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Beyond Accuracy and Speed: Task Demands and Mathematical Performance

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It is an important issue to explore classroom environments which are conducive to developing students’ mathematical performance. This study explores the effects of different classroom environments (solution-demand and corresponding-time setting) on mathematical performances. Fourteen and eighteen prospective teachers were required to prove a task under different conditions respectively:a) Cognitive demand of multiple-solution corresponding time of three hours, and b) Cognitive demand of a right solution corresponding time of 20 minutes. We used SOLO as the assessment tool for mathematical performance from quality perspective. Significant differences were found in the quantity and quality of math-ematical performance. The regular environment focusing on speed and accuracy were found to be directly linked to low levels of performance. The findings above provide implications to the cognitive benefits of multiple-solution demand and cor-responding time setting.

Abstract

It is an important issue to explore classroom environments which are conducive to developing students’ mathematical performance. This study explores the effects of different classroom environments (solution-demand and corresponding-time setting) on mathematical performances. Fourteen and eighteen prospective teachers were required to prove a task under different conditions respectively:a) Cognitive demand of multiple-solution corresponding time of three hours, and b) Cognitive demand of a right solution corresponding time of 20 minutes. We used SOLO as the assessment tool for mathematical performance from quality perspective. Significant differences were found in the quantity and quality of math-ematical performance. The regular environment focusing on speed and accuracy were found to be directly linked to low levels of performance. The findings above provide implications to the cognitive benefits of multiple-solution demand and cor-responding time setting.

참고문헌 (33)

  1. Ball, D. L, "With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics", Elementary School Journal, 93(4), pp.373~397 (1993)
  2. Bayazit, I., "Task selection and task implementation: seven constraints affecting the teacher’s instruction", Proceedings of the British Society for Research into Learning Mathematics, 26(1), pp.23~28 (2006), BSRLM
  3. Biggs, J. B, "Evaluating the Quality of Learning: The SOLO Taxonomy" (1982), Academic Press
  4. Boston, M. D, "Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms", J. Res. Math. Educ, 40(2), pp.119~156 (2009)
  5. Cai, J, "Problem solving in Chinese mathematics education: research and practice", ZDM, 39(6), pp.459~473 (2007)
  6. Collis, K. F, "A technique for assessing mathematical problem solving ability", Journal for Research in Mathematics Education, (17), pp.206~221 (1986)
  7. "Repeated Measures Design"[URL]
  8. Doyle, W, "Academic work", Review of Educational Research, 53(2), pp.159~199 (1983)
  9. Doyle, W, "Work in mathematics classes: The context of students’ thinking during instruction", Educational Psychologist, 23(2), pp.167~180 (1988)
  10. Henningsen, M, "Mathematical tasks and student cognition: Classroom based factors that support and inhibit high-level mathematical thinking and reasoning", Journal for Research in Mathematics Education, 28(5), pp.524~549 (1997)
  11. Hiebert, J, "Instructional tasks, classroom discourse, and students’ learning in second grade arithmetic", American Educational Research Journal, (30), pp.393~425 (1993)
  12. Krutetskii, V. A, "The psychology of mathematical abilities in school children" (1976), University of Chicago Press
  13. Leikin, R, "Multiple proof tasks: teacher practice and teacher education Proceedings of International Commission on Mathematical Instruction", ICMI STUDY, (19) (2009), Proof and proving in mathematics education
  14. Leikin, R, "Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks", Educational Studies in Mathematics, (66), pp.349~371 (2007)
  15. Mathematics Textbook Developer Group for Elementary School, "Mathematics, Vol. 1, Grade 4(in Chinese), Vol. 1, Grade 4 (in Chinese)" (2003), People’s Education Press
  16. "Conducting Repeated Measures Analyses: Experimental Design Considerations"[URL]
  17. National Council of Teachers of Mathematics (NCTM), "Professional standards for teaching mathematics" (1991), NCTM
  18. National Council of Teachers of Mathemat, "Principles and standards for school mathematics" (2000), NCTM
  19. Schoenfeld, A. H, "Reflections on doing and teaching mathematics, In Mathematical thinking and problem solving", pp.53~70 (1994), Erlbaum
  20. Silver, E. A, "The QUASAR project: The “revolution of the possible” in mathematics instructional reform in urban middle schools", Urban Education, 30, pp.476~522 (1996)
  21. Silver, E. A, "Moving from rhetoric to praxis: issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom", J. Math. Behav, 24(4), pp.287~301 (2005)
  22. Siu, M. K, "Proof and pedagogy in ancient China: Examples from Liu Hui’s commentary on Jiu Zhang Suan Shu", Educational Studies in Mathematics, 24(4), pp.345~357 (1993)
  23. Smith, M. S, "Thinking through a lesson protocol: A key for successfully implementing high-level tasks", Math. Teach. M. Sch, 14(3), pp.132~138 (2008)
  24. Stein, M. K, "Instructional Tasks and the Development of Students Capacity to Think and Reason: An Analysis of the Relationship between Teaching and Learning in a Reform Mathematics Project", Educational Research and Evaluation, 2(1), pp.50~80 (1996)
  25. Stein, M. K, "Implementing standards-based mathematics instruction: A casebook for professional development" (2000), Teachers College Press
  26. Stigler, J. W, "The teaching gap: Best ideas from the world’s teachers for improving education in the classroom" (1999), Free Press
  27. Sun, X, "An approach to mathematics interest development by using the notion of “One problem multiple solutions”", Teacher Magazine, (12), pp.54~58 (2008)
  28. Sun, X, "Renew the Proving Experiences: An experiment for enhancement of a trapezoid area formula proof constructions of student teachers by ‘One problem multiple solutions’", the International Commission on Mathematical Instruction (ICMI), pp.178~183 (2009), Proof and Proving in Mathematics Education
  29. Sun, X, "Exploring Proof Space: prospective teachers’ multiple-proof construction of a trapezoid area formula. Paper presented at the Chinese American Educational Research and Development Association (CAERDA)", International Conference: Educational Research, Policy, and Practice for the Globalizing World (2012)
  30. Sun, X, "Regenerating the proving experience: An attempt for improvement original theorem proof construction of student teachers by using spiral variation curriculum", International Commission on Mathematical Instruction (ICMI), Study 19 conference: Proof and Proving in Mathematics Education, pp.172~177 (2009), ept of Math., Nat’l Taiwan Normal Univ
  31. Watson, A, "The nature of participation afforded by tasks, questions and prompts in mathematics classrooms", Research in Mathematics Education, (9), pp.111~126 (2007)
  32. Yakes, C, "Using comparison to develop teachers' flexibility in algebra", J. Math. Teach. Educ, 14(3), pp.175~191 (2011)
  33. Zhang J. Z, "From mathematical education to educational mathematics" (2005), Juvenile and children publishing house

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