Presents background information about Vygotskian theories. Describes Vygotsky's Zone of Proximal Development (ZPD). Discusses a model of attitude development that incorporates the ZPD, meta-awareness, the components of an attitude, and factors influencing attitude development. Suggests educational implications. (45 references) (MDH)

Ties together the educational threads of teaching thinking skills and improving the intellectual performance in deaf learners. Identifies six criteria for curriculum or research decisions related to teaching for higher-level problem solving. Applications of these ideas to mathematics are left to the reader. (MDH)

Describes Vygotsky's zones of proximal development, the importance of social interaction in learning through problem solving, and the benefits of modeling. Presents three implications for teaching and learning mathematics based on a teaching experiment focusing on these constructs. (MDH)

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)

Challenged is the traditional model for the transmission of mathematics in the elementary school classroom. An inquiry approach to learning mathematics is proposed and supported with results of a year long research project that exposed second graders to mathematical learning experiences using this approach. (MDH)

Discussed are some situations students face that result in cognitive conflict, possible sources of these conflicts, and strategies which students use to resolve, remove, or circumvent them. A global account for observed systematic errors is offered based on a general problem-solving rule called the "Matching Rule." (KR)

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)

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)