Abstract
This paper is one of a series of presentations at this Congress commemorating the work of Ed Begle. Begle’s (1979) last work, “Critical Variables in Mathematics Education”, served as a basis for these presentations. In particular, I will address “The use of critical variables to organize research, problems of synthesizing research, and the kind of empirical research that would be most useful to mathematics education.”
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Anderson, J.R. Language, memory, and thought. Hillsdale, N.J.: Erlbaum, 1976.
Anderson, J.R., Kline, P.J., Beasley, C.M., Jr. Complex learning processes. In Snow, R.E., Federico, P-A, Montague, W.E. (Eds.) Aptitude, learning, and instruction Vol. 2: Cognitive process analyses of learning and problem solving. Hillsdale, N.J.: Erlbaum, 1980.
Begle, E.G. Critical variables in mathematics education. Washington, D.C.: Mathematical Association of America and the National Council of Teachers of Mathematics, 1979.
Crist-Whitzel, J.L., Hawley-Winne, B.J. Individual differences and mathematics achievement: An investigation of aptitude-treatment interactions in an evaluation of three instructional approaches. Paper presented at the meeting of the American Educational Research Association, San Francisco, 1976.
Cronbach, L.J., Snow, R.E. Aptitudes and instructional methods. N.Y.: Irvington, 1977.
Greeno, J.G. A study in problem solving. In Glaser, R. (Ed.) Advances in instructional psychology. Vol I: Hillsdale, N.J.: Erlbaum, 1978.
Greeno, J.G. Some examples of cognitive task analysis with instructional implications. In Snow, R.E., Federico, P-A., Montague, W.E. (Eds.) Aptitudes, learning, and instruction Vol 2: Cognitive process analyses of learning and problem solving. Hillsdale, N.J.: Erlbaum, 1980.
Kennedy, M.M. Findings from the Follow Through Planned Variation Study. Educational Researcher 1978, 7 (6), 3–11.
Newell, A. Simon, H.A. Human problem solving. Englewood Cliffs, N.J.: Prentice-Hall, 1972.
Norman, D.A. Rumelhart, D.E. Explorations in cognition. San Francisco: Freeman, 1975.
Pellegrino, J.W. Glaser, R. Cognitive correlates and components in the analysis of individual differences. Intelligence, 1979, 1, 187–214.
Pelligrino, J.W. Glaser, R. Components of inductive reasoning. In Snow, R.E., Federico, P-A., Montague, W.E. (Eds.) Aptitude, learning, and instruction Vol I: Cognitive process analyses of aptitude. Hillsdale, N.J.: Erlbaum, 1980.
Sharps, R. A study of interactions between fluid and crystallized abilities of two methods of teaching reading and arithmetic. Unpublished doctoral dissertation. Pennsylvania State University, 1973.
Snow, R.E. Research on aptitude for learning: A progress report. In Shulman, L.S. (Ed.) Review of research in education. Vol 4. Itasca, Ill.: Peacock, 1977.
Snow, R.E. Theory and method for research on aptitude processes: A prospectus. Intelligence, 1978, 2, 225–278.
Snow, R.E., Yalow, E. Intelligence and education. In Sternberg, R.J. (Ed.) Handbook of Human Intelligence. N.Y.: Cambridge University Press, in press.
Spearman, C. The nature of “intelligence” and the principles of cognition. London: MacMillan, 1923.
Sternberg, R.J. Intelligence, information processing and analogical reasoning: The componential analysis of human abilities. Hillsdale, N.J.: Erlbaum, 1977.
Sternberg, R.J. The nature of mental abilities. American Psychologist. 1979, 34, 214–230.
Sternberg, R.J., Guyote, M.J., Turner, M.E. Deductive reasoning. In Snow, R.E., Federico, PA., Mongague, W.E. (Eds.) Aptitude, learning, and instruction Vol. I: Cognitive process analyses of aptitude.
Webb, N.M. Learning in individual and small group settings. Technical Report No. 7. Aptitude Research Project, School of Education, Stanford University, 1977.
Begle, E.G. Critical Variables in Mathematics Education: Findings from a Survey of the Empirical Literature. Washington: Mathematical Association of America and National Council of Teachers of Mathematics, 1979.
Begle, E.G. The Effects of Varyinq_the Number of Practice Problems, Number or Examples, and Location of the Practice Problems in Elementary School Geometry. Palo Alto, CA: Stanford University, 1976. ( ERIC Document Reproduction Service No. ED 142 408 )
Bird, B.A. Effect of Systematic Drill System on Computational Ability of Primary Children (Doctoral Dissertation, Brigham Young University, 1977.) Dissertation Abstracts International, 1978, 34, 1317A. (University Microfilms No. 78–16188)
Bright, G.W.; Harvey, J.G.; and Wheeler, M.M. Using Games to Retrain Skills with Basic Multiplicatin Facts. Journal for Research in Mathematics Education, 9 (2), 103–110.
Butcher, J.E. Comparison of the Effects of Distributed and Massed Problem Assignments on the Homework of Ninth-Grade Algebra Students. (Doctoral Dissertation, Rutgers University, I 975.) Dissertation Abstracts International, 1976, 36 6586A–6588A. (University Microfilms No. 76–868
Cranford, H.R. A Study of the Effects of Computer-Assisted Instruction in Mathematics on the Achievement and Attitude of Pupils in Grades Five and Six in a Rural Setting. (Doctoral Dissertation, University of Southern Mississippi, 1976.) Dissertation Abstracts International, 1977, 37A, 5660A. (University Microfilms No. 77–5932)
Cummins, J.K. The Arithmetic Achievement of Sixth Grade Pupils and the Effect of Short Term, Well Designed Practice on Their Computational Abilities. (Doctoral Dissertation, University of California, Los Angeles, 1974.) Dissertation Abstracts International, 1975, 35, 403IB-40328. (University Microfilms No. 75–222
Davidson, T.E. The Effects of Drill on Addition, Subtraction Learning with Implication of Piagetian Reversibility. (Doctoral Dissertation, Utah State University, 1975.) Dissertation Abstracts International, 1975, 36, 102A, (University Microfilms No. 75–14427)
Dienes, A.B. The Time Factor in Computer-Assisted Instruction. (Doctoral Dissertation, University of Toronto, 1972.) Dissertation Abstracts International, 1974, 34 498IA. (National Library of Canada at Ottawa)
Hohlfeld, J.F. Effectiveness of an Immediate Feedback Device for Learning Basic Multiplication Facts (Doctoral Dissertation, Indiana University, 1973.) Dissertation Abstracts International, 1974, 34, 4563A. (University Microfilms No. 74–2670)
Horwitz, S. Effects of Amount of Immediate and of Delayed Practice on Retention of Mathematical Rules. Tallahassee, Florida: Florida State University, 1975. (ERIC Document Reproduction Service No. ED 120010)
Howell, K.W. Using Peers in Drill-Type Instruction. Journal of Experimental Education, 46 (3), 52–56.
Katz, W.H. Effects of Item Placement in Exercise Sets on Achievement in Elementary Algebra. (Doctoral Dissertation, The University of Connecticut, 1974.) Dissertation Abstracts International, 1974, 34, 369IA–3692A. (University Microfilms No. 749205)
Malone, T.W. and Others. Projecting Student Trajectories in a Computer-Assisted Instruction Curriculum. Journal of Educational Psychology, 979, 71 (1), 75–84.
McClung, C.J. The Effects of Cognitive Style on Type of Practice. (Doctoral Dissertation, University of Southern California, 1976.) Dissertation Abstracts International, 1977, 37, 5706A.
Palmer, H. Three Evaluation Reports of Computer-Assisted Instruction in Drill-and-Practice Mathematics. Los Angeles, California: Los Angeles County Schools, 1973. ( ERIC Document Reproduction Service No. ED 087 422 )
Parrish, D.C. An Investigation of the Effects of Required Drill Homework Versus No Homework on Attitudes Toward and Achievement in Mathematics. (Doctoral Dissertation, University of Houston, 1976.) Dissertation Abstracts International, 1976,.37 2040A. (University Microfilms No. 76–23369)
Pence, B. and Begle, E.G. Effects of Varying the Number of Examples and Practice Problems. SMESG Working Paper No. 7. Palo Alto, California: Stanford University, 1974. ( ERIC Document Reproduction Service No. ED 142 405 )
Starr, R.J. Modern Math Plus Computational Drills: Affective and Cognitive Results. School Science and Mathematics, 1977, 77, 601–604.
Suppes, P. and Others. Evaluation of Computer-Assisted Instruction in Elementary Mathematics for Hearing-Imparied Students. Palo Alto, California: Stanford University, 1973. ( ERIC Document Reproduction Service No. ED 084 722 )
Suydam, M. and Dessart, D.J. Skill Learning. In R.J. Shumway (Ed.) Research in Mathematics Education. Reston, VA: National Council of Teachers of Mathematics, 1980.
Taylor, S.C. The Effects of Mastery, Adaptive Mastery, and Non-Mastery Models on the Learning of a Mathematical Task. Tallahassee, Florida: Control Data Corporation, 1975. (ERIC Document Reproduction Service No. ED106 145)
Weaver, J.R. The Relative Effects of Massed Versus Distributed Practice Upon the Learning and Retention of Eighth Grade Mathematics. (Doctoral Dissertation, The University of Oklahoma, 1976.) Dissertation Abstracts International, 1976, 37, 2698A. (University Microfilms No. 76–24394)
Begle, E.G. Critical Variables in Mathematics Education. Washington: Mathematics Association of American and National Council of Teachers of Mathematics, 1979.
Carry, L.R. Interaction of Visualization and General Reasoning Abilities with Instructional Treatment in Algebra. Doctoral Dissertaion, Stanford University, 1967.
Cronbach, L.J. and Snow, R.E. Individual Differences in Learning Ability as a Function of Instructional Variables. Contract No. OCE 4–6–061269–1217 USOE, Stanford Unviersity, 1969.
Cronbach, L.J. and Snow, R.E. Aptitudes and Instructional Methods. New York: Irvington, 1977.
DuRapau, V.J. Interaction of General Reasoning Ability and Gestalt and Analytic Strategies of Processing Spatial Tasks with Transformational and Non-Transformational Treatments in Secondary School Geometry. Doctoral Dissertation, The University of Texas at Austin, 1979.
Eastman, P.M. and Carry, L.R. Interaction of Spatial Visualization and General Reasoning Abilities with Instructional Treatment in Quadratic Inequalities: A Further Investigation. Journal for Reserach in Mathematics Education, 1975, 6 142–149.
Hickey, P.A. A Long Range Test of the Aptitude Treatment Interaction Hypothesis in College Level Mathematics. Doctoral Dissertation, The University of Texas at Austin, 1980.
Larkin J. et al. Expert and Novice Performance in Solving Physics Problems. Science, 1980, 208, 1335–1342.
McLeod, D.B. and Briggs, J.T. Interactions of Field Independence and General Reasoning with Inductive Instruction in Mathemaatics. Journal for Research in Mathematics Education, 1980, 11, 94–103.
Romberg, T.A. and Wilson, J.W. The Development of Tests. NLSMA Report No. 7 (Wilson, Cahen, Begle, Ec—riT Stanford: School Mathematics Study Group, 1969.
Salhab, M.T. The Interaction Between Selected Cognitive Abilities and Instructional Treatments on Absolute Value Equations. Doctoral Dissertation, The University of Texas at Austin, 1973.
Skemp, R.R. Relational Understanding and Instrumnental Understanding. Arithmetic Teacher, 1980, 26, 9–15.
Webb, L.F. and Carry, L.R. Interaction of Spatial Visualization and General Reasoning Abilities with Instructinal Treatment: A Follow-Up Study. Journal for Research in Mathematics Education, 1975, 6 132–140.
Begle, E.G. Critical Variables in Mathematics Education. Washington, D.C.: Mathematical Association of America and National Council of Teachers of Mathematics, 1979.
Branca, N.A. Kilpatrick, J. The consistency of strategies in the learning of mathematical structures. Journal of Research in Mathematics Education, 1972, 3, 132–40.
Brown, J.S., Collins, A., Harris, G. Artificial intelligence and learning strategies. In H.F. O’Neil (Ed.), Learning strategies. New York: Academic Press, 1978.
Days, H.C. Classifying algebra problems according to the complexity of their mathematical representation. Inn G.A. Goldin C.E. McClintock (Eds.), Task variables in mathematical problem solving. Columbus, Ohio: ERIC, 1980.
Dienes, Z.P., Jeeves, J.A. Thinking in structures. London: Hutchinson Educational, 1965.
Dienes, Z.P., Jeeves, M.A. The effects of structural relations on transfer. London: Hutchinson Educational, I970.
Goldin, G.A. Structure variables in problem-solving. In G.A. Goldin C.E. McClintock (Eds.), Task variables in mathematical problem solving. Columbus, Ohio: ERIC, 1980.
Kantowski, M.G. The use of heuristics in problem-solving: An exploratory study. (NSF Technical Report SED 77 18543 ). Gainesville, Florida: University of Florida, 1979.
Klahr, D. Goal formation, planning, and learning by pre-school problem solvers or “My socks are in the dryer”. In R.S. Siegler (Ed.), Children’s thinking: What develops? Hillsdale, N.J.: Lawrence hrlbaum, 1978.
Kruteskii, V.A. The psychology of mathematical abilities in school children, J. Kilpatrick I. Wirzup (Eds.). Chicago: University of Chicago Press, 1976.
Kuhm, G. The classification of problem-solving research variables. In G.A. Goldin C.E. McClintock (Eds.), Task variables in mathematical problem solving. Columbus, Ohio: ERIC 1980.
Landa, L.N. The ability to think how cm it be taught? Soviet Education, 1976, 5 4–66.
Lester, F.K. Issues in mathematical problem-solving research. A paper presented at a Research Pression of the Annual Meeting of the National Council of Teachers of Mathematics, Seattle, WA, April 1980.
Luger, G.F. Applications of problem structure. In G.A. Goldin C.E. McClintock (Eds.), Task variables in mathematical problem solving. Columbus, Ohio: ERIC, 1980.
Malin, J.T. Strategies in mathematical problem solving. Journal of Educational Research, 1979, 73, 10I - 08.
McClintock, C.E. Heuristic processes as task variables. In G.A. Goldin C.E. McClintock (Eds.), Task variables in mathematical problem solving. Columbus, Ohio: ERIC, 1980.
Pereira-Mendoza, L. Heuristic strategies utilized by high school students. The Alberta Journal of Educational Research, 1979, 25, 213–20.
Polya, G. How to solve it. ( 2nd ed. ). Garden City, N.Y.: Doubleday, 1957.
Rigney, J.W. Learning strategies: A theoretical perspective. In H.F. O’Neil (Ed.), Learning strategies. New York: Academic Press, 1978.
Schoenfeld, A.H. Heuristic behavior variables in instruction. In G.A. Goldin C.E. McClintock (Eds.), Task variables in mathematical problem solving. Columbus, Ohio: ERIC, 1980.
Snow, R.E. Aptitude processes. In Snow, Federico, Montague (Eds.), Aptitude, learning instruction: V I Cognitive process analysis of aptitude. Hillsdale, N.J.: Lawrence Erlbaum, 1980.
Waters, W. Concept acquisition tasks. In G.A. Goldin C.E. McClintock (Eds.), Task variables in mathematical problem solving. Columbus, Ohio: ERIC, 1980.
Webb, N. A review of the literature related to problem-solving tasks and problem-solving strategies used by students in grades four, five and six. (Technical Report). Bloomington, Indiana: Mathematics Education Development Center, 1977.
Wittman, E. Matrix strategies in heuristics. International Journal of Mathematical Education in Science and Technology. 1975, 6, 187–98.
Bobrow, D.G. Natural Language Input for a Computer Problem-Solving System. In M. Minsky (Ed.), Semantic information processing. Cambridge, Mass.: MIT Press, 1968.
Brown, J.S. Burton, R.R. Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 1978, 2, 155–192.
Bundy, A. Analyzing mathematical proofs. Edinburgh: University of Edinburgh, Department of Artificial Intelligence, Research Report No. 2, 1975.
Case, R. Implications of developmental psychology for the design of effective instruction. In A.M. Lesgold, J.W. Pellegrino, S.D. Fokkema R. Glaser (Eds.) Cognitive Psychology and Instruction. New York: Plenum, 1978.
Carry, L.R., Lewis, C. Bernard, J.E. Psychology and equation solving: An information processing study. Austin: University of Texas, Department of Curriculum and Instruction, NSF Final Report 7822293, 1980.
Davis, R.B. McKnight, C.C. Modeling and processes of mathematical thinking. The Journal of Children’s Mathematical Behavior, 1979, 2 91-I 13.
Greeno, J.G. Trends in the theory of knowledge for problem solving. In D.T. Tuma F. Reif (Eds.), Problem solving and education: Issues in teaching and research. Hillsdale, N.J.: Erlbaum, 1980.
Groen, G.J. Parkman, J.M. A chronometric analysis of simple addition. Psychological Review, 1972, 79, 329–343.
Hayes, J.R. Simon, H.A. Understanding written instructions. In L.W. Gregg (Ed.), Knowledge and cognition. Hillsdale, N.J.: Erlbaum, 1974.
Hayes, J.R., Waterman, D.A. Robinson, C.S. Identifying relevant aspects of a problem text. Cognitive Science, 1977, 297–313.
Heiler, J. Greeno, J.G. Semantic processing in arithmetic word problem solving. Paper presented at the Midwestern Psychological Association, 1978.
Hinsley, D., Hayes, J.R. Simon, H.A. From words in equations. In P. Carpenter M. Just (Eds.), Cognitive processes in comprehension. Hillsdale, N.J.: Erlbaum, 1977.
Hunt, E. Mechanics of verbal ability. Psychological Review, 1978, 85, 109–130.
Hunt, E., Lunneborg, C. Lewis, J. What does it mean to be high verbal? Cognitive Psychology, 1975, 2, 194–277.
Johnson, J., Ryan, K., Cook, L. Mayer, R.E. From words to equations: An instructional study. Santa Barbara: Department of Psychology, Series on Learning and Cognition, Report No. 80–4, 1980.
Klatzky, R. Human memory: Second Edition. San Francisco: Freeman, 1980.
Larkin, J.H. Information processing models and science instruction. In J. Lochhead J. Clement (Eds.), Cognitive process instruction. Philadelphia: Franklin Institute Press, 1979.
Larkin, J.H. Teaching problem solving in physics: The psychological laboratory and the practical classroom. In D.T. Tuma and F. Reif (Eds.), Problem solving and education: Issues in teaching and research. Hillsdale, N.J.: Erlbaum, 1980.
Lochhead, J. Clement, J. Cognitive process instruction. Philadelphia: Franklin Institute Press, 1979.
Loftus, G.R. Loftus, E.F. Human memory: The processing of information. Hillsdale, N.J.: Erlbaum, 1976.
Loftus, E.F. Suppes, P. Structural viables that determine problem-solving difficulty in computer-assisted instruction. Journal of Educational Psychology, 1972, 63, 53I - 542.
Luchins, A.S. Mechanization in problem solving. Psychological Monographs, 1942, 54:6, Whole No. 248.
Matz, M. Towards a process model for high school algebra errors. Paper presented at Conference on Cognitive Processes in Algebra, University of Pittsburgh, 1979.
Mayer, R.E. Information processing variables in learning to solve problems. Review of Educational Research, 1975, 45, 525–541.
Mayer, R.E. Effects of meaningfulness on the representation of knowledge and the process of inference for mathematical problem solving. In R. Revlin R.E. Mayer (Eds.), Human Reasoning, Washington: Winston-Wiley, 1978.
Mayer, R.E. Schemas for algebra story problems. Santa Barbara: Department of Psychology, Series in Learning Cognition, Report No. 80–3, 1980.
Mayer, R.E. Bayman, P. Analysis of students’ intuitions about the operation of electronic calculators. Santa Barbara: Department of Psychology, Series in Learning Cogntion, Report No. 80–4, 1980.
Mayer, R.E. Bromage, B. Recall of algebra story problems. Santa Barbara: Department of Psychology, Series in Learning and Cognition. Report No. 80–5, 1980.
Mayer, R.E. Greeno, J.G. Structural differences between learning outcomes produced by different instructional methods. Journal of Educational Psychology, 1972, 63, 165–173.
Mayer, R.E. Greeno, J.G. Effects of meaningfulness and organization on problem solving and computability judgments. Memory Cognition, 1975, 3 356–362.
Mayer, R.E. Larkin, J.H. Kadane, J. Analysis of the skill of solving equations. Santa Barbara: Department of Psychology, Series in Learning Cognition, Report No. 80–2, 1980.
Newell, A. Simon, H.A. Human problem solving. Englewood Cliffs, N.J.: Prentice-Hall, 1972.
Paige, J.M. Simon, H.A. Cognitive process in solving algebra word problems. In B. Kleinmuntz (ed.), Problem solving: Research, method and theory. New York: Wiley, 1966.
Polya, G. Mathematical discovery. New York: Wiley, 1968.
Resnick, L.B. Task analysis in instructional design: Some cases from mathematics. In D. Klahr (Ed.), Cognition and instruction. Hillsdale, N.J.: Erlbaum, 1976.
Riley, M.S. Greeno, J.G. Importance of semantic structure in the difficulty of arithmetic word problems. Paper presented at the Midwestern Psychological Association, 1978.
Robinson, C.S. Hayes, J.R. Making inferences about relevance in understanding problems. In R. Revlin R.E. Mayer (Eds.), Human reasoning. Washington: Winston/Wiley, 1978.
Simon, H.A. Problem solving and education. In D.T. Tuma F. Reif (Eds.),Problem solving and education: Issues in teaching and research. Hillsdale, N.J.: Erlbaum, 1980.
Simon, D.P. Simon, H.A. Individual differences in solving physics problems. In R. Siegler (Ed.), Cihldren’s thinking: What develops? Hillsdale, N.J.: Erlbaum, 1978.
Wickelgren, W. How to solve problems. San Francisco: Freeman, 1974.
Bobrow, D.G. Norman, D.A. Some principles of memory schemata. In D.G. Bobrow A Collins (Eds.), Representation and understanding. New York: Academic Press, 1975.
Brown, A.L. Knowing when, where, and how to remember: A problem of metacognition. In R. Glaser (Ed.), Advances in instructional psychology (Vol. I ). Hillsdale, N.J.: Erlbaum, 1978.
Brown, J.S. Burton, R.R. Diagnostic models for procedural bugs in mathematical skills. Cognitive Science, 1978, 2 155–192.
Carroll, J.B. Psychometric tests as cognitive tasks: “A new structure of intellect.” In L.B. Resnick (Ed.), The nature of intelligence. Hillsdale, N.J.: Erlbaum, 1976.
Case, R. Gearing the demands of instructions to the developmental capacities of the learner. Review of Educational Research, 1975, 45, 59–87.
Case, R. Intellectual development from birth to adulthood: A new-Piagetian interpretation. In R.S. Siegler (Ed.), Children’s thinking: What develops? Hillsdale, N.J.: Erlbaum, 1978.
Davis, R.B., Jockusch, E., McNight, C. Cognitive processes in learning algebra. The Journal of Children’s Mathematical Behavior, 1978, 2 (1), 10320.
Ericsson, K.A., Simon, H.A. Verbal reports as data. Psychological Review, 1980, 87 (3), 215–251.
Flavell, J.H. Metacognitive aspects of problem solving. In L.B. Resnick (Ed.), The nature of intelligence. Hillsdale, N.J.: Erlbaum, 1976.
Flavell, J.H. Wellman, H.M. Metamemory. In R.V. Kail J.W. Hagen (Eds.), Perspectives on the development of memory and cognition. Hillsdale, N.J.: Erlbaum, 1977.
Gagne, R.M. White, R.T. Memory structures and learning outcomes. Review of Educational Research, 1978, 48 (2), 187–222.
Goldin, G.A. McClintock, C.E. Task variables in mathematical problem solving. Columbus, OH: ERIC/SMEAC, 1979.
Greeno, J.G. Trends in the theory of knowledge for problem solving. In D.T. TUma F. Reif (Eds.), Problem solving and education. Hillsdale, N.J.: Erlbaum, 1980.
Gurova, L.L. Schoolchildren’s awareness of their own mental operations in solving arithmetic problems (Originally published in 1959). In J. Kilpatrick I. Wirszup (Eds.) Soviet studies in the psychology of learning and teaching mathematics (Vol. 3 ). Stanford: SMSG, 1969.
Hadamard, J. The psychology of invention in the mathematical field. Princeton, N.J.: Princeton University Press, 1945.
Hinsley, D.A., Hayes, J.R., Simon, H.A. From words to equations - meaning and representations in algebra word problems. In M. Just P. Carpenter (Eds.), Cognitive processes in comprehension. Hillsdale, N.J.: Erlbaum, 1977.
Hunt, E., Lunneborg, C., Lewis, J. What does it mean to be high verbal? Cognitive Psychology, 1975, 7 197–227.
Kalmykova, Z.I. Psychological analysis of the formation of a concept of a problem type (Originally published in 1947.). In J. Kilpatrick I Wirszup (Eds.). Soviet studies in the psychology of learning and teaching mathematics (Vol. 6 ). Stanford: SMSG, 1969.
Krutetskii, V.A. The psychology of mathematical abilities in schoolchildren, J. Kilpatrick and I. Wirszup (Eds.). Chicago: University of Chicago Press, 1976.
Larkin, J.I. Skilled problem solving in physics: A hierarchical planning model. Unpublished manuscript, University of California at Berkeley, September 1977.
Paivio, A. Imagery and verbal processes. New York: Holt, Rinehart and Winston, 1971.
Piaget, J. Inhelder, B. Memory and Intelligence. New York: Basic Books, 1973.
Poincare, H. Mathematical creation. In The Foundations of Science. (Translated by G.H. Halstead.) New York: Science Press, 1913.
Polya, G. How to solve it ( 2nd ed. ). Garden City, N.Y.: Doubleday, 1957.
Potts, G.R. Information processing strategies used in the encoding of linear orderings. Journal of Verbal Learning and Verbal Behavior, 1972 I I, 727–740.
Rumelhart, D.E. Ortony, A. The representation of knowledge in memory. In R.C. Anderson, R.J. Spiro, W.E. Montague (Eds.), Schooling and the acquisition of knowledge. Hillsdale, N.J.: Erlbaum, 1977.
Shavelson, R.J. Porton, V.M. An information processing approach to research on mathematics learning and problem solving. Paper presented at the Conference on Modeling Mathematical Cognitive Development, Athens, GA., May, 1979.
Silver, E.A. Recall of mathematical problem information: Solving related problems. Journal for Research in Mathematics Education, in press.
Silver, E.A. Student perceptions of relatedness among mathematical verbal problems. Journal for Research in Mathematics Education, 1979, 10, 195–210.
Simon, H.A. Problem solving and education. In D.T. Tuma F. Reif (Eds.), Problem solving and education. Hillsdale, N.J.: Erlbaum, 1980.
Simon, H.A. Gilmartin, K. A simulation of memory for chess positions. Cognitive Psychology, 1973, 5 29–46.
Simon, D.P. Simon, H.A. Individual differences in solving physics problems. In R. Siegler (Ed.), Children’s thinking: What develops? Hillsdale, N.J.: Erlbaum, 1978.
Sternberg, R.J. Intelligence, information processing, and analogical reasoning: The componential analysis of human abilities. Hillsdale, N.J.: hrlbaum, 1976.
Beth E., Piaget, J. Mathematical Epistemology and Psychology. Dordrecht, Holland: D. Riedel, 1966.
Bruner, J.A. The Process of Education. Cambridge, Massachusetts: Harvard University Press, 1960.
Lesh, R.A. An interpretation of advanced organizers. Journal for Research in Mathematics Education, 1976, 7 69–74.
Lesh, R. Mathematical learning disabilities: Considerations for identification, diagnosis, and remediation. In R. Lesh, D. Mierkiewicz, M.C. Kantowski (Eds.), Applied Mathematical Problem Solving. Columbus, Ohio: ERIC/Clearinghouse for Science, Mathematics, and Environmental Education, 1979, Lesh, R. Applied mathematical problem solving. To appear in Educational Studies in Mathematics.
Lesh, R., Landau, M., Hamilton, E. Rational number ideas and the role of representational systems. To appear in Proceedings of the Fourth International Conference for the Psychology of Mathematics Education, August, 1980.
I. Bauersfeld, H.: Hidden dimensions in the so-called reality of a mathematics classroom. Educational Studies in Mathematics 11, (1980), pp. 23–41.
Begle, E.G.: Critical Variables in Mathematics Education. Mathematical Association of American and National Council of Teachers of Mathematics, Washington, 1979.
Bussmann, H., Heymann, H.-W., Lorenz, J.-H., Reiss, V., Scholz, R.W. and Seeger, F.: “Begle, E.G.: Critical Variables in Mathematics Education”. Zentralblatt fur Didaktik der Mathematik, Jhrg, 12, Heft I, 1980.
Dienes, Z.P.: Learning mathematics, In Wain, G.T. (Ed.): Mathematical Education, Van Nostrand Reinhold Col, Wokingham, 1978.
Freudenthal, H.: Address to the first conference of I.G.P.M.E., at Utrecht 29 August 1977. Educational Studies in Mathematics 9 (1978), pp. 1–5.
Freudenthal, H. Weeding and sowing. Preface to A Science of Mathematical Education, D. Reidel, Dordrecht, 1978.
Freudenthal, H.: New math or new education. Prospects, Vol. IX, No. 3, (1979), pp. 321–331.
Jackson, P.W.: Life in Classrooms. Holt, Rinehart and Winston, New York, 1968.
NCTM: An Agenda for Action. National Council of Teachers of Mathematics, Reston, 1980.
Australian Council for Educational Research. Background in Mathematics: A Guidebook to Elementary Mathematics for Teachers ih Primary Schools. Melbourne: Department of Education, Victoria, 1966.
Begle, E.G. Critical Variables in Mathematics Education. Washington, D.C.: Mathematical Association of America, 1978.
Blakers, A.L. Change in Mathematics Education since the late 1950’s - Ideas and Realisation. Australia. Educational Studies in Mathematics, 1978, 9 147158.
Bloom, B.S. Alterable variables: the new direction in educational research. Edinburgh: SCRE., 1979.
Carroll, J.B. A Model of School Learning. Teachers College Record 1963, 64, 723–733.
Glass, G.V. and Smith, M.L. Meta-analysis of Research on the Relationship of Class size and Achievement. San Francisco: Far West Laboratory for Educational Research and Development, 1978.
Husen, T. (ed.) International Study of Achievement in Mathematics (2 vols.) New York: Wiley, and Stockholm: Almqvist and Wiksell, 1967.
Keeves, J.P. Educational Environment and Student Achievement. Stockholm: Almqvist and Wiksell, and Melbourne: ACER, 1972.
Keeves, J.P. The Performance Cycle: Motivation and Attention as Mediating Variables in School Performance. Melbourne: ACER, 1974.
Keeves, J.P. Curricular Factors Influencing School Learning: Time and Opportunity to Learn. Melbourne: SCER, 1976.
McGaw, B., Keeves, J., Sorbom, D. and Cumming, Joy. The Mediated Influence of Prior Performance on Subsequent Performace: An Analysis of Linear Structural Relationships. (Paper presented at Australian Association for Research in Education Conference, Melbourne 1979 ).
Rosier, M.J. Changes in Secondary School Mathematics in Australia: 1964 to 1978. Hawthorn, Victoria: ACER (in press).
Ausubel, D.P. Educational psychology: A cognitive view. New York: Holt, Rinehart, and Winston, Inc., 1968.
Berliner, D.C. Allocated time, engaged time, and academic learning time in elementary school mathematics instruction. Paper presented at the 56th Annual Meeting of the National Council of Teacher of Mathematics, San Diego, April 1978.
Brophy, J.E. Evertson, C.M. Learning from teaching: A developmental perspective. Boston: Allyn Bacon, 1976.
Bush, A.J., Kennedy, J.J., Cruickshank, D.R. An empirical investigation.of teacher clarity. Journal of Teacher Education. March-April 1977, 28 (2), 5358.
Cooney, T.J., Davis, E.J., Henderson, K.B. Dynamics of teachin. secondary school mathemtics. Boston: Houghton-Mifflin, 1975.
Cruickshank, D., Kennedy, J., Myers, B., Bush, A. Teacher clarity What is it? Paper presented at the Conference on Innovative Practices in Teacher Education, Atlanta, January 1976.
Evertson, C.M., Emmer, E.T. Brophy, J.E. Predictors of effective teaching in junior high mathematics classrooms. Journal of Research in Mathematics Education, May 1980, 11 (3), 167–178.
Good, T. Grouws, D. Teaching effects: A process-product study in fourth-grade mathematics classrooms. Journal of Teacher Education, 1977, 28, 49–54.
Heath, R.W., Nielson, M.A. The research basis for performance-based teacher education. Review of Educational Research. Fall 1974, 44 (4), 463–484.
Kolb, J.R. A predictive model for teaching strate.ies research. Part I: Derivation of the model. Athens: The Georgia Center for the Study of Learning and Teaching Mathematics, 1977.
Kounin, J.S. Discipline and group management in classrooms. New York: Holt, Rinehart Winston, 1970.
Rosenshine, B., Furst, N. Research in teacher performance criteria in B.O. Smith (Ed.), Symposium on research in teacher education. Englewood Cliffs, N.J.: Prentice-Hall, 1971.
Stiff, L.V. C. (Doctoral dissertation, North Carolina State University, 1978 ). Dissertation Abstracts International. 1978, 39, 2803-A.
Thornton, C.D. An evaluation of the mathematics-methods program involving the study of teaching characteristics and pupil achievement in mathematics. Journal for Research in Mathematics Education. January 1977, 8 (I), 17–25.
Tikunoff, W.J., Berliner, D.C. Rist, R.C. An ethnographic study of the forty classrooms of the beginning teacher evaluation study known sample (Tech. Rep. 75–5). San Francisco: Far West Laboratory, 1975.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Birkhäuser Boston, Inc.
About this chapter
Cite this chapter
Snow, R.E. et al. (1983). The Begle Memorial Series on Research in Mathematics Education. In: Zweng, M.J., Green, T., Kilpatrick, J., Pollak, H.O., Suydam, M. (eds) Proceedings of the Fourth International Congress on Mathematical Education. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4684-8223-2_12
Download citation
DOI: https://doi.org/10.1007/978-1-4684-8223-2_12
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3082-9
Online ISBN: 978-1-4684-8223-2
eBook Packages: Springer Book Archive