A4 Article in conference proceedings
Automated Checking of Flexible Mathematical Reasoning in the Case of Systems of (In)Equations and the Absolute Value Operator (2021)
Valmari, A. (2021). Automated Checking of Flexible Mathematical Reasoning in the Case of Systems of (In)Equations and the Absolute Value Operator. In B. Csapó, & J. Uhomoibhi (Eds.), CSEDU 2021 : Proceedings of the 13th International Conference on Computer Supported Education. Vol. 2 (pp. 324-331). SCITEPRESS - Science and Technology Publications. https://doi.org/10.5220/0010493103240331
JYU authors or editors
Publication details
All authors or editors: Valmari, Antti
Parent publication: CSEDU 2021 : Proceedings of the 13th International Conference on Computer Supported Education. Vol. 2
Parent publication editors: Csapó, Beno; Uhomoibhi, James
Place and date of conference: Online, 23.-25.4.2021
eISBN: 978-989-758-502-9
eISSN: 2184-5026
Publication year: 2021
Pages range: 324-331
Number of pages in the book: 376
Publisher: SCITEPRESS - Science and Technology Publications
Place of Publication: Setúbal
Publication country: Portugal
Publication language: English
DOI: https://doi.org/10.5220/0010493103240331
Publication open access: Not open
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/75712
Abstract
We present an approach and a tool for automatically providing feedback on solutions that involve complicated reasoning patterns. Currently the tool supports linear systems of equations and inequations that may also contain the absolute value operator and a restricted form of rational functions. This suffices for designing problems that are laborious to solve with standard mechanical procedures, but much easier using short-cuts that students may find by creative thinking. Earlier research has found that struggling with important mathematics promotes conceptual development. Our goal is to encourage students to such struggling. A crucial feature is to give them great freedom to choose the paths via which they solve problems, and at any time ask the tool to check the work done so far, no matter what path was chosen. This was implemented by adopting standard notation from mathematical logic, and developing some new logical notation. The tool has been used in a course on elementary universi ty-level mathematics. It has worked reliably, but there is not yet any statistics on the pedagogical merits. The tool is expected to also support quadratic (in)equations in the near future.
Keywords: mathematics; mathematical thinking; reasoning; inference; feedback; computer-assisted learning; educational software
Free keywords: High School Mathematics; Elementary University Mathematics; Automatic Feedback; eLearning Software; Non-trivial Reasoning Patterns; Higher Order Thinking Skills
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2021
JUFO rating: 0