Considered are two commonly used techniques, the interview and word association techniques. Highlighted is a third technique called the repertory grid. This third technique can be used to interpret students' knowledge based on an explicit, psychological theory of human behavior. (Author/CW)

Undergraduates in an abstract algebra course were interviewed to see how they learned the concept of isomorphism. Analysis showed students used step-by-step procedures, exhibited various degrees of personification in their language, and chose properties they perceived as simpler. (MKR)

Documents the patterns of coherence and persistence in energy conceptions. Describes the derivation of the Interview Vee technique and the procedure for putting an interview on the Vee. Discusses the production of Vee maps to help understand childrens' learning of concepts. (CW)

Reports a study designed to identify 9 and 11 year olds' ways of drawing nets of solids and to provide opportunities for them to reflect on their models in whole class discussions. Results indicated that children's views of solids' nets progressed from more global and holistic to more quantitative and analytic. (MDH)

Reviews recent research in the area of mathematical understanding and compares and contrasts it with a model formulated for the growth of understanding. Uses the analysis of a transcript from an interview with an eight-year-old boy to illustrate the power of the model to describe and map the growth of his mathematical understanding. (18…

Kindergarten (n=30) and grade 1 (n=15) students of contrasting socioeconomic backgrounds were interviewed to assess their knowledge of number word sequences and spatial patterns and their ability to recognize numerals and use counting to establish numerosity of visible and screened collections. Findings indicate greater variation in abilities…

Examines whether participation in physical experiments together with social interaction with adults and school-mates favor the development of causal knowledge and the understanding of a complex physical subject. Concludes that the treatments can lead students to give up pre-causal explanations and to resort to physical ones. (Author/YP)

Interviews with 72 mixed ability students, aged 7 to 12, about arithmetic problem-solving strategies, indicated that the preference between procedural and deductive strategies becomes a divergent reality across ability levels. Among the conclusions is that more able children tend to be doing a qualitatively different sort of mathematics than their…

Investigated the upper limits of (n=22) seventh-grade students' informal processes in solving first degree equations in one unknown prior to instruction. Results indicated the existence of a cognitive gap between arithmetic and algebra characterized as the students' inability to operate spontaneously with or on the unknown. (37 references)…

Sex differences on Perry's stages of epistemological development were investigated in a study of 100 freshmen (50 men and 50 women) at a large midwestern university. A semi-structured interview probed six domains related to Perry's theory, including the role of the learner, instructor, and peers in the learning situation, the question of…

Videotaped interviews of 29 Australian students from grades 1-3 were analyzed to assess and compare the processing loads of mathematical representations and strategies used by teachers and children to learn the concept of place value. Results indicated that some representations and strategies impose an unnecessary processing load that can…

Two naturalistic research studies observed 45 eleventh grade students carrying out research paper assignments, and a third such study focused on 26 third grade students. The studies took place in Alberta (Canada) in 1993, Texas in 1996, and Washington state in 1999. From data analyzed in the interviews and written documents, the initial findings…