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Assessing Learners’ Conceptual Understanding of Introductory Group Theory Using the CI²GT: Development and Analysis of a Concept Inventory

Veith JM, Bitzenbauer P, Girnat B (2022)

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Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2022

Journal

Book Volume: 12

Pages Range: 376

Journal Issue: 6

URI: https://www.mdpi.com/2227-7102/12/6/376

DOI: 10.3390/educsci12060376

Open Access Link: https://www.mdpi.com/2227-7102/12/6/376

Abstract

Prior research has shown how incorporating group theory into upper secondary school or undergraduate mathematics education may positively impact learners’ conceptual understanding of mathematics in general and algebraic concepts in particular. Despite a recently increasing number of empirical research into student learning of introductory group theory, the development of a concept inventory that allows for the valid assessment of a respective conceptual understanding constitutes a desideratum to date. In this article, we contribute to closing this gap: We present the development and evaluation of the Concept Inventory of Introductory Group Theory—the CI²GT. Its development is based on a modern mathematics education research perspective regarding students‘ conceptual mathematics understanding. For the evaluation of the CI²GT, we follow a contemporary conception of validity: We report on results from two consecutive studies to empirically justify that our concept inventory allows for a valid test score interpretation. On the one hand, we present N=9" role="presentation" style="max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">N=9 experts‘ opinions on various aspects of our concept inventory. On the other hand, we administered the CI²GT to N=143" role="presentation" style="max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">N=143 pre-service primary school teachers as a post-test after a two weeks course into introductory group theory. The data allow for a psychometric characterization of the instrument, both from classical and probabilistic test theory perspectives. It is shown that the CI²GT has good to excellent psychometric properties, and the data show a good fit to the Rasch model. This establishes a valuable new concept inventory for assessing students’ conceptual understanding of introductory group theory and, thus, may serve as a fruitful starting point for future research into student learning of abstract algebra.

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How to cite

APA:

Veith, J.M., Bitzenbauer, P., & Girnat, B. (2022). Assessing Learners’ Conceptual Understanding of Introductory Group Theory Using the CI²GT: Development and Analysis of a Concept Inventory. Education Sciences, 12(6), 376. https://doi.org/10.3390/educsci12060376

MLA:

Veith, Joaquin M., Philipp Bitzenbauer, and Boris Girnat. "Assessing Learners’ Conceptual Understanding of Introductory Group Theory Using the CI²GT: Development and Analysis of a Concept Inventory." Education Sciences 12.6 (2022): 376.

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