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Cramer, Kathleen A.; Monson, Debra S.; Wyberg, Terry; Leavitt, Seth; Whitney, Stephanie B. (2009, September). Models for initial decimal ideas. Teaching Children Mathematics, v16 n2 p106-117 Sept 2009.


Models for Initial Decimal Ideas

Kathleen A. Cramer, Debra S. Monson, Terry Wyberg,
Seth Leavitt and Stephanie Whitney
NOTE --- At this time, NCTM is granting permission for this site to publish just the abstract, and references for this article.


The Rational Number Project group put a twist on the familiar 10 x 10 grid in their latest curriculum development project to build meaning for decimals and improve students’ understanding of addition and subtraction with decimals.


Cramer, Kathleen A. “Using a Translation Model for Curriculum Development and Classroom Instruction.” In Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching, edited by Richard Lesh, and Helen M. Doerr, (pp. 449–64). Mahwah, n.J: Lawrence Erlbaum Associates, 2003.

Cramer, Kathleen A., Merlyn Behr, Thomas Post, and Richard Lesh. Rational Number Project: Fraction Lessons for the Middle Grades—Level 1. Dubuque, IA: Kendall Hunt Publishing, 1997.

Cramer, Kathleen A., and Apryl Henry. “Using Manipulative Models to Build Number Sense for Addition of Fractions.” In Making Sense of Fractions, Ratio, and Proportion, 2002 Yearbook of the National Council of Teachers of Mathematics (NCTM), edited by Bonnie Litwiller, pp. 41-48. Reston, VA: NCTM, 2002.

Cramer, Kathleen A., Thomas Post, and Robert delMas. “Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational number Project Curriculum.” Journal for Research in Mathematics Education 33, no. 2 (March 2002):111–44.

National Council of Teachers of Mathematics (NCTM). Principles and Standards for School Mathematics. Reston, VA: NCTM, 2000.

National Council of Teachers of Mathematics (NCTM). Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: NCTM 2006.


Kathleen A. Cramer is an associate professor at the University of Minnesota and the Project Director for the Rational number Project (RNP). Her research interests focus on the teaching and learning of fractions, decimals, and proportionality.

Debra S. Monson taught mathematics at Harding High School in St. Paul, Minnesota. She is currently a doctoral student at the University of Minnesota and is interested in mathematics education for preservice elementary teachers.

Terry Wyberg is a lecturer and co-principal investigator on the latest RNP grant at the University of Minnesota. His research interests include the teaching and learning of rational number.

Seth Leavitt is a middle school mathematics teacher in Minneapolis who is interested in helping math teachers secure the best teaching resources available.

Stephanie B. Whitney taught middle school and high school mathematics in Bloomington. She is currently a doctoral student at the University of Minnesota and is studying ways to help English Language Learners in the mathematics classroom.