The thinking-out-loud procedure provides teachers with an excellent mechanism for collecting information about students' thought processes and affective states during problem solving. Mathematics teachers can implement this process by modeling it during whole-class problem-solving sessions, proceeding slowly and encouragingly, working with small…

The advantages of using interviews to diagnose children's needs are discussed. General interview strategies and specific questions for gaining insight into a student's understanding of the four operations are presented. (MNS)

In teaching mathematics, diagnosis should form the basis of any instructional plan and is essential in an individualized approach. (Author)

Diagnosis of student errors in mathematics is discussed and 12 guidelines for effective diagnostic procedures are presented. (MK)

Diagnostic evaluation is a major way to help students overcome errors. How such evaluation can be done is discussed, with comments on what should be checked and recorded by the teacher. (MNS)

Requirements for assessment under Public Law 94-142, the development of an Individualized Education Program for each handicapped child, the least restrictive environment, handicapping conditions, implementation procedures, diagnostic teaching strategies and learning conditions, teaching ideas, and a format for diagnostic interviews are each…

Four informal assessment techniques to detect student mistakes in math, increase motivation, and improve achievement include the following: building models and generating word problems, thinking aloud, building mathematical sentences, and making mathematical sentences to answer questions in word problems. (DB)

An overview is provided of the curriculum and instructional practices in general and for handicapped learners. Diagnostic teaching and other features of good instruction are reviewed. (MNS)

A scheme for diagnostic teaching is discussed, and aspects of the approach are illustrated from three teaching experiments. Instruction that aims towards free and relaxed discussion of single points of difficulty or conflicts and towards pupils seeking to learn how a particular system works is promoted. (MP)

Difficulties experienced by algebra students are listed, with comments on what can be done and some implications for teaching. (MNS)

Teachers are encouraged to use the results of assessments to plan specific educational programs. Information is provided about the nature of diagnostic testing, with both content and process error analysis discussed. The nature of prescriptive teaching is detailed to show how to devise remediate activities after student problems are analyzed. (MP)

Research is reviewed in four categories: teachers' beliefs about mathematics, mathematics learning, and mathematics teaching, and some other important teacher beliefs. Reflections are also included. (MNS)

Why students have difficulty with a proof (such as Cantor's) is discussed, with the focus on proof by contradiction. Methods may fail due to the difficulty of the concept and lack of understanding of how students are thinking. (MNS)

Analysis of errors children make is modeled both with and without computers. Patterns of thinking are traced for a fifth grader, with the discussion focused on getting clues for remedial instruction by analyzing the dialog. (MNS)

An experiment is described which started with exploratory interviews, evolved to design and administration of diagnostic tests, and led to the preparation and use of calculator-enriched teaching materials. (MP)