Prospective elementary teachers’ number sense performance in Taiwan
Abstract
To examine prospective teachers’ number sense performance, two-hundred and eighty prospective teachers who majored in elementary teaching from one teacher training institution of southern Taiwan were selected to participate in this study. Results showed that about one-fifths of the prospective teachers could apply number sense based method (such as using benchmarks or estimation appropriately) and about a half of prospective teachers relied on rule-based methods when responding to number sense questions. Results also indicated that these prospective teachers highly focused on written method to solve the number sense questions. It is reasonable to believe that if we want to improve students’ number sense, then an important action that should be taken is to improve the quality of their teachers’ knowledge on number sense.
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References
ANGHILERI, Julia. Teaching number sense. Trowbridge. Wiltshire: Cromwell Press Ltd, 2000.
BALL, Deborah Loewenberg; BASS, Hyman. Making Mathematics Reasonable in School. In: MARTIN, Gary. (Ed.). Research Compendium for the Principles and Standards for School Mathematics. Reston, VA: NCTM, 2003, p. 27-44.
BALL, Deborah Loewenberg; HILL, Heather C.; BASS, Hyman. Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, v. 30, n. 3, p. 14-17, 20-22, 43-46, fall. 2005
BERCH, Daniel B. Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, v. 38, n. 4, p. 333-339, jul./aug. 2005.
CRAMER, Kathleen A.; POST, Thomas R.; DELMAS, Robert C. Initial fraction learning by fourth-and fifth- grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, v. 33. n. 2, p. 111-144, mar. 2002.
DUNPHY, Elizabeth. The primary mathematics curriculum: Enhancing its potential for developing young children’s number sense in the early years at school. Irish Educational Studies, v. 26, n. 1, 5-25, feb. 2007.
GRAEBER, Anna O.; TIROSH, Dina. Insights fourth and fifth graders bring to multiplication and division with decimals. Educational Studies in Mathematics, v. 21. n. 6, p. 565-588, dec. 1990.
GREER, Brian. Nonconservation of multiplication and division involving decimals. Journal for Research in Mathematics Education, v. 18. n. 1, p. 37-45, jan. 1987.
HILL, Heather C.; SCHILLING, Stephen G; BALL, Deborah Loewenberg. Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, v. 105. n. 1, p. 11–30. Sep. 2004.
HILL, Heather C.; SLEEP, Laurie; LEWIS, Jennifer; BALL, Deborah Loewenberg. Assessing Teachers’ Mathematical Knowledge: What Knowledge Matters and What Evidence Counts? In: FRANK, Lester. (Ed.). Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Publishing, 2007. p. 111–155.
JORDAN, Nancy C.; GLUTTING, Joseph; RAMINENI, Chaitanya. The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, v. 20. n. 2, p. 82-88, apr. 2010.
LESH, Richard; LAMON, Susan J. Assessing authentic mathematics performance. In: RICHARD, Lesh; SUSAN J. Lamon. (Ed.). Assessments of Authentic Performance in School Mathematics. Washington, DC: American Association for the Advancement of Sciences Press, 1992, p. 17-62.
MA, Liping. Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum, 1999.
MARKOVITS, Zvia; SOWDER, Judith. Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, v. 25. n. 1, p. 4-29, jan. 1994.
MCINTOSH, Alistair; REYS, Barbara J; REYS, Robert E; BANA, Jack., FARREL, Brian. Number Sense in School Mathematics: Student Performance in Four Countries. Mathematics, Science & Technology Education Centre, Edith Cowan University, 1997.
MCINTOSH, Alistair; REYS, Barbara J; REYS, Robert E. A proposed framework for examining basic number sense. For the Learning of Mathematics, v. 12. n. 3, p. 2-8, nov. 1992.
NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS (NCTM). Principles and standards for school mathematics. Reston, VA: NCTM, 2000.
ORGANIZATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT (OECD). Learning for tomorrow’s world: First results from PISA 2003. Paris, France: OECD, 2004.
REYS, Robert E.; YANG, Der-Ching. Investigating the development of number sense in a 6th grade class in Taiwan. Nordic Studies in Mathematics Education, v. 10. n. 1, p. 43-55. 2005.
REYS, Robert E.; YANG, Der-Ching. Relationship between computational performance and number sense among sixth- and eighth-grade students in Taiwan. Journal for Research in Mathematics Education, v. 29. n. 2, p. 225-237, mar. 1998.
SCHIFTER, D. Reasoning about Operations: Early Algebraic Thinking in Grades K-6. In: LEE, Stiff V. (Ed.). Developing Mathematical Reasoning in Grades K-12, 1999 Yearbook of NCTM. Reston, VA: NCTM, 1999, p. 62-81.
SOWDER, Judith. Estimation and Number Sense. In DOUGLAS A. Grouws. (Ed.). Handbook of Research on Mathematics Teaching and Learning. New York, NY: Macmillan, 1992, p. 371-389.
VERSCHAFFEL, Lieven; GREER, Brian; DE CORTE, Erick. Whole Number Concepts and Operations. In: LESTER JR., F. (Ed.). Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Publishing, 2007, p. 557-628.
YANG, Der-Ching; LI, Mao-Neng. Assessment of animated self-directed learning activities modules for children’s number sense development. Journal of Educational Technology and Society, v. 16. n. 3, p. 44-58, jul. 2013.
YANG, Der-Ching; REYS, Robert E. Fractional number sense strategies possessed by sixth grade students in Taiwan. Hiroshima Journal of Mathematics Education, v. 10. n. 3, p. 53-70, dec. 2002.
YANG, Der-Ching. Developing number sense through real-life situations in school. Teaching Children Mathematics, v. 13. n. 2, p. 104-110, sep. 2006.
YANG, Der-Ching. Investigating the strategies used by pre-service teachers in Taiwan when responding to number sense questions. School Science and Mathematics, v. 107. n. 7, p. 293-30, nov. 2007.
YANG, Der-Ching. Teaching and learning number sense – An intervention study of fifth grade students in Taiwan. International Journal of Science and Mathematics Education, v. 1. n. 1, p. 115-134, mar. 2003.
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