# Rational Numbers: An Integration of Research

By Thomas A. Romberg; Elizabeth Fennema et al. | Go to book overview

Label a fraction on a number line when given the fraction symbol. (WS → P)

Explain what a fraction means when represented on a number line. (P → VS)

Represent a fraction with one type of physical material when given the fraction with another physical material (rods to number line; number line to rods). (M/P → M/P)

Change improper fractions to mixed fractions symbolically. (WS → WS)

Estimate which fractions are greater than 1/2, less than 1/2; close to 1; close to zero by estimating their location on a number line. (WS → P)

*Key:

M - Manipulative Aids

WS - Written Symbols

P - Pictorial

VS - Verbal Symbols

RW - Real World

REFERENCES

Ball, D. ( 1988). "I haven't done these since high school: Prospective teachers' understanding of mathematics". In M. Behr, C. Lacampagne, & M. Wheeler (Eds.), Proceedings of Tenth Annual Meeting of PME-NA (pp. 268-274). DeKalb, IL: PME-NA.

Behr, M. ( 1976). "The effect of manipulatives in second graders' learning of mathematics". (Tech. Rep. No. 11, Vol. 1). Tallahassee, FL. PMDC.

Behr, M., Harel, G., Post T., Lesh, R. ( 1992). "Rational numbers, ratio and proportion". In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-333). New York: Macmillan.

Behr, M., Wachsmuth, I., Post, R., & Lesh, R. ( 1984). "Order and equivalence of rational numbers: A clinical teaching experiment". Journal for Research in Mathematics Education, 15( 5), 323-341.

Bezuk, N., & Cramer, K. ( 1989). "Teaching about fractions: What, when, and how?" In P. Trafton & R. Ashulte (Eds.), New directions for elementary school mathematics (pp 156-167). Reston, VA: National Council of Teachers of Mathematics.

Bright, G., Behr, M., Post, T., & Wachsmuth, I. ( 1988). "Identifying fractions on number lines". Journal for Research in Mathematics Education, 19( 3), 215-232.

Brownell, W. A. ( 1938). "The critique of the committee of seven's investigations of the grade placement of arithmetic topics". Elementary School Journal, 38, 495-508.

Burger, W., & Shaughnessy, J. ( 1986). "Characterizing the Van Hiele levels of development in geometry". Journal for Research in Mathematics Education, 17, 31-48.

Carpenter, T., Fennema, E., Peterson, P., & Carey, D. ( 1988). "Teachers' pedagogical contentknowledge of students' problem solving in mathematics"

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