Maureen Grady

Research on Mathematics Instruction with Students with Significant Cognitive Disabilities: Has Anything Changed?.

In 2008, Browder and colleagues published a meta-analysis on mathematics instruction for learners with significant cognitive disabilities and found that most skills taught to these students were only from two of the five strands recommended by the National Council for Teachers of Mathematics (i.e., Number and Operations, and Measurement). A review of the literature since Browder et al. yielded an additional 29 studies. When results from both reviews were compared, a greater percentage of studies taught skills from three strands (i.e., Number and Operations, Geometry, and Algebra), whereas the percentage teaching skills from the Measurement strand decreased and the percentage teaching skills from the Data Analysis and Probability strand was unchanged. In addition, a systematic evaluation of the studies’ instructional components found evidence to support the use of systematic instruction, in vivo instruction, system of least prompts strategy, constant time delay strategy, and task-analytic instruction as evidence-based practices for teaching mathematics to learners with significant cognitive disabilities. Implications for practice include the use of systematic instruction and in vivo procedures, the need for practitioners to have a deep understanding of mathematics, and the importance of relevancy when teaching a variety of mathematics skills.

A Processes Lens on a Beginning Teacher’s Personal and Classroom Mathematics

This study examines the relationship between mathematical knowledge—evidenced by a teacher’s engagement in mathematical processes and actions on the products of those processes—displayed by a beginning secondary mathematics teacher (Fiona) in her personal mathematical problem solving and in her classroom instruction. This process and action approach involved analysis of Fiona’s use of four mathematical process/product pairs (representing/representation, justifying/justification, generalizing/generalization, and defining/definition). Two themes arose in the analysis of interview and classroom observation data: (a) Despite demonstrating the ability to do so, Fiona did not regularly engage in processes in her personal mathematics or classroom mathematics, and (b) Fiona focused on selected features of a product or mathematical object rather than attending to a sufficient set of relevant features. These themes suggest a treatment of mathematics as not entirely connected that limited both Fiona’s own problem solving and her students’ mathematical opportunities.