Cognitive principles of problem solving and instruction

Abstract : Research in this project studied cognitive processes involved in understanding and solving problems used in instruction in the domain of mathematics, and explored implications of these cognitive analyses for the design of instruction. Three general issues were addressed: knowledge required for understanding problems, knowledge of the conditions for applying problem-solving operators, and strategic knowledge for problem solving. Computational systems were developed in which graphical displays present explicit information to students that allows them to reflect on processes that are usually implicit, construct representations of problem information, specify assignments of variables, and learn from strategic errors. Research is described that provided analyses of cognitive processes on which instructional designs were based, and preliminary empirical results from use of the systems are presented. (Author)

[1]  Alan Bundy.  Analysing Mathematical Proofs (Or Reading Between the Lines) , 1975, IJCAI.

[2]  Dorothea P. Simon,et al.  Expert and Novice Performance in Solving Physics Problems , 1980, Science.

[3]  W Kintsch,et al.  Understanding and solving word arithmetic problems. , 1985, Psychological review.

[4]  Mary S. Riley,et al.  Development of Children's Problem-Solving Ability in Arithmetic. , 1984 .

[5]  John Seely Brown,et al.  Diagnostic Models for Procedural Bugs in Basic Mathematical Skills , 1978, Cogn. Sci..

[6]  Diane J. Briars,et al.  An integrated model of skill in solving elementary word problems cognition and instruction , 1984 .

[7]  Valerie L. Shalin,et al.  Structural Differences Between Two-Step Word Problems. , 1985 .

[8]  Frederick Reif,et al.  Prescribing Effective Human Problem-Solving Processes: Problem Description in Physics. Working Paper ES-19. , 1984 .

[9]  John Seely Brown,et al.  An Investigation of Computer Coaching for Informal Learning Activities. , 1978 .

[10]  Andrea A. diSessa,et al.  Unlearning Aristotelian Physics: A Study of Knowledge-Based Learning , 1982, Cogn. Sci..

[11]  Paul J. Feltovich,et al.  Categorization and Representation of Physics Problems by Experts and Novices , 1981, Cogn. Sci..

[12]  John R. Anderson.  Acquisition of cognitive skill. , 1982 .

[13]  Allen Newell,et al.  The Knowledge Level , 1989, Artif. Intell..

[14]  Alan H. Schoenfeld,et al.  Explicit Heuristic Training as a Variable in Problem-Solving Performance**Chapter 6 is an expanded and revised version of Schoenfeld (1979b). Permission from the Journal for Research in Mathematics Education to reproduce parts of the article is gratefully acknowledged. , 1979 .

[15]  John R. Anderson,et al.  Cognitive principles in the design of computer tutors , 1984 .

[16]  Alan Bundy.  Analyzing mathematical proofs (or reading between the lines) , 1975, IJCAI 1975.

[17]  James G. Greeno,et al.  Investigations of a Cognitive Skill. , 1985 .

[18]  Tamar Katriel,et al.  A semantic analysis of addition and subtraction word problems in arithmetic , 1977 .

[19]  Mikhail V. Matz,et al.  Towards a computational theory of algebraic competence , 1980 .