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Additional Readings

Alcaro, P., Alston, A., & Katims, N. (2000). Fractions attack! Children thinking and talking mathematically. Teaching Children Mathematics, 6, 562-565.

Beckman, C., Thompson, D. R., & Austin, R. A. (2004). Exploring proportional reasoning through movies and literature. Mathematics Teaching in the Middle School, 9(5), 256-262.

Ben-Chaim, D., Fey, J. T., Fitzgerald, W. M., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36, 247-273.

 

Boston, M., Smith, M. S., & Hillen, A. F. (2003). Building on students’ intuitive strategies to make sense of cross-multiplication. Mathematics Teaching in the Middle School, 9(3), 150-155.

Cai, J., & Sun, W. (2002). Developing students’ proportional reasoning: A Chinese perspective. In B. Litwiller (Ed.), Making sense of fractions, ratios, and proportions (pp. 195-205). Reston, VA: National Council of Teachers of Mathematics.

 

Chapin, S. & Anderson, N. (2003). Crossing the bridge to formal proportional reasoning. Mathematics Teaching in the Middle School, 8(8), 420-425.

Cramer, K., Post, T. R., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 159-178). Old Tappan, NJ: Macmillan.

Karp, K. S., & Brown, T. E. (2001). Geo-dolls: Traveling in a mathematical world. Teaching Children Mathematics, 8, 132-137.

Kenney, P. A., Lindquist, M. M., & Heffernan, C. L. (2002). Butterflies and caterpillars: Multiplicative and proportional reasoning in the early grades. In B. Litwiller (Ed.), Making sense of fractions, ratios, and proportions (pp. 87-99). Reston, VA: National Council of Teachers of Mathematics.

Lamon, S. J. (1999). More: In-depth discussion of the reasoning activities in “Teaching fractions and ratios for understanding.” Mahwah, NJ: Lawrence Erlbaum.

Lamon, S. J. (2002). Part-whole comparisons with unitizing. In Litwiller, B. (Ed.) Making sense of fractions, ratios, and proportions (pp. 79-86). Reston, VA: National Council of Teachers of Mathematics.

Lappan, G., Fitzgerald, W., Winter, M. J., & Phillips, E. (1986). Middle grades mathematics project: Similarity and equivalent fractions. Menlo Park, CA: AWL Supplemental.

Martinie, S. L., & Bay-Williams, J. M. (2003). Using literature to engage students in proportional reasoning. Mathematics Teaching in the Middle School, 9(3), 142-148.

Middleton, J. A., & Van den Heuvel-Panhuizen, M. (1995). The ratio table. Mathematics Teaching in the Middle School, 1, 283-287.

Miller, J. L., & Fey, J. T. (2000). Proportional reasoning. Mathematics Teaching in the Middle School, 5, 310-313.

Moss, J. (2002). Percents and proportion at the center: Altering the teaching sequence for rational number. In B. Litwiller (Ed.) Making sense of fractions, ratios, and proportions (pp. 109-120). Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics. (2003). Focus Issue: Proportional Reasoning. Mathematics Teaching in the Middle School, 8(8).

Smith, J. P., III. (2002). The development of students’ knowledge of fractions and ratios. In B. Litwiller (Ed.) Making sense of fractions, ratios, and proportions (pp. 3-17). Reston, VA: National Council of Teachers of Mathematics.

Thompson, D. R., Austin, R. A., & Beckmann, C. E. (2002). Using literature as a vehicle to explore proportional reasoning. In B. Litwiller (Ed.), Making sense of fractions, ratios, and proportions (pp. 130-137). Reston, VA: National Council of Teachers of Mathematics.






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