A focus on elementary number sense and operations for students with mathematics learning disabilities (MLD) has the potential to change lifelong learning outcomes for these students and other students who struggle with the subject. In addition, addressing the issues around formative assessment will promote adaptive expertise for teachers and learning and knowledge transfer for students. To produce useful and interpretable data for teachers, assessments should be aligned with a model of student cognition that is coherent, focused, and interconnected with learning objectives. Learning progressions in this domain can inform the design of assessments that scaffold learning, rather than merely measure it, assist teachers in understanding how knowledge and skill increases in sophistication from elementary to advanced levels, and suggest a learning trajectory along which students may be expected to progress.

 

Accordingly, we propose to develop theoretically grounded and empirically validated learning progressions and assessments to evaluate and support learning of pre-algebraic concepts, specifically number sense and operations for whole numbers and elementary fractions, for elementary and early middle school students with MLD. Our purpose is to ultimately increase the capacity of teachers to use assessment data to understand the particular source of a student’s difficulties with math and to then design individualized instruction to address those needs.