This newsletter describes an ongoing empirical field study involving a description and analysis of practical teaching situations aimed at describing the content and structure of pupils' frames of reference. The project takes the form of a series of case studies in classes of the 3-year lines of upper secondary schools in Sweden. The study seeks to…

Recent contributions from theory, research, and practice in second-language instruction are discussed in relation to mathematics education. Three methods of teaching and learning second languages are described--"Delayed Oral Production," the "Silent Way," and the "Counseling Learning/Community Language Learning." (KR)

Described are inconsistencies, definitions, and examples and their complex relationship which can be used to interpret students' reactions to the geometric tasks used to investigate inconsistencies in student thinking. Discusses the nature of definitions, the value of precise vocabulary, the use and limitations of prototypes, and the power of…

Discussed are inconsistencies and cognitive conflict with respect to current mathematical knowledge of students and how that knowledge might be modified is discussed. The inconsistencies that students generate for themselves and those produced by the teacher are described. (KR)

Advances in cognitive science have greatly increased our knowledge of how the human mind stores and uses information. That knowledge can be used to decompose curricular objectives so as to increase the specificity of instruction to a level of precision that should greatly enhance student writing. This article identifies some major types of…

Discussed are possible reasons behind the inconsistencies in the learning of calculus. Implicated are students' beliefs, mathematical paradigms including concept image and concept definition, language use, and curriculum sequencing. (KR)

Discussed are the issues of inconsistencies and compartmentalization and the use of inconsistencies in the classroom. Included are discussions on paradoxes, the naive student, logical reasoning ability, and the development of the students' cognitive structures. (KR)

Discusses a system of classification for students' inconsistent ideas in mathematics, the sources of students' mathematical inconsistency, and instructional strategies for helping students to resolve apparent learning inconsistencies. Language, curriculum, and instruction are included in the discussion. (KR)

Reports on an interview with Frances Rauscher, a research psychologist and musician who has studied the effects of music on the brain. Maintains that students who have studied music have enhanced spatial reasoning. Recommends that music education begin at younger ages. (CFR)