Based on suggestions of participants at the second annual Instructional Methods Forum held in June 1989, the monograph considers cognitive-based approaches to teaching mathematics to students with learning problems. It addresses identification of characteristics of successful cognitive approaches and the role of media and materials. An introductory chapter looks at possible reasons for United States students' difficulties with mathematics and proposes that cognitive-based approaches be used. The second chapter looks at mathematical learning among students with disabilities. Cognitive-based principles for teaching mathematics are presented in chapter 3, including findings from research and a taxonomy of word problem types. Chapter 4 offers two examples of such approaches including the Cognitively Guided Instruction program (which improves teacher understanding of how children learn mathematics) and the Verbal Problem Solving Among the Mildly Handicapped Project (which uses specially designed materials in its problem-solving focus). The fifth chapter considers instructional components of cognitive-based mathematics concerned with both content and teaching methods. The sixth chapter considers the role of the teacher in cognitive-oriented programs, and a summary chapter suggests areas for further research. Appended are a list of the forum participants, sample records from the instructional materials database of the Information Center for Special Education Media and Materials, and a bibliography of approximately 170 items. (DB)