**ERIC Number:**ED338496

**Record Type:**RIE

**Publication Date:**1991-Apr

**Pages:**33

**Abstractor:**N/A

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**N/A

Reasoning and Proof in Precalculus and Discrete Mathematics.

Thompson, Denisse R.

Precalculus and Discrete Mathematics (PDM) is the sixth and final course in the secondary mathematics curriculum developed by the University of Chicago (Illinois) School Mathematics Project. During the 1989-90 academic year, a formative evaluation of the third field-trial edition of PDM was conducted among a volunteer sample of 9 high schools with widely varying demographics across 8 states comprising a total of 180 students. Part of the evaluation focused on that portion of student achievement associated with mathematical proof in a nongeometric context, specifically content and/or process properties of the following: even and odd integers and divisibility, proof by contradiction, trigonometric identities, and proof using the principle of mathematical induction. Results of student success on these nongeometric proofs generally settled into three nonoverlapping categories: (1) success with proofs involving trigonometric identities extended to an 80% level, a result most likely due to the fact that trigonometry had been studied immediately prior to the evaluation; (2) roughly one-third of the students were able to find a counter-example to disprove a number theory statement--this is in line with the findings from the 1989 National Assessment of Educational Progress; and (3) students showed an enormous difficulty with indirect proofs, that is, proof by contradiction and proof by induction, a finding not completely unexpected due to the considered overemphasis on form rather than substance within the mathematics curriculum. For the most part, the errors that occurred in proof achievement were consistent across all nine schools, a finding that suggests that the teacher is not a significant variable in determining proof achievement. (JJK)

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

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**General Electric Foundation, Ossining, NY.

**Authoring Institution:**N/A

**Identifiers:**Discrete Mathematics; Number Theory; School Mathematics Project

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