Fractions are one of the most relentless areas of difficulty in mathematics for all students (National Center for Educational Statistics, 2009). Yet fourth and fifth-grade elementary students with learning disabilities (LD), in particular, begin their study of fractions with diminished conceptual understandings compared to their peers. This is alarming because it is conceptual knowledge that mediates the achievement gap in fractions between students with and without LD (Hecht & Vagi, 2010; Vukovic, 2012). Without conceptual understanding, students with LD show significantly less improvement in their ability to solve problems, estimate, and apply computational procedures with fractions over time and in higher mathematics courses such as Algebra I (Hecht & Vagi, 2010; National Mathematics Advisory Panel, 2008). Research is urgently needed to discover why students with LD might evidence pervasive difficulties learning fraction concepts and how conceptual knowledge of fractions can be developed and nurtured through instruction.

Fraction Activities and Assessment for Conceptual Teaching for Students with Learning Disabilities is a research proposal in the Faculty Early Career Development (CAREER) Program. The proposed project will build on established research on fraction learning in mathematics education (e.g., Behr, Harel, Post, & Lash, 1994; Cramer, 2003; Empson, 1999; Mack, 2001; Steffe & Olive, 2009) to augment conceptual understanding of fractions for students with LD. Change occurs through the creation and validation of instructional trajectories. Instructional trajectories model key developmental understandings, or critical transitions in how a student conceives of a mathematical idea (Simon, 2006), along with a carefully sequenced combination of tasks and varying instructional guidance (Daro, Mosher, and Corcoran, 2011). The research will also document how instruction based on such models impacts student outcomes. The research questions are: 1) What initial and developing understandings of fractions do students with learning disabilities evidence through strategies, language, and representations?; 2) How do students with learning disabilities progress in developing and solidifying conceptual understandings of fraction concepts through their mathematical activity?; and 3) To what extent does an intervention reflective of a research-based instructional trajectory facilitate strategic development and increased fraction conceptual knowledge in students with learning disabilities?

## Partners / Collaborators

National Science Foundation (NSF)

## Key Personel

**Jessica Hunt, Ph.D.** (The University of Texas at Austin)

Principal Investigator

## Publications

Tzur, R., & **Hunt, J.H.** (2015). Iteration: Unit fraction knowledge and the French fry tasks. Teaching Children Mathematics, 22(3), 149-157. http://www.nctm.org/Publications/Teaching-Children-Mathematics/2015/Vol22/Issue3/Iteration_-Unit-Fraction-Knowledge-and-the-French-Fry-Tasks/

**Hunt, J.H. **(2015). Understanding the diverse mathematical thinking of learners. Australian Primary Mathematics Classroom, 20(2), 15-21. http://connection.ebscohost.com/c/articles/108357842/how-better-understand-diverse-mathematical-thinking-learners

**Hunt, J.H. **and Empson, S. (2015). Strategies and representations used in equal partitioning problems by students with mathematics learning disability. Learning Disabilities Quarterly, 38(4), 208-220. http://ldq.sagepub.com/content/38/4/208

**Hunt, J.H. **& Little, M.E. (2014). Intensifying interventions for students by identifying and remediating conceptual understandings in mathematics. Teaching Exceptional Children, 46(6), 187-196. http://tcx.sagepub.com/content/46/6/187.citation