Skip to main content

The Begle Memorial Series on Research in Mathematics Education

  • Chapter
  • 379 Accesses

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, J.R. Language, memory, and thought. Hillsdale, N.J.: Erlbaum, 1976.

    Google Scholar 

  2. 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.

    Google Scholar 

  3. Begle, E.G. Critical variables in mathematics education. Washington, D.C.: Mathematical Association of America and the National Council of Teachers of Mathematics, 1979.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. Cronbach, L.J., Snow, R.E. Aptitudes and instructional methods. N.Y.: Irvington, 1977.

    Google Scholar 

  6. Greeno, J.G. A study in problem solving. In Glaser, R. (Ed.) Advances in instructional psychology. Vol I: Hillsdale, N.J.: Erlbaum, 1978.

    Google Scholar 

  7. 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.

    Google Scholar 

  8. Kennedy, M.M. Findings from the Follow Through Planned Variation Study. Educational Researcher 1978, 7 (6), 3–11.

    Google Scholar 

  9. Newell, A. Simon, H.A. Human problem solving. Englewood Cliffs, N.J.: Prentice-Hall, 1972.

    Google Scholar 

  10. Norman, D.A. Rumelhart, D.E. Explorations in cognition. San Francisco: Freeman, 1975.

    Google Scholar 

  11. Pellegrino, J.W. Glaser, R. Cognitive correlates and components in the analysis of individual differences. Intelligence, 1979, 1, 187–214.

    Article  Google Scholar 

  12. 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.

    Google Scholar 

  13. 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.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. Snow, R.E. Theory and method for research on aptitude processes: A prospectus. Intelligence, 1978, 2, 225–278.

    Google Scholar 

  16. Snow, R.E., Yalow, E. Intelligence and education. In Sternberg, R.J. (Ed.) Handbook of Human Intelligence. N.Y.: Cambridge University Press, in press.

    Google Scholar 

  17. Spearman, C. The nature of “intelligence” and the principles of cognition. London: MacMillan, 1923.

    Google Scholar 

  18. Sternberg, R.J. Intelligence, information processing and analogical reasoning: The componential analysis of human abilities. Hillsdale, N.J.: Erlbaum, 1977.

    Google Scholar 

  19. Sternberg, R.J. The nature of mental abilities. American Psychologist. 1979, 34, 214–230.

    Article  Google Scholar 

  20. 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.

    Google Scholar 

  21. Webb, N.M. Learning in individual and small group settings. Technical Report No. 7. Aptitude Research Project, School of Education, Stanford University, 1977.

    Google Scholar 

  22. 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.

    Google Scholar 

  23. 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 )

    Google Scholar 

  24. 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)

    Google Scholar 

  25. 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.

    Google Scholar 

  26. 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

    Google Scholar 

  27. 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)

    Google Scholar 

  28. 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

    Google Scholar 

  29. 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)

    Google Scholar 

  30. 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)

    Google Scholar 

  31. 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)

    Google Scholar 

  32. 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)

    Google Scholar 

  33. Howell, K.W. Using Peers in Drill-Type Instruction. Journal of Experimental Education, 46 (3), 52–56.

    Google Scholar 

  34. 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)

    Google Scholar 

  35. Malone, T.W. and Others. Projecting Student Trajectories in a Computer-Assisted Instruction Curriculum. Journal of Educational Psychology, 979, 71 (1), 75–84.

    Google Scholar 

  36. 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.

    Google Scholar 

  37. 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 )

    Google Scholar 

  38. 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)

    Google Scholar 

  39. 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 )

    Google Scholar 

  40. Starr, R.J. Modern Math Plus Computational Drills: Affective and Cognitive Results. School Science and Mathematics, 1977, 77, 601–604.

    Article  Google Scholar 

  41. 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 )

    Google Scholar 

  42. 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.

    Google Scholar 

  43. 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)

    Google Scholar 

  44. 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)

    Google Scholar 

  45. Begle, E.G. Critical Variables in Mathematics Education. Washington: Mathematics Association of American and National Council of Teachers of Mathematics, 1979.

    Google Scholar 

  46. Carry, L.R. Interaction of Visualization and General Reasoning Abilities with Instructional Treatment in Algebra. Doctoral Dissertaion, Stanford University, 1967.

    Google Scholar 

  47. 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.

    Google Scholar 

  48. Cronbach, L.J. and Snow, R.E. Aptitudes and Instructional Methods. New York: Irvington, 1977.

    Google Scholar 

  49. 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.

    Google Scholar 

  50. 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.

    Article  Google Scholar 

  51. 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.

    Google Scholar 

  52. Larkin J. et al. Expert and Novice Performance in Solving Physics Problems. Science, 1980, 208, 1335–1342.

    Article  Google Scholar 

  53. 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.

    Article  Google Scholar 

  54. 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.

    Google Scholar 

  55. 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.

    Google Scholar 

  56. Skemp, R.R. Relational Understanding and Instrumnental Understanding. Arithmetic Teacher, 1980, 26, 9–15.

    Google Scholar 

  57. 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.

    Article  Google Scholar 

  58. Begle, E.G. Critical Variables in Mathematics Education. Washington, D.C.: Mathematical Association of America and National Council of Teachers of Mathematics, 1979.

    Google Scholar 

  59. 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.

    Article  Google Scholar 

  60. 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.

    Google Scholar 

  61. 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.

    Google Scholar 

  62. Dienes, Z.P., Jeeves, J.A. Thinking in structures. London: Hutchinson Educational, 1965.

    Google Scholar 

  63. Dienes, Z.P., Jeeves, M.A. The effects of structural relations on transfer. London: Hutchinson Educational, I970.

    Google Scholar 

  64. 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.

    Google Scholar 

  65. 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.

    Google Scholar 

  66. 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.

    Google Scholar 

  67. Kruteskii, V.A. The psychology of mathematical abilities in school children, J. Kilpatrick I. Wirzup (Eds.). Chicago: University of Chicago Press, 1976.

    Google Scholar 

  68. 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.

    Google Scholar 

  69. Landa, L.N. The ability to think how cm it be taught? Soviet Education, 1976, 5 4–66.

    Google Scholar 

  70. 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.

    Google Scholar 

  71. 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.

    Google Scholar 

  72. Malin, J.T. Strategies in mathematical problem solving. Journal of Educational Research, 1979, 73, 10I - 08.

    Google Scholar 

  73. 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.

    Google Scholar 

  74. Pereira-Mendoza, L. Heuristic strategies utilized by high school students. The Alberta Journal of Educational Research, 1979, 25, 213–20.

    Google Scholar 

  75. Polya, G. How to solve it. ( 2nd ed. ). Garden City, N.Y.: Doubleday, 1957.

    Google Scholar 

  76. Rigney, J.W. Learning strategies: A theoretical perspective. In H.F. O’Neil (Ed.), Learning strategies. New York: Academic Press, 1978.

    Google Scholar 

  77. 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.

    Google Scholar 

  78. 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.

    Google Scholar 

  79. Waters, W. Concept acquisition tasks. In G.A. Goldin C.E. McClintock (Eds.), Task variables in mathematical problem solving. Columbus, Ohio: ERIC, 1980.

    Google Scholar 

  80. 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.

    Google Scholar 

  81. Wittman, E. Matrix strategies in heuristics. International Journal of Mathematical Education in Science and Technology. 1975, 6, 187–98.

    Article  Google Scholar 

  82. Bobrow, D.G. Natural Language Input for a Computer Problem-Solving System. In M. Minsky (Ed.), Semantic information processing. Cambridge, Mass.: MIT Press, 1968.

    Google Scholar 

  83. Brown, J.S. Burton, R.R. Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 1978, 2, 155–192.

    Article  Google Scholar 

  84. Bundy, A. Analyzing mathematical proofs. Edinburgh: University of Edinburgh, Department of Artificial Intelligence, Research Report No. 2, 1975.

    Google Scholar 

  85. 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.

    Google Scholar 

  86. 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.

    Google Scholar 

  87. Davis, R.B. McKnight, C.C. Modeling and processes of mathematical thinking. The Journal of Children’s Mathematical Behavior, 1979, 2 91-I 13.

    Google Scholar 

  88. 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.

    Google Scholar 

  89. Groen, G.J. Parkman, J.M. A chronometric analysis of simple addition. Psychological Review, 1972, 79, 329–343.

    Article  Google Scholar 

  90. Hayes, J.R. Simon, H.A. Understanding written instructions. In L.W. Gregg (Ed.), Knowledge and cognition. Hillsdale, N.J.: Erlbaum, 1974.

    Google Scholar 

  91. Hayes, J.R., Waterman, D.A. Robinson, C.S. Identifying relevant aspects of a problem text. Cognitive Science, 1977, 297–313.

    Google Scholar 

  92. Heiler, J. Greeno, J.G. Semantic processing in arithmetic word problem solving. Paper presented at the Midwestern Psychological Association, 1978.

    Google Scholar 

  93. 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.

    Google Scholar 

  94. Hunt, E. Mechanics of verbal ability. Psychological Review, 1978, 85, 109–130.

    Article  Google Scholar 

  95. Hunt, E., Lunneborg, C. Lewis, J. What does it mean to be high verbal? Cognitive Psychology, 1975, 2, 194–277.

    Article  Google Scholar 

  96. 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.

    Google Scholar 

  97. Klatzky, R. Human memory: Second Edition. San Francisco: Freeman, 1980.

    Google Scholar 

  98. Larkin, J.H. Information processing models and science instruction. In J. Lochhead J. Clement (Eds.), Cognitive process instruction. Philadelphia: Franklin Institute Press, 1979.

    Google Scholar 

  99. 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.

    Google Scholar 

  100. Lochhead, J. Clement, J. Cognitive process instruction. Philadelphia: Franklin Institute Press, 1979.

    Google Scholar 

  101. Loftus, G.R. Loftus, E.F. Human memory: The processing of information. Hillsdale, N.J.: Erlbaum, 1976.

    Google Scholar 

  102. Loftus, E.F. Suppes, P. Structural viables that determine problem-solving difficulty in computer-assisted instruction. Journal of Educational Psychology, 1972, 63, 53I - 542.

    Article  Google Scholar 

  103. Luchins, A.S. Mechanization in problem solving. Psychological Monographs, 1942, 54:6, Whole No. 248.

    Google Scholar 

  104. Matz, M. Towards a process model for high school algebra errors. Paper presented at Conference on Cognitive Processes in Algebra, University of Pittsburgh, 1979.

    Google Scholar 

  105. Mayer, R.E. Information processing variables in learning to solve problems. Review of Educational Research, 1975, 45, 525–541.

    Google Scholar 

  106. 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.

    Google Scholar 

  107. Mayer, R.E. Schemas for algebra story problems. Santa Barbara: Department of Psychology, Series in Learning Cognition, Report No. 80–3, 1980.

    Google Scholar 

  108. 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.

    Google Scholar 

  109. 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.

    Google Scholar 

  110. Mayer, R.E. Greeno, J.G. Structural differences between learning outcomes produced by different instructional methods. Journal of Educational Psychology, 1972, 63, 165–173.

    Article  Google Scholar 

  111. Mayer, R.E. Greeno, J.G. Effects of meaningfulness and organization on problem solving and computability judgments. Memory Cognition, 1975, 3 356–362.

    Article  Google Scholar 

  112. 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.

    Google Scholar 

  113. Newell, A. Simon, H.A. Human problem solving. Englewood Cliffs, N.J.: Prentice-Hall, 1972.

    Google Scholar 

  114. 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.

    Google Scholar 

  115. Polya, G. Mathematical discovery. New York: Wiley, 1968.

    Google Scholar 

  116. Resnick, L.B. Task analysis in instructional design: Some cases from mathematics. In D. Klahr (Ed.), Cognition and instruction. Hillsdale, N.J.: Erlbaum, 1976.

    Google Scholar 

  117. 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.

    Google Scholar 

  118. 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.

    Google Scholar 

  119. 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.

    Google Scholar 

  120. 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.

    Google Scholar 

  121. Wickelgren, W. How to solve problems. San Francisco: Freeman, 1974.

    MATH  Google Scholar 

  122. 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.

    Google Scholar 

  123. 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.

    Google Scholar 

  124. Brown, J.S. Burton, R.R. Diagnostic models for procedural bugs in mathematical skills. Cognitive Science, 1978, 2 155–192.

    Article  Google Scholar 

  125. 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.

    Google Scholar 

  126. Case, R. Gearing the demands of instructions to the developmental capacities of the learner. Review of Educational Research, 1975, 45, 59–87.

    Google Scholar 

  127. 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.

    Google Scholar 

  128. Davis, R.B., Jockusch, E., McNight, C. Cognitive processes in learning algebra. The Journal of Children’s Mathematical Behavior, 1978, 2 (1), 10320.

    Google Scholar 

  129. Ericsson, K.A., Simon, H.A. Verbal reports as data. Psychological Review, 1980, 87 (3), 215–251.

    Article  Google Scholar 

  130. Flavell, J.H. Metacognitive aspects of problem solving. In L.B. Resnick (Ed.), The nature of intelligence. Hillsdale, N.J.: Erlbaum, 1976.

    Google Scholar 

  131. 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.

    Google Scholar 

  132. Gagne, R.M. White, R.T. Memory structures and learning outcomes. Review of Educational Research, 1978, 48 (2), 187–222.

    Google Scholar 

  133. Goldin, G.A. McClintock, C.E. Task variables in mathematical problem solving. Columbus, OH: ERIC/SMEAC, 1979.

    Google Scholar 

  134. 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.

    Google Scholar 

  135. 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.

    Google Scholar 

  136. Hadamard, J. The psychology of invention in the mathematical field. Princeton, N.J.: Princeton University Press, 1945.

    Google Scholar 

  137. 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.

    Google Scholar 

  138. Hunt, E., Lunneborg, C., Lewis, J. What does it mean to be high verbal? Cognitive Psychology, 1975, 7 197–227.

    Article  Google Scholar 

  139. 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.

    Google Scholar 

  140. Krutetskii, V.A. The psychology of mathematical abilities in schoolchildren, J. Kilpatrick and I. Wirszup (Eds.). Chicago: University of Chicago Press, 1976.

    Google Scholar 

  141. Larkin, J.I. Skilled problem solving in physics: A hierarchical planning model. Unpublished manuscript, University of California at Berkeley, September 1977.

    Google Scholar 

  142. Paivio, A. Imagery and verbal processes. New York: Holt, Rinehart and Winston, 1971.

    Google Scholar 

  143. Piaget, J. Inhelder, B. Memory and Intelligence. New York: Basic Books, 1973.

    Google Scholar 

  144. Poincare, H. Mathematical creation. In The Foundations of Science. (Translated by G.H. Halstead.) New York: Science Press, 1913.

    Google Scholar 

  145. Polya, G. How to solve it ( 2nd ed. ). Garden City, N.Y.: Doubleday, 1957.

    Google Scholar 

  146. 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.

    Google Scholar 

  147. 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.

    Google Scholar 

  148. 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.

    Google Scholar 

  149. Silver, E.A. Recall of mathematical problem information: Solving related problems. Journal for Research in Mathematics Education, in press.

    Google Scholar 

  150. Silver, E.A. Student perceptions of relatedness among mathematical verbal problems. Journal for Research in Mathematics Education, 1979, 10, 195–210.

    Article  Google Scholar 

  151. Simon, H.A. Problem solving and education. In D.T. Tuma F. Reif (Eds.), Problem solving and education. Hillsdale, N.J.: Erlbaum, 1980.

    Google Scholar 

  152. Simon, H.A. Gilmartin, K. A simulation of memory for chess positions. Cognitive Psychology, 1973, 5 29–46.

    Article  Google Scholar 

  153. 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.

    Google Scholar 

  154. Sternberg, R.J. Intelligence, information processing, and analogical reasoning: The componential analysis of human abilities. Hillsdale, N.J.: hrlbaum, 1976.

    Google Scholar 

  155. Beth E., Piaget, J. Mathematical Epistemology and Psychology. Dordrecht, Holland: D. Riedel, 1966.

    Google Scholar 

  156. Bruner, J.A. The Process of Education. Cambridge, Massachusetts: Harvard University Press, 1960.

    Google Scholar 

  157. Lesh, R.A. An interpretation of advanced organizers. Journal for Research in Mathematics Education, 1976, 7 69–74.

    Article  Google Scholar 

  158. 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.

    Google Scholar 

  159. 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.

    Google Scholar 

  160. I. Bauersfeld, H.: Hidden dimensions in the so-called reality of a mathematics classroom. Educational Studies in Mathematics 11, (1980), pp. 23–41.

    Google Scholar 

  161. Begle, E.G.: Critical Variables in Mathematics Education. Mathematical Association of American and National Council of Teachers of Mathematics, Washington, 1979.

    Google Scholar 

  162. 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.

    Google Scholar 

  163. Dienes, Z.P.: Learning mathematics, In Wain, G.T. (Ed.): Mathematical Education, Van Nostrand Reinhold Col, Wokingham, 1978.

    Google Scholar 

  164. 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.

    Article  Google Scholar 

  165. Freudenthal, H. Weeding and sowing. Preface to A Science of Mathematical Education, D. Reidel, Dordrecht, 1978.

    Google Scholar 

  166. Freudenthal, H.: New math or new education. Prospects, Vol. IX, No. 3, (1979), pp. 321–331.

    Article  Google Scholar 

  167. Jackson, P.W.: Life in Classrooms. Holt, Rinehart and Winston, New York, 1968.

    Google Scholar 

  168. NCTM: An Agenda for Action. National Council of Teachers of Mathematics, Reston, 1980.

    Google Scholar 

  169. Australian Council for Educational Research. Background in Mathematics: A Guidebook to Elementary Mathematics for Teachers ih Primary Schools. Melbourne: Department of Education, Victoria, 1966.

    Google Scholar 

  170. Begle, E.G. Critical Variables in Mathematics Education. Washington, D.C.: Mathematical Association of America, 1978.

    Google Scholar 

  171. Blakers, A.L. Change in Mathematics Education since the late 1950’s - Ideas and Realisation. Australia. Educational Studies in Mathematics, 1978, 9 147158.

    Google Scholar 

  172. Bloom, B.S. Alterable variables: the new direction in educational research. Edinburgh: SCRE., 1979.

    Google Scholar 

  173. Carroll, J.B. A Model of School Learning. Teachers College Record 1963, 64, 723–733.

    Google Scholar 

  174. 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.

    Google Scholar 

  175. Husen, T. (ed.) International Study of Achievement in Mathematics (2 vols.) New York: Wiley, and Stockholm: Almqvist and Wiksell, 1967.

    Google Scholar 

  176. Keeves, J.P. Educational Environment and Student Achievement. Stockholm: Almqvist and Wiksell, and Melbourne: ACER, 1972.

    Google Scholar 

  177. Keeves, J.P. The Performance Cycle: Motivation and Attention as Mediating Variables in School Performance. Melbourne: ACER, 1974.

    Google Scholar 

  178. Keeves, J.P. Curricular Factors Influencing School Learning: Time and Opportunity to Learn. Melbourne: SCER, 1976.

    Google Scholar 

  179. 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 ).

    Google Scholar 

  180. Rosier, M.J. Changes in Secondary School Mathematics in Australia: 1964 to 1978. Hawthorn, Victoria: ACER (in press).

    Google Scholar 

  181. Ausubel, D.P. Educational psychology: A cognitive view. New York: Holt, Rinehart, and Winston, Inc., 1968.

    Google Scholar 

  182. 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.

    Google Scholar 

  183. Brophy, J.E. Evertson, C.M. Learning from teaching: A developmental perspective. Boston: Allyn Bacon, 1976.

    Google Scholar 

  184. 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.

    Google Scholar 

  185. Cooney, T.J., Davis, E.J., Henderson, K.B. Dynamics of teachin. secondary school mathemtics. Boston: Houghton-Mifflin, 1975.

    Google Scholar 

  186. 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.

    Google Scholar 

  187. 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.

    Article  Google Scholar 

  188. Good, T. Grouws, D. Teaching effects: A process-product study in fourth-grade mathematics classrooms. Journal of Teacher Education, 1977, 28, 49–54.

    Article  Google Scholar 

  189. Heath, R.W., Nielson, M.A. The research basis for performance-based teacher education. Review of Educational Research. Fall 1974, 44 (4), 463–484.

    Google Scholar 

  190. 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.

    Google Scholar 

  191. Kounin, J.S. Discipline and group management in classrooms. New York: Holt, Rinehart Winston, 1970.

    Google Scholar 

  192. 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.

    Google Scholar 

  193. Stiff, L.V. C. (Doctoral dissertation, North Carolina State University, 1978 ). Dissertation Abstracts International. 1978, 39, 2803-A.

    Google Scholar 

  194. 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.

    Article  Google Scholar 

  195. 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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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

Publish with us

Policies and ethics