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ERIC Number: EJ886399
Record Type: Journal
Publication Date: 2010-May
Pages: 7
Abstractor: ERIC
Reference Count: 0
ISSN: ISSN-1072-0839
The Whole Is the Sum of Its Parts
Bieda, Kristen N.
Mathematics Teaching in the Middle School, v15 n9 p540-546 May 2010
A math classroom is complex. Teachers navigate through a lesson using a variety of activities and tools that are designed to address students' needs and help them build conceptual understanding. Manipulatives, drawings, and other such concrete representations can help students explore mathematical ideas in physically grounded manifestations. Manipulatives can also be used to help generate remarkable change over time in students' justifications, but little is known about how explorations with manipulatives can influence their justifications. The use of manipulatives in mathematics instruction does not guarantee meaningful learning outcomes. That said, aligning various components of a lesson, including explorations with manipulatives, to support students' justifying and proving is important. This article focuses on presenting and discussing actual classroom scenarios of students who are using manipulatives to explore and justify mathematical ideas. The importance of aligning all aspects of proof-related instruction, from pattern generalization to conjecture validation, is highlighted to show that students can be prepared to generate justifications that are based on general statements. (Contains 6 figures.)
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:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Grade 6; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A