Models For Initial Decimal Ideas

This article is well worth the time for any math teacher to read. In one article, a wealth of knowledge and research is shifted to the readers, examples supporting the text.

The Rational Number Project (RNP), a group focused on children's learning tendencies of fractions, decimals, proportions, and ratios, developed a curriculum using the Lesh Translation model, which depicts five areas where representations should be used: real world situations, manipulatives, pictures, spoken symbols, and written symbols. Students should be able to represent any rational number (e.g. 0.26) in each of these categories. They should also be able to translate a representation from any one category into another representation from a different category. Theoretically, the students will develop a deeper understanding of rational numbers as opposed to rote memorization of how to manipulate them (adding, subtracting, etc.)

The crux of the RNP curriculum was using the traditional 10 x 10 grid. Students connected their spoken language of rational numbers (e.g. twenty-sixth hundredths, not point twenty-six!) with the pictorial representation. They also wrote the numbers with written symbols and translated the grid to a number line - another picture representation. The group discovered through their research that the 10 x 10grid was the most effective representation for students to begin studying rational numbers with. They found that students' initial ideas about decimals or other forms of rational numbers was a crucial element in how deeply they came to understand them.

The more I read about representation, the more I can see the how America's traditional math curriculum and teaching approach hindered mathematical reasoning. I just hope that when I become a teacher I will not become so caught up in preparing students for high-stakes testing that I cannot truly teach math from the "bottom up" and the "inside out."

Cramer, K. A., Monson, D. S., Wyberg, T., Leavitte, S. and Whitney, S. B. (2009). Models for initial decimal ideas. Teaching children mathematics 16(2), 106-116.