From Research to Practice and Back: The Animation Tutor Project

The Animation TutorTM is a curriculum project that uses software to supplement instruction in courses such as intermediate algebra. Its purpose is to ground mathematical reasoning in concrete experiences through the use of interactive animation and the virtual manipulation of objects. This article summarizes how the project has progressed from research to practice and back. The first section shows how research helped implement six instructional objectives: emphasize interactivity with reflection, integrate multiple representations, reduce cognitive load, facilitate transfer, replace ineffective static images with animated images, and provide domain-specific knowledge. The last section illustrates the reciprocal nature of research and practice by describing how formative evaluations of the Animation TutorTM program led to laboratory studies aimed at improving instructional materials and student strategies.

[1]  Lieven Verschaffel,et al.  The Effects of Different Problem Presentations and Formulations on the Illusion of Linearity in Secondary School Students , 2002 .

[2]  Daniel C. Edelson Design Research: What We Learn When We Engage in Design , 2002 .

[3]  K. Holyoak,et al.  Schema induction and analogical transfer , 1983, Cognitive Psychology.

[4]  R Ruurd Taconis,et al.  Teaching Science Problem Solving: An Overview of Experimental Work. , 2001 .

[5]  Wolff-Michael Roth,et al.  Professionals Read Graphs: A Semiotic Analysis , 2001 .

[6]  K. Holyoak,et al.  The use of diagrams in analogical problem solving , 2001, Memory & cognition.

[7]  S. K. Reed Estimating answers to algebra word problems. , 1984 .

[8]  S. Stump High School Precalculus Students' Understanding of Slope as Measure , 2001 .

[9]  Stephen K Reed,et al.  Use of temporal and spatial information in estimating event completion time , 2004, Memory & cognition.

[10]  Richard E. Mayer,et al.  Multimedia Learning , 2001, Visible Learning Guide to Student Achievement.

[11]  Zhe Chen,et al.  Analogical transfer: From schematic pictures to problem solving , 1995, Memory & cognition.

[12]  Chris Dede,et al.  If Design-Based Research is the Answer, What is the Question? A Commentary on Collins, Joseph, and Bielaczyc; diSessa and Cobb; and Fishman, Marx, Blumenthal, Krajcik, and Soloway in the JLS Special Issue on Design-Based Research , 2004 .

[13]  Herbert A. Simon,et al.  Why a Diagram is (Sometimes) Worth Ten Thousand Words , 1987, Cogn. Sci..

[14]  S. K. Reed,et al.  A Comparison of Computation, Discovery, and Graph Procedures for Improving Students' Conception of Average Speed , 1986 .

[15]  J. Sweller COGNITIVE LOAD THEORY, LEARNING DIFFICULTY, AND INSTRUCTIONAL DESIGN , 1994 .

[16]  Stephen K. Reed,et al.  A schema-based theory of transfer. , 1996 .

[17]  Susan M. Barnett,et al.  When and where do we apply what we learn? A taxonomy for far transfer. , 2002, Psychological bulletin.

[18]  Brian Greer,et al.  The Mathematical Modeling Perspective on Wor(l)d Problems. , 1993 .

[19]  Barbara Tversky,et al.  Animation: can it facilitate? , 2002, Int. J. Hum. Comput. Stud..

[20]  Robert S. Siegler,et al.  Metrics and Mappings: A Framework for Understanding Real-World Quantitative Estimation. , 1993 .

[21]  E. Corte,et al.  Making sense of word problems , 2000 .

[22]  S. K. Reed,et al.  Building Complex Solutions From Simple Solutions in the Animation Tutor: Task Completion , 2002 .

[23]  Robert L. Goldstone,et al.  The transfer of abstract principles governing complex adaptive systems , 2003, Cognitive Psychology.

[24]  Thomas P. Hogan,et al.  Quantitative Estimation: One, Two, or Three Abilities? , 2003 .

[25]  Stephen K. Reed,et al.  Learning functional relations: A theoretical and instructional analysis , 1987 .

[26]  Shaaron Ainsworth,et al.  The functions of multiple representations , 1999, Comput. Educ..

[27]  Stephen K. Reed,et al.  Using Multiple Representations to Improve Conceptions of Average Speed , 2002 .

[28]  P. Ackerman,et al.  Cognitive, perceptual-speed, and psychomotor determinants of individual differences during skill acquisition. , 2000, Journal of experimental psychology. Applied.

[29]  L. Miles,et al.  2000 , 2000, RDH.

[30]  최영한,et al.  미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론 , 2002 .

[31]  Susan R. Goldman,et al.  Word problems: research and curriculum reform , 2001 .

[32]  Paul Cobb,et al.  Individual and Collective Mathematical Development: The Case of Statistical Data Analysis. , 1999 .

[33]  J. Greeno,et al.  Transfer of situated learning , 1996 .

[34]  Richard E. Mayer,et al.  The effects of graphic organizers giving cues to the structure of a hypertext document on users' navigation strategies and performance , 2002, Int. J. Hum. Comput. Stud..

[35]  R. Mayer,et al.  Multimedia Learning: The Promise of Multimedia Learning , 2001 .

[36]  Lloyd P. Rieber,et al.  Animation in computer-based instruction , 1990 .

[37]  Stephen K. Reed,et al.  A structure-mapping model for word problems. , 1987 .

[38]  E. Paul Goldenberg,et al.  Mathematics, Metaphors, and Human Factors: Mathematical, Technical, and Pedagogical Challenges in the Educational Use of Graphical Representation of Functions , 1988 .

[39]  Stephen K. Reed,et al.  Effect of computer graphics on improving estimates to algebra word problems. , 1985 .

[40]  Andrea A. diSessa,et al.  Ontological Innovation and the Role of Theory in Design Experiments , 2004 .

[41]  David H. Jonassen,et al.  Designing Research-Based Instruction for Story Problems , 2003 .