Home | Chapter 19 |

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.