Using an Intelligent Tutor and Math Fluency Training to Improve Math Performance

This article integrates research in intelligent tutors with psychology studies of memory and math fluency (the speed to retrieve or calculate answers to basic math operations). It describes the impact of computer software designed to improve either strategic behavior or math fluency. Both competencies are key to improved perlormance and both address working memory limitations as students solve math problems. This research evaluated software interventions to improve strategies and fluency and tested their relative magnitude on math post-tutor pertbrmance. We discovered that both interventions appear to complement one another, impacting math achievement. Results suggest that training both strategy and fluency provide an advantage in accuracy and speed at answering math problems, due to more available memory capacity. Mathematics fluency has an impact on students' cognitive resources that are needed lbr more difficult (computationally intensive) math problems. We suggest that intelligent tutors can be enhanced with math fluidity training activities that help students to make calculations automatically with minimal memory load.

[1]  L. Frank The Society for Research in Child Development , 1935 .

[2]  Leslie P. Steffe,et al.  Children's counting types: Philosophy, theory, and application , 1983 .

[3]  Walter Schneider,et al.  Training High-Performance Skills: Fallacies and Guidelines , 1985 .

[4]  Alan H. Schoenfeld,et al.  Mathematical Problem Solving , 1985 .

[5]  Ted S. Hasselbring,et al.  Developing Math Automaticity in Learning Handicapped Children: The Role of Computerized Drill and Practice. , 1988 .

[6]  Sydney S. Zentall,et al.  Fact-retrieval automatization and math problem solving by learning disabled, attention-disordered, and normal adolescents. , 1990 .

[7]  Irene Fortunato Metacognition and Problem Solving. , 1991 .

[8]  W. Kintsch The role of knowledge in discourse comprehension : a construction-integration model , 1991 .

[9]  David C. Geary,et al.  INDIVIDUAL DIFFERENCES IN THE DEVELOPMENT OF SKILL IN MENTAL ADDITION: INTERNAL AND EXTERNAL VALIDATION OF CHRONOMETRIC MODELS , 1992 .

[10]  C. Skinner,et al.  Cognitive Cover, Copy, and Compare , 1993 .

[11]  M. Carr,et al.  Metacognition and mathematics strategy use , 1994 .

[12]  Robbie Case,et al.  The Role of Central Conceptual Structures in the Development of Children's Thought , 1995 .

[13]  D. Kuhn Strategies of Knowledge Acquisition , 1995 .

[14]  John E. Hummel,et al.  Distributed representations of structure: A theory of analogical access and mapping. , 1997 .

[15]  G. Hancock,et al.  Modeling the mathematics achievement of Asian-American elementary students , 1997 .

[16]  James M. Royer,et al.  Math-Fact Retrieval as the Cognitive Mechanism Underlying Gender Differences in Math Test Performance. , 1999, Contemporary educational psychology.

[17]  A Desoete,et al.  Metacognition and Mathematical Problem Solving in Grade 3 , 2001, Journal of learning disabilities.

[18]  S. Ian Robertson,et al.  Problem-solving , 2001, Human Thinking.

[19]  Tom Murray,et al.  Toward Measuring and Maintaining the Zone of Proximal Development in Adaptive Instructional Systems , 2002, Intelligent Tutoring Systems.

[20]  Guy Gouardères,et al.  Proceedings of the 6th International Conference on Intelligent Tutoring Systems , 2002 .

[21]  Mary K. Hoard,et al.  Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. , 2004, Journal of experimental child psychology.

[22]  Beverly Park Woolf,et al.  Web-Based Intelligent Multimedia Tutoring for High Stakes Achievement Tests , 2004, Intelligent Tutoring Systems.

[23]  Asha K. Jitendra,et al.  Teaching Mathematics to Middle School Students with Learning Difficulties. , 2006 .

[24]  A. Baroody,et al.  The Application and Development of an Addition Goal Sketch , 2006 .

[25]  Beverly Park Woolf,et al.  Repairing Disengagement With Non-Invasive Interventions , 2007, AIED.

[26]  C. Skinner,et al.  Evaluating and Comparing Interventions Designed to Enhance Math Fact Accuracy and Fluency: Cover, Copy, and Compare Versus Taped Problems , 2007 .

[27]  Beverly Park Woolf,et al.  On-line Tutoring for Math Achievement Testing: A Controlled Evaluation , 2007 .

[28]  Beverly Park Woolf,et al.  Affective Gendered Learning Companions , 2009, AIED.

[29]  Beverly Park Woolf,et al.  Gender Matters: The Impact of Animated Agents on Students' Affect, Behavior and Learning , 2010 .

[30]  Beverly Park Woolf,et al.  Effort-based Tutoring: An Empirical Approach to Intelligent Tutoring , 2010, EDM.

[31]  Kasia Muldner,et al.  The Effect of Motivational Learning Companions on Low Achieving Students and Students with Disabilities , 2010, Intelligent Tutoring Systems.

[32]  Beverly Park Woolf,et al.  Evaluation of AnimalWatch: An Intelligent Tutoring System for Arithmetic and Fractions , 2010 .

[33]  James M. Royer,et al.  Combined fluency and cognitive strategies instruction improves mathematics achievement in early elem , 2011 .

[34]  Angeliki Kolovou,et al.  Mathematical problem solving in primary school , 2011 .