.edu/jz326qf1474. https://doi.org/10.25740/jz326qf1474.
Collection
Undergraduate Theses, Department of Physics
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- Contact
- gmurillo@stanford.edu
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