CAREER: Fraction Activities and Assessments for Conceptual Teaching (FAACT) for Students with Learning Disabilities


This project is documenting how students with learning disabilities (LD) access and advance their conceptual understanding of fractions.  Rather than focusing on the knowledge students do not have, this work is focused on uncovering students' informal knowledge that can bridge to fractions and how instruction can be used to promote conceptual change. 


Project Evaluator: 
Dr. Mary Little
Full Description: 

Dr. Hunt, a former middle school and elementary school mathematics in inclusive settings in a state-demonstration STEM school, works with students deemed to be at risk for mathematics difficulties or labeled as having disabilities. Hunt contends that research and pedagogical practice for children with disabilities should begin from a respect for children's ways of knowing and learning. Rather than focusing on whether students can or cannot develop conceptual understanding, research should attempt to uncover the complex understanding students DO have. She argues that teaching based in learning theory that positions children's learning as adaptation advances reasoning, sense-making, and co-construction of meaning.


The overall goal of this CAREER award project is to re-direct and re-conceptualized research and practice across mathematics education and special education to support students to build rich concepts in mathematics through student-based instructional interventions. FAACT accomplishes this goal by - toward (a) uncovering the understandings students with LD do have of fraction concepts, (b) documenting how cognitive and/or early mathematics skills might affect the processes and products of learning, and (c) understanding how growth of conceptual knowledge occurs in these students and how to nurture this growth through the learning process.


Through this award, Dr. Hunt is re-conceptualizing intensive intervention as children's knowing and learning in "Small Environments". This approach suggests a redirect of research and instructional practice in mathematics for an underserved population of students. The project has the potential to offer a transformative approach to mathematics instruction for students with LD, bringing together expertise on learning disabilities and mathematics education to address an area in which there is very little research. 


The main outcomes of the project include (1) a theory of knowing, learning, and teaching connected to students with LDs in the small environment of supplemental and intensive intervention, (2) a six stage research-based trajectory specific to the conceptual understandings of fractions evidenced by students with LD, and (3) an adaptive intervention program consisting of (a) a clinical interview educators can use to understand students’ initial fraction thinking, (b) an instructional trajectory [lesson planning framework, four task sets, and corresponding teacher moves to support student learning], and (c) an instructional decision making guide based on the instructional trajectory to aid teachers in designing student-centered instruction both in small groups and individualized formats.


This project was previously funded under award #1253254 and 1446250.



Project Videos

2019 STEM for All Video Showcase

Title: Fractional Reasoning: Students with Learning Disabilities

Presenter(s): Jessica Hunt, Andy Khounmeuang, Kristi Martin, Blain Patterson, & Juanita Silva


Hunt. J.H. & Ainslie, J. (accepted). Designing effective math interventions:  An educator’s guide to learner-driven instruction. New York, NY: Routledge.

Tzur, R. & Hunt. J.H. & (in press). Fractional reasoning. In Y. Xin, H. Thouless, & R. Tzur (Eds). Enabling learning of struggling students.  New York, NY: Springer.

Hunt. J.H. & Tzur, R. (in press). Connecting theory to concept building. In Y. Xin, H. Thouless, & R. Tzur (Eds). Enabling learning of struggling students. New York, NY: Springer.

Tzur, R. & Hunt. J.H. (in press). A theory-backed framework for knowing and learning. In Y. Xin, H. Thouless, & R. Tzur (Eds). Enabling learning of struggling students.  New York, NY: Springer.

Hunt. J.H. & Lewis, K. (in press). Extending students’ knowledge of fractions as relational quantities: Teaching for understanding. In D.P. Bryant (Ed.), Intensifying mathematics interventions for students who struggle learning mathematics. New York, N.Y.: The Guilford Press.

Hunt, J. H., Martin, K., Khounmeuang, A., Silva, J., Patterson, B., & Welch-Ptak, J. (2020). Design, Development, and Initial Testing of Asset-Based Intervention Grounded in Trajectories of Student Fraction Learning. Learning Disability Quarterly, 0731948720963589.

Hunt, J., & Stein, M. K. (2020). Constructing Goals for Student Learning through Conversation. Mathematics Teacher: Learning and Teaching PK-12113(11), 904-909.

Hunt, J. H. & Silva, J. (Accepted for publication). Emma's negotiation of number: Implicit intensive intervention. Journal for Research in Mathematics Education.

Hunt, J. H., MacDonald, B. L., & Silva, J. (Revisions). Thinking, tricks, or teaching: Gina's mathematical reality.

Hunt, J. H., Silva, J., & Welch-Ptak, J. (2018). Changing the goal: Reasoning and sense making in children's small environments. Manuscript submitted for publication.

Hunt, J. H., MacDonald, B., Lambert, R., Sugita, T., & Silva, J. (2018). Think, pair, show, share to increase classroom discourse. Teaching Children Mathematics (Focus Issue - Invited contribution), 25(2), 80–84.

Lambert, R., Tan, P., Hunt, J. H., & Candella, A. (2018). Re-humanizing the mathematics education of students with disabilities: Critical perspectives on research and practice. Investigations in Mathematics Learning, 10(3), 129–132.

Lynch, S., Hunt, J. H., & Lewis, K. (2018). Productive struggle for all: Differentiated instruction. Mathematics Teaching in the Middle School, 24(4), 194–201.

Hunt, J. H. & Tzur, R. (2017). Where is difference? Processes of mathematical remediation through a constructivist lens. Journal of Mathematical Behavior, 48, 62–76.

Hunt, J. H., *Welch-Ptak, J., & *Silva, J. (2016). Initial understandings of fraction concepts evidenced by students with learning disabilities and difficulties: A framework. Learning Disabilities Quarterly, 39(4), 213–225.

Recent Presentations:

Hunt, J. H. & Silva, J. (2019, April). Emma's numbers: Whose knowledge is valued? What knowledge is valued? Paper presented at the American Educational Research Association, Toronto, Ontario, Canada.

Hunt, J. & Wilson, J. (2019, April). Marginalized within a marginalized community: Supporting meaning making. Paper presented at the American Educational Research Association, Toronto, Ontario, Canada.

Hunt, J., MacDonald, B., Lambert, R., & Silva, J. (2019, April). Think-pair-show-share: UDL and talk moves. Presented at the annual meeting of the National Council of Teachers of Mathematics, San Diego, CA.

Hunt, J. H., et al. (November 2018). Complex conceptions of fractions: Negotiating meaning in the small environment. Presented at the Regional meeting of the National Council of Teachers of Mathematics, Kansas City, MO.


Project Materials

Title Type Post date
Webinar Resources: Strengthening Educators’ Practices for Engaging and Empowering Students with Disabilities and Difficulties as Mathematics Learners Resource 06/05/2020 - 12:05pm
Fraction Activities and Assessment for Conceptual Teaching (FAACT) (NSF #1708327) CAREER Spotlight 05/12/2020 - 5:18pm
Empowering Students with Specific Learning Disabilities: Jim’s Concept of Unit Fraction Resource 12/11/2019 - 8:55am
Gina’s mathematics: Thinking, tricks, or “teaching”? Resource 08/30/2019 - 5:09pm
Illuminating Fractional Reasoning of Students with Learning Disabilities Resource 03/14/2019 - 2:00pm
Case Studies Resource 11/28/2018 - 5:36pm
A Handbook and Tool for Uncovering Children’s Conceptions of Fractions Resource 11/28/2018 - 5:32pm
Initial Understandings of Fraction Concepts Evidenced by Students With Mathematics Learning Disabilities and Difficulties Resource 11/27/2018 - 8:20pm
Productive Struggle for All: Differentiated Instruction Resource 11/27/2018 - 8:14pm
Rehumanizing the Mathematics Education of Students with Disabilities: Critical Perspectives on Research and Practice Resource 11/27/2018 - 8:10pm
Think-Pair-Show-Share to Increase Classroom Discourse Resource 11/27/2018 - 7:55pm
Fraction Activities and Assessments for Conceptual Teaching (FAACT) for Students with Learning Disabilities Poster 06/14/2018 - 12:42pm
Navigating “Disability”: Complexity and Small Environments Resource 05/02/2018 - 2:13pm
From Trajectories, Deficit, and Differences to Neurodiversity: The Case of Jim Resource 05/02/2018 - 2:08pm
Where is Difference? Processes of Mathematical Remediation through a Constructivist Lens Resource 05/02/2018 - 1:53pm
AERA 2017 Poster: Unit Coordination and Partitioning Activity of One Child With Mathematics Learning Disability: A Case Study Poster 05/18/2017 - 12:15pm
Evolution of Unit Fraction Conceptions in Two Fifth-Graders with a Learning Disability: An Exploratory Study Resource 02/08/2017 - 12:08pm
How to better understand the diverse mathematical thinking of learners Resource 01/15/2016 - 2:32pm
Exploratory Study of Informal Strategies for Equal Sharing Problems of Students With Learning Disabilities Resource 01/15/2016 - 2:13pm
Iteration: Unit Fraction Knowledge and the French Fry Tasks Resource 01/15/2016 - 2:01pm