ERIC Number: EJ1044625
Record Type: Journal
Publication Date: 2014-Oct
Reference Count: 9
Reasoning and Sense Making with Pythagoras
Roscoe, Matt B.
Mathematics Teacher, v108 n3 p176-182 Oct 2014
In 1996, a new proof of the Pythagorean theorem appeared in the "College Mathematics Journal" (Burk 1996). The occurrence is, perhaps, not especially notable given the fact that proofs of the Pythagorean theorem are numerous in the study of mathematics. Elisha S. Loomis in his treatise on the subject, "The Pythagorean Proposition" (1968), presents more than 350 unique proofs. What is notable about Burk's discovery is that his proof provides mathematics students who have not been exposed to the theorem opportunities to make connections among a rich set of mathematical topics that all precede the presentation of the Pythagorean theorem in the Common Core State Standards (2010). The intent of this article is to demonstrate the connections that Burk's approach to the Pythagorean theorem offers and to make a case for its consideration as a new vehicle for students to arrive at a deep understanding of this venerable theorem.
Descriptors: Geometric Concepts, Mathematical Logic, Validity, Mathematics Instruction, Teaching Methods, Concept Formation, Secondary School Mathematics, Middle Schools, High Schools, Preservice Teacher Education
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: firstname.lastname@example.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Evaluative
Education Level: Secondary Education; Middle Schools; Junior High Schools; High Schools; Higher Education; Postsecondary Education
Authoring Institution: N/A