Assessing Mathematics Misunderstandings via Bayesian Inverse Planning

Autor/inn/en	Rafferty, Anna N.; Jansen, Rachel A.; Griffiths, Thomas L.
Titel	Assessing Mathematics Misunderstandings via Bayesian Inverse Planning
Quelle	In: Cognitive Science, 44 (2020) 10, (46 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1551-6709
DOI	10.1111/cogs.12900
Schlagwörter	Computer Assisted Testing; Mathematics Tests; Mathematics Skills; Student Evaluation; Algebra; Equations (Mathematics); Problem Solving; Bayesian Statistics; Planning; Models; Error Patterns; Test Interpretation; Educational Technology; Fractions; Arithmetic + Suchen Sie Ihr Suchwort? Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Schulnote; Studentische Bewertung; Equations; Mathematics; Gleichungslehre; Problemlösen; Ablaufplanung; Planungsprozess; Analogiemodell; Fehlertyp; Test analysis; Testauswertung; Unterrichtsmedien; Bruchrechnung; Addition; Arithmetik; Arithmetikunterricht; Rechnen
Abstract	Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how to solve the equation and the ways in which they might answer incorrectly offers the opportunity to obtain a more nuanced perspective of their algebra skills. To automatically make sense of step-by-step solutions, we propose a Bayesian inverse planning model for equation solving that computes an assessment of a learner's skills based on her pattern of errors in individual steps and her choices about what sequence of problem-solving steps to take. Bayesian inverse planning builds on existing machine learning tools to create a generative model relating (mis)-understandings to equation solving choices. Two behavioral experiments demonstrate that the model can interpret people's equation solving and that its assessments are consistent with those of experienced teachers. A third experiment uses this model to tailor guidance for learners based on individual differences in misunderstandings, closing the loop between assessing understanding, and using that assessment within an educational technology. Finally, because the bottleneck in applying inverse planning to a new domain is in creating the model of possible student misunderstandings, we show how to combine inverse planning with an existing production rule model to make inferences about student misunderstandings of fraction arithmetic. (As Provided).
Anmerkungen	Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01