Teaching the Concept of Unit in Measurement Interpretation of Rational Numbers

Year 2008, Volume: 7 Issue: 3, 693 - 705, 26.06.2008

H. Bahadir Yanik Brandon Helding ve Alfinio Flores Alfinio Flores

Abstract

This study investigated middle school students understanding of unit and unitization concepts in
measurement interpretations of rational numbers using the number line as a tool. Fifty-six seventh-grade students
were pretested and five consecutive whole-class teaching experiments were developed and administered based on
pretest results. Five students were later chosen for semi-structured clinical interviews, based on their conceptions of
unit and unitization. Students’ reasoning was induced from the analysis of pre- and post-tests, observations of
classroom teaching episodes, videotapes of interviews, and transcriptions and photographs of student artifacts.
Results suggested that unit identification created difficulty for students in locating rational numbers on number lines.

Keywords

Rational Numbers, Unit, Unitization, Measurement

Teaching the Concept of Unit in Measurement Interpretation of Rational Numbers

Abstract

-

Keywords

-

References

• Behr, M., Lesh, R., Post, T., & Silver E. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91-125). New York: Academic Press.
• Behr, M., Wachsmuth, I., Post T., & Lesh R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15(5), 323-341.
• Behr, M., Wachsmuth, I., & Post, T. (1985). Construct a sum: A measure of children's understanding of fraction size. Journal for Research in Mathematics Education, 16(2), 120-131.
• Behr, M., Harel, G., Post, T., Lesh, R. (1992). Rational number, ratio and proportion. In D.Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 296-333). New York: McMillan Publishing.
• Bright, G., Behr, M., Post, T., & Wachsmuth, I. (1988, May).Identifying fractions on number lines. Journal for Research in Mathematics Education., 19(3), 215-232
• Hiebert J., & Tonnessen, L., (1978). Development of the fraction concept in two physical contexts: An exploratory investigation. Journal for Research Mathematics Education 9(5), 374-378.
• Kieren, T.E. (1980). The rational number construct: Its elements and mechanisms. In T.E. Kieren (Eds.), Recent research on number learning (pp. 125- 150). ERIC/SMEAC, Columbus, OH.
• Kieren, T.E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Eds.), Number and measurement (pp. 101-150). ERIC/SMEAC, Columbus, OH.
• Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: an integration of research (pp. 49-84). Hillsdale, NJ: Lawrence Erlbaum.
• Lamon, S. (1999). Teaching fractions and ratios for understanding (1 st Ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
• Lamon, S. (2005). Teaching fractions and ratios for understanding (2 nd Ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
• Mack, N. (1995). Confounding whole-number and fraction concept when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441.
• Martin, W., & Strutchens, M. E. (2000). Geometry and measurement. In E. A. Silver (Eds.), Results of the 1996 NAEP mathematics assessment, (pp. 193-234). Reston, VA: NCTM, 2000.
• Middleton, J.A., Flores, A., Carlson, M., Baek, J. M., & Atkinson, R. (2004). A longitudinal study of the development of rational number knowledge in the middle grades. Proposal submitted to the National Science Foundation. Arizona State University, Tempe, Arizona.
• Miles M., & Huberman, M. (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks, CA: Sage.
• National Center for Education Statistics (NCES) (2005). “The nation's report card: Mathematics 2003 major results.” [Online] Retrieved on September 14, 2005, at URL: http://nces.ed.gov/nationsreportcard/mathematics/results2003/.
• Novillis, C. (1976). An analysis of the fraction concept into a hierarchy of selected subconcepts and the testing of the hierarchical dependencies, Journal for Research in Mathematics Education, 7, 131-144.
• Payne, J. N. (1976). Review of research on fractions. In R. Lesh (Eds.), Number and measurement (pp.145-188). Athens, GA: University of Georgia.
• Pothier, Y., & Sawada, D. (1983). Partitioning: The emergence of rational number ideas in young children, Journal for Research in Mathematics Education 14, 307-317.
• Stephen M., & Clements. D.H. (2003). Linear and area measurement in prekindergarten to grade 2. In D.H. Clements & G. Bright (Eds.), Learning and Teaching Measurement 2003 Yearbook (pp. 3-16). Reston VA: National Council of Teachers of Mathematics.
• Tzur, R. (2004). An integrated research on children’s construction of meaningful, symbolic, partitioningrelated conceptions and the teachers’ role in fostering that learning. Journal of Mathematical Behavior, 18(2), 123-147.
• van de Walle, J. (2006). Elementary and middle school mathematics: Teaching developmentally (6 th Ed.). Boston, MA: Allyn & Bacon.