This five-year project documented fraction learning trajectories of students with learning disabilities (LD) and difficulties (MD). From this work, we constructed an adaptive instructional program with a clinical interview, four task sets, and responsive pedagogies to build from students’ strengths (i.e., uncover students’ fractional thinking, generate instruction to support access and advancement of reasoning).
Historically, the qualitative complexity of learning disabilities (LD) led to deficit depictions of students and a continued explicit instructional focus on quick and accurate performance as a proxy for understanding (Woodward, 2004). However, we argue that ambiguity of cognitive effects on these children’s capacity to learn and the qualitative complexity of LD emphasizes a need to move away from questioning whether students with LD are capable of constructing fraction knowledge and toward (a) uncovering the mathematical understandings that students with LD do have, (b) how prior knowledge and skills interplay with learning, and (c) how construction of fractional knowledge occurs and can be nurtured through the learning process.
The FAACT project is grounded in an instructional theory called “Small Environments” (Hunt et al, 2019, 2020; Hunt & Silva, 2020). “Small Environments” defines learning as adaptation as opposed to remediation. It is proposed as a student-centered innovation to traditional, teacher-directed interventions (supplementary and intensive). Learning happens through a complex adaption of prior experience with a students’ interactions with their environment. Adaptation is first constructed through goal-driven activity and second through bi-directional reasoning and sense making started by the student and facilitated by the teacher as a response to the student’s thinking.
Students’ trajectories of conceptual advance in fractions are similar to yet nuanced from those documented in mathematics education. They are non-linear and evident of strengths and challenges that every person utilizes to make sense. Access to and advancement of knowledge can be facilitated by supporting students to notice and reflect upon their reasoning. Restating/reshowing students’ explanations and their actions supports students' noticing. Pressing for justification and connections between old and newly constructed reasoning supports students’ reflection; students consider how and why the new knowledge is useful and works toward richer understandings. Prediction supports students to reflect across problems and solidify their reasoning.