ERIC Number: EJ1339257
Record Type: Journal
Publication Date: 2021
Pages: 29
Abstractor: As Provided
ISBN: N/A
ISSN: EISSN-2692-241X
EISSN: N/A
General Proof Tasks Provide Opportunities for Varied Forms of Reasoning about the Domain of Mathematical Claims
Electronic Journal for Research in Science & Mathematics Education, v25 n4 p42-70 2021
Proofs are attempts to conclusively demonstrate the validity of the claim for all cases indicated within its domain, which implies that proving should involve thoughtful consideration of the domain. This study analyzed the enactment of three general claim tasks, or tasks where the domain of the claim referred to an infinite number of cases, that were used during an introduction-to-proof teaching experiment with 10 ninth grade students. We analyzed the tasks in terms of the opportunities students experienced to engage in reasoning-and-proving and attend to the domain of the claims. The use of general claim tasks provided students with opportunities to engage in varied reasoning-and-proving activities, including forms not typically found in textbooks. Students' attention to the domain of the claims increased over the course of study as a result of the teacher-researcher's continued focus on this aspect of the tasks, although their attention did not always encompass all cases within the domain. By making the domain of mathematical claims a central focus, we emphasize its important role in the reasoning-and-proving opportunities afforded to students and contribute to an understanding of students' early interpretations of this aspect of proof tasks.
Descriptors: Secondary School Mathematics, Secondary School Students, Mathematics Skills, Mathematical Logic, Grade 9, Abstract Reasoning, Attention
Southwestern University and Texas Christian University. TCU Box 297900, Fort Worth, TX 76129. Tel: 817-257-6115; e-mail: ICRSME.Consultation@gmail.com; Web site: http://ejrsme.icrsme.com
Publication Type: Journal Articles; Reports - Research
Education Level: Secondary Education; Grade 9; High Schools; Junior High Schools; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A