Teaching Constant Rate-of-Change Problem-Solving to Secondary Students With or at Risk of Learning Disabilities.

Rate of change (i.e., slope) is a critical mathematics concept for success in everyday life, academics, and professional careers. Students with or at risk of learning disabilities struggle with solving rate-of-change problems, especially word problems. Interventions that incorporate representations and problem-solving strategies are effective for improving the word problem-solving performance of students with disabilities. This multiple-probe, multiple-baseline, single-case design study evaluated the effects of an intervention that included an integrated, concrete-representational-abstract teaching framework with an embedded problem-solving strategy (POD Check) on students' rate-of-change word problem-solving performance. The intervention was delivered virtually via video conferencing technology. Four middle- and high-school students with or at risk of mathematics learning disabilities in the Intermountain West participated in the intervention. Results indicate evidence of a functional relation between the intervention and students' word problem-solving performance, and effects were maintained 2-4 weeks after the intervention. The findings of this study provide implications for mathematics intervention research and practice for students with learning disabilities.

Features of Direct Instruction: Content Analysis.

The goal of Direct Instruction (DI) is to teach content as effectively and efficiently as possible. To do this, instructional designers must identify generative relations or strategies that allow the learner to respond correctly to untaught situations. The purpose of content analysis is to identify generative relations in the domain to be taught and arrange the content in such a way that it supports maximally generative instruction. This article explains the role of content analysis in developing DI programs and provides examples and nonexamples of content analysis in five content domains: spelling, basic arithmetic facts, earth science, basic language, and narrative language. It includes a brief sketch of a general methods of conducting a content analysis. It concludes that content analysis is the foundation upon which generative instruction is built and that instructional designers could produce more effective, efficient, and powerful programs by attending explicitly and carefully to content analysis.

Features of Direct Instruction: Interactive Lessons.

Direct Instruction (DI) teaches challenging academic content to a range of diverse learners. In order to do so, DI includes a complex system for organizing and directing teacher-student interactions to maximize learning. This system includes: instructional formats that specify the interactions between teacher and student, flexible skills-based groupings, active student responding, responsive interactions between students and teachers, ongoing data-based decision making, and mastery teaching. In this article, we describe each of these main features of the system, define their functions, reveal how they are interwoven throughout all DI lessons, and provide specific examples of their application during instruction. Our goal is to describe and clarify critical features of DI lesson presentation and teacher-student interaction so that instructional designers, teachers, and other practitioners can use existing DI programs effectively and include these features in newly developed programs.