Fundamentals of the Design and the Operation of an Intelligent Tutoring System for the Learning of the Arithmetical and Algebraic Way of Solving Word Problems

Autor/inn/en	Arnau, David; Arevalillo-Herraez, Miguel; Puig, Luis; Gonzalez-Calero, Jose Antonio
Titel	Fundamentals of the Design and the Operation of an Intelligent Tutoring System for the Learning of the Arithmetical and Algebraic Way of Solving Word Problems
Quelle	In: Computers & Education, 63 (2013), S.119-130 (12 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0360-1315
DOI	10.1016/j.compedu.2012.11.020
Schlagwörter	Intelligent Tutoring Systems; Computer System Design; Word Problems (Mathematics); Problem Solving; Mathematics Instruction; Arithmetic; Algebra; Equations (Mathematics); Mathematical Formulas; Mathematical Logic + Suchen Sie Ihr Suchwort? Intelligentes Tutorsystem; Textaufgabe; Problemlösen; Mathematics lessons; Mathematikunterricht; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Equations; Mathematics; Gleichungslehre; Mathematische Formel; Mathematical logics; Mathematische Logik
Abstract	Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate supervision during the resolution. This is done without imposing any restriction on the resolution paths that are allowed. Instead, the system attempts to enforce metacognitive learning by requiring an appropriate definition of quantities before they are used. The program (a) supports both the arithmetical and algebraic way of solving problems; (b) allows the recurrence to one or more equations when solving a problem in an algebraic way; (c) determines the validity of the expressions when they are introduced; and (d) admits the incorporation of new problems without the need of being reprogrammed. In this paper, we explain the design foundations, which are mainly based on (a) a reflection of the steps that a student should follow to solve a problem in an algebraic way, and (b) the use of a domain specific notation to represent both the problem structure and the current state of the resolution process. In particular, hypergraphs are introduced as an adequate way to support tracking in both the arithmetical and algebraic case. Moreover, we offer an extensive experimental evaluation which highlights the potential of the ITS as a learning tool. (Contains 18 figures and 2 tables.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10