**ERIC Number:**ED332875

**Record Type:**RIE

**Publication Date:**1991-Apr

**Pages:**34

**Abstractor:**N/A

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**N/A

Developing a Pedagogically Useful Content Knowledge in Elementary Mathematics.

Peck, Donald M.; Connell, Michael L.

Elementary school teacher candidates typically enter their professional training with deficiencies in their conceptual understanding of the topics of elementary school mathematics and with a reliance upon procedural (algorithmic) approaches to the solutions of mathematical problems. If elementary school teacher candidates are expected to teach mathematics in a manner conducive to student conceptual development, then it is critical for the individual candidate to possess personal meanings for the topics of elementary school mathematics and to develop an understanding of the processes involved in student conceptual development. This report describes the pedagogy common to two mathematics methods courses designed to help teacher education students actively restructure their existing mathematical knowledge and expand their views of what understanding mathematics might involve. The teacher candidates are given the opportunity to restructure their own content knowledge using curriculum and instructional approaches similar to those which they will later hopefully use in their own classrooms. Data on mathematical content understandings (rational numbers, fractions, area, volume) and behavioral perceptions (anxiety, confidence, and justification patterns) were gathered from four undergraduate sections and one graduate section of the methods courses. These data indicate significant changes in candidates' mathematical understandings and views of pedagogy. Item analysis of content responses using Student-Problem Curve Theory shows that the candidates' conceptualization of content improves in focus over the course of the class, indicating a deeper level of knowledge structure. Preliminary analysis of structured interviews shows significant shifts in teacher candidates' conceptions of what mathematics is, their view of potential roles in instruction, and methods for evaluating students' success in mathematics relative to their original pre-class positions. A copy of the pretest is included. (37 references) (Author/JJK)

Descriptors: Cognitive Development, Cognitive Processes, Cognitive Structures, College Mathematics, Concept Formation, Elementary Education, Elementary School Mathematics, Elementary School Teachers, Higher Education, Instructional Effectiveness, Knowledge Base for Teaching, Mathematical Concepts, Mathematics Education, Mathematics Instruction, Mathematics Skills, Mathematics Teachers, Methods Courses, Preservice Teacher Education, Teacher Attitudes, Teacher Effectiveness, Teacher Expectations of Students, Teacher Response, Teacher Role, Teaching Skills

**Publication Type:**Reports - Research; Speeches/Meeting Papers

**Education Level:**N/A

**Audience:**Policymakers; Practitioners; Researchers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers:**Conceptual Approach; Conceptual Frameworks

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