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Strengthening Grade 3-5 Students’ Foundational Knowledge of Rational Numbers


by Thomas L. Good, Marcy B. Wood, Darrell Sabers, Amy M. Olson, Alyson Leah Lavigne, Huaping Sun & Crystal Kalinec-Craig — 2013

Background: American students have done poorly in algebra and that has generated policy concerns about preparing students for STEM careers. There has been growing recognition that the algebra problem may begin in earlier grades when students do not adequately master rational numbers.

Purpose: The study provided a series of workshops organized around problematic issues that students have in learning rational numbers. The research was designed to help all grade 3-5 teachers in a single school district help students gain in their knowledge of rational numbers.

Population: The population was drawn from one large school district (13 schools) and included 140 teachers and 2,845 students matched pre to post.

Research Design: The study used a quasi-experimental design. As all teachers in the district were involved, there was no control group.

Findings: On the basis of pre-post testing, girl and boy students, as well as students from diverse SES schools demonstrated large gains in their knowledge of rational numbers. There were no significant differences in gains for girls and boys at any of the three grade levels, but SES remained a main effect for gains in achievement for grades 3 and 4 even after entering prior achievement as a covariate and the interaction between SES and gender was significant for grade 5.

Recommendations: The findings provide clear evidence that students can make notable gains in learning rational numbers if they are given the opportunity to do so. The authors provide their intentions to further analyze the quantitative data (presented in this paper) with qualitative data that were collected in the study (e.g., providing open-ended response opportunities for students to respond to rational number questions like, “What is a fraction? What is a decimal? What is a percent?”



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Cite This Article as: Teachers College Record Volume 115 Number 7, 2013, p. 1-45
http://www.tcrecord.org ID Number: 17021, Date Accessed: 12/11/2017 4:10:30 PM

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About the Author
  • Thomas Good
    University of Arizona
    THOMAS L. GOOD is a Professor and Department Head in the Department of Educational Psychology at The University of Arizona. His research interests include teacher effects, teacher expectations effects, and student learning in classrooms – especially in grades 3 through 6.
  • Marcy Wood
    University of Arizona
    MARCY B. WOOD is an assistant professor in the University of Arizona’s College of Education. Her research interests include the role of discourse in mathematical learning and teaching, and analysis of mathematical learning and teaching through the lenses of identity and metaphor.
  • Darrell Sabers
    University of Arizona
    E-mail Author
    DARRELL SABERS is a Professor Emeritus, Educational Psychology, University of Arizona. He retired after over 40 years at the University of Arizona, and is now a consultant and a part-time professor. His research interests are educational testing and evaluation.
  • Amy Olson
    University of Arizona
    E-mail Author
    AMY M. OLSON is a graduate research associate in the Department of Educational Psychology at the University of Arizona. Her research interests include teacher effects, teacher use and understanding of assessment, and educational evaluation.
  • Alyson Lavigne
    Roosevelt University
    E-mail Author
    ALYSON LEAH LAVIGNE is an assistant professor of Curriculum Studies at Roosevelt University. Her research interests include student and teacher motivational dynamics, teacher retention, and early childhood and elementary education, particularly in schools serving minority students and students of poverty.
  • Huaping Sun
    American Board of Anesthesiology
    E-mail Author
    HUAPING SUN is a research associate at the American Board of Anesthesiology. Her research interests include psychometrics, educational assessment, and professional licensure.
  • Crystal Kalinec-Craig
    University of Arizona
    E-mail Author
    CRYSTAL KALINEC-CRAIG is currently a post-doctoral researcher in the University of Arizona's College of Education. Her research interests include examining the experiences of pre-service teachers as they learn to teach mathematics for understanding and integrate a diverse child's out-of-school mathematical knowledge and experiences.
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