**ERIC Number:**ED335215

**Record Type:**RIE

**Publication Date:**1991-Apr

**Pages:**24

**Abstractor:**N/A

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**N/A

A Model for Inferring Components of Belief Systems by Interpreting the Content and Context Cues Used by Students to Situate Mathematical Tasks.

Kouba, Vicky L.; McDonald, Janet L.

Confrontation with a mathematical task causes a student to focus initial attention upon particular content and context cues based upon that student's belief system; the student assigns subsequent meaning to that task based upon previous mathematical experience and knowledge. In order to make effective use of students' belief systems, educators need delineations both of the components of those systems and of the interactions of those systems with students' cognition. A model is presented for the inference of the positive and negative components of students' belief systems by interpretation of the content and the context cues that students use within their mathematical identification and construction techniques. Three assumptions that parallel those concerning teachers' belief systems are noted: (1) notions and beliefs are implicit within responses to questions or issues related to mathematical tasks and hence can be identified and described; (2) some beliefs can impede effective and efficient mathematical understanding and performance; and (3) eventually, educators may be able to modify instruction based upon knowledge of the components of students' belief systems. (33 references) (JJK)

Descriptors: Beliefs, Cognitive Development, Context Effect, Cues, Elementary School Mathematics, Elementary Secondary Education, Learning Processes, Mathematical Linguistics, Mathematics Education, Mathematics Instruction, Mathematics Teachers, Performance Factors, Secondary School Mathematics, Teaching Methods

**Publication Type:**Information Analyses; Speeches/Meeting Papers

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers:**Constructivist Theory; Mathematics Education Research

**Note:**Paper presented at the Annual Meeting of the American Educational Research Association (Chicago, IL, April 3-7, 1991).