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IES Grant

Title: Teaching Fractions and Integers: The Development of a Research-Based Instructional Practice
Center: NCER Year: 2007
Principal Investigator: Saxe, Geoffrey Awardee: University of California, Berkeley
Program: Science, Technology, Engineering, and Mathematics (STEM) Education      [Program Details]
Award Period: 4 years Award Amount: $1,584,613
Type: Development and Innovation Award Number: R305B070299

Purpose: By fourth grade, students scoring at the Proficient level of achievement on the 2005 National Assessment of Educational Progress mathematics test should demonstrate an understanding of fractions and decimals. However, only 35 percent of fourth-grade students scored at or above the Proficient level of achievement on the assessment. The National Council of Teachers of Mathematics considers integers and fractions central to elementary mathematics education, and foundational for learning algebra and other topics in secondary mathematics. The purpose of this project is to develop a 16-lesson sequence aimed at improving understanding of integers and fractions among fifth-graders.

Project Activities: The research team will develop and refine the lessons on integers and fractions and assess the potential efficacy of the 16-lesson sequence on student understanding of integers and fractions using an experimental design. To assess the potential efficacy of the curriculum, 20 fifth-grade teachers will be randomly assigned to use the experimental curriculum, and 20 fifth-grade teachers will continue to teach the standard mathematics curriculum in their school.

Products: Products from this project include a mathematics curriculum for fifth-graders, and published reports describing the potential impact of the curriculum on student mathematics achievement.

Structured Abstract

Purpose: The purpose of this project is to develop a 16-lesson sequence aimed at improving understanding of integers and fractions among fifth-graders.

Setting: The schools are in California.

Population: The research is being conducted in urban fifth-grade classrooms with ethnically and socioeconomically diverse students who span a wide range of achievement levels.

Intervention: Key elements of the planned curriculum include: a vector interpretation of the number line with translations to other representational contexts, such as area and discrete models; lesson plans that provide teachers opportunities to build on student thinking while guiding students' conceptual grasp of mathematical ideas and definitions; and a sequence of lessons that enables diverse students to build coherent and rich connections between integers and fractions.

Research Design and Methods: To develop and refine the curriculum, the research team is conducting three types of coordinated studies. First, researchers will conduct interview studies to document urban students' understanding of targeted mathematical ideas in lessons; the results of the interviews will inform the design of the tutorial studies. Second, researchers will conduct tutorial studies or "teaching experiments" to investigate individual student learning trajectories through contrasting pre- to post-test performances, as well as the performance of students who are randomly assigned to different tutorial conditions. Building on the results of both the interview and tutorial studies, researchers will implement the lessons in classrooms and observe teacher and student use of the lessons to develop and refine the lessons and lesson sequences. These iterative cycles of implementation and refinement will use both quantitative analyses of student learning gains and qualitative analyses of classroom processes. Finally, the research team will assess the potential efficacy of the entire lesson sequence using an experimental design, in which 40 fifth-grade teachers will be randomly assigned to experimental or control conditions.

Control Condition: In the control condition, teachers will continue to implement the school's current mathematics curriculum.

Key Measures: The researchers are using a test that focuses on integers and fractions and spring scores on the California State fifth-grade mathematics test.

Data Analytic Strategy: The research team is using hierarchical linear models to analyze the data.


Book chapter

Saxe, G.B., de Kirby, K. Le, M., Sitabkhan, Y., and Earnest, D. (in press). Understanding Learning Across Lessons in Classroom Communities: A Multi-leveled Analytic Approach. In A. Bikner-Ahsbahs, C. Knipping, and N. Presmeg (Eds.), Doing (Qualitative) Research: Methodology and Methods in Mathematics Education. ZDM Research Handbook Series: Advances in Mathematics Education. Springer.

Saxe, G.B., Gearhart, M., Shaughnessy, M., Earnest, D., Cremer, S., Sitabkhan, Y., Platas, L., and Young, A. (2009). A Methodological Framework and Empirical Techniques for Studying the Travel of Ideas in Classroom Communities. In B. Schwartz, T. Dreyfus, and R. Hershkowitz (Eds.), Transformation of Knowledge in Classroom Interaction (pp. 203–222). New York: Routledge.

Journal article, monograph, or newsletter

Gearhart, M., and Saxe, G.B. (2014). Differentiated Instruction in Shared Mathematical Context. Teaching Children Mathematics, 20(7): 426.

Saxe, G.B., Diakow, R., and Gearhart, M. (2013). Towards Curricular Coherence in Integers and Fractions: The Efficacy of a Lesson Sequence That Uses the Number Line as the Principal Representational Context. ZDM-The International Journal on Mathematics Education, 45(3): 343–364.

Saxe, G.B., Earnest, D., Sitabkhan, Y., Haldar, L., Lewis, K., and Zheng, Y. (2010). Supporting Generative Thinking on the Integer Number Line in Elementary Mathematics. Cognition and Instruction, 28(4): 433–474.

Saxe, G.B., Shaughnessy, M., Gearhart, M., and Haldar, L.C. (2013). Coordinating Numeric and Linear Units: Elementary Students' Strategies for Locating Whole Numbers on the Number Line. Mathematical Thinking and Learning, 15(4): 235–258.