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The Teaching Fractions Toolkit: Equipping educators to develop effective grade 6 instruction in fractions

Midwest | July 12, 2022

Mathematics shapes and tools

A strong understanding of fractions lays the groundwork for later success in mathematics.1 For most students, grade 6 marks the last chance to hone their fractions skills before moving on to more advanced mathematical topics (see figure 1). Students who develop a solid foundation in fractions are equipped to take on higher level mathematics courses. These courses, in turn, pave the way for future careers in high-paying, in-demand fields, such as science, technology, engineering, and mathematics (STEM).2

Many grade 6 students struggle with fractions, however, which can lead to difficulty in later mathematics classes.3 Compounding the challenge, many teachers—including practicing and preservice teachers—also have difficulty with fraction operations.4

Grade 6 through Postsecondary mathematical learning progression sequence

Partnering to develop a Teaching Fractions Toolkit in Illinois

Through the Teaching Fractions Toolkit partnership, Regional Educational Laboratory (REL) Midwest is collaborating with the Illinois State Board of Education and several Illinois school districts to develop a collection of tools, resources, and training. The Teaching Fractions Toolkit will guide educators in developing effective grade 6 instruction that builds students’ conceptual understanding of fractions and how to solve fraction computation, ratio, and rate problems. The ultimate goal is to narrow gaps in mathematics achievement among Illinois student groups that are farthest from opportunity.

Over 5 years, the partnership will develop, evaluate, and refine the Teaching Fractions Toolkit, which will consist of the following two major components:

  • Professional development and supports for grade 6 mathematics teachers on evidence-based practices for teaching fractions, rational number computation, and related concepts.
  • Tools and supports for mathematics leaders and school/district administrators to reinforce the broader developmental trajectory of fraction understanding—including how to teach fractions—across prekindergarten to grade 8.

To ground the resources in evidence, the toolkit will draw on recommendations in the What Works Clearinghouse (WWC) practice guide Developing Effective Fractions Instruction for Kindergarten Through 8th Grade. This guide presents five evidence-based recommendations intended to help educators improve students’ understanding of fractions (see below). Recommendations 2-5 include strategies that grade 6 mathematics teachers can use to help students understand the meaning of fractions and build on their existing knowledge base to solve problems involving fractions, ratios, rates, and proportions. All five recommendations provide guidance to help administrators and mathematics leaders reinforce the broader developmental trajectory of fraction understanding.

  • WWC practice guide recommendations for effective fractions instruction
  1. Build on students’ informal understanding of sharing and proportionality to develop initial fraction concepts.
  2. Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.
  3. Help students understand why procedures for computations with fractions make sense.
  4. Develop students’ conceptual understanding of strategies for solving ratio, rate, and proportion problems before exposing them to cross-multiplication as a procedure to use to solve such problems.
  5. Professional development programs should place a high priority on improving teachers’ understanding of fractions and of how to teach them.

Looking ahead

The first phase of the work focuses on developing, piloting, and refining the Teaching Fractions Toolkit. During this phase, REL Midwest will partner with Elmhurst Community Unit School District 205 and Matteson School District 162, both suburban districts in the greater Chicago metropolitan area. Elmhurst serves more than 8,000 students across 14 schools, whereas Matteson has more than 2,900 students across seven schools. This phase will incorporate training, coaching, and tools to assist district partners in piloting and refining the toolkit. Over time, the partnership will expand to include additional Illinois districts to further pilot and refine the toolkit as well as test whether it improves students’ skills and achievement in fractions.

"Developing effective fractions instruction is pivotal for students’ access to and success in mathematics in high school and beyond," said Pamela Buffington, a member of the REL Midwest team who leads the toolkit development. "Members of the partnership are essential in the development of the Teaching Fractions Toolkit, which is designed to address this critical problem of practice. Partnership members will work collaboratively with REL Midwest researchers and mathematics education experts, contributing their deep knowledge of policy and practice."

References

1 Booth, J. L., & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37(4), 247–253. http://eric.ed.gov/?ID=EJ977998; Empson, S. B., Levi, L., & Carpenter, T. P. (2011). The algebraic nature of fractions: Developing relational thinking in elementary school. In J. Cai & E. Knuth (Eds.), Early algebraization. Advances in mathematics education (pp. 409–428). Springer. https://doi.org/10.1007/978-3-642-17735-4_22

2 Siegler, S. F., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909–918. https://doi.org/10.1037/edu0000025

3 Harvey, R. (2012). Stretching student teachers’ understanding of fractions. Mathematics Education Research Journal, 24(4), 493–511. https://eric.ed.gov/?id=EJ984997

4 Tekin-Sitrava, R. (2020). Middle school mathematics teachers’ reasoning about students’ nonstandard strategies: Division of fractions. International Journal for Mathematics Teaching and Learning, 21(1), 77–96; Whitehead, A. N., & Walkowiak, T. A. (2017). Preservice elementary teachers’ understanding of operations for fraction multiplication and division. International Journal for Mathematics Teaching & Learning, 18(3), 293–317. https://eric.ed.gov/?id=EJ1164169

Author(s)

Joni Wackwitz

Joni Wackwitz

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