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ERIC Number: EJ1020163
Record Type: Journal
Publication Date: 2013-Dec
Pages: 8
Abstractor: ERIC
ISSN: ISSN-1073-5836
Mysterious Subtractions
Hillen, Amy F.; Watanabe, Tad
Teaching Children Mathematics, v20 n5 p294-301 Dec 2013
Recent documents suggest that all students, even young children, should have opportunities to engage in reasoning and proof (CCSSI 2010; NCTM 2000, 2006, 2009). One mathematical practice that is central to reasoning and proof is making conjectures (CCSSI 2010; NCTM 2000; Stylianides 2008). In the elementary grades, "formulating conjectures and assessing them on the basis of evidence should become the norm" (NCTM 2000, p. 188). When given opportunities to formulate conjectures, students will make conjectures that turn out to be true as well as those that turn out to be false. Even false ideas "often are opportunities for important mathematical discussions and discoveries" (NCTM 2000, p. 191). Therefore, teachers may not want to restrict their students' work to situations in which only true conjectures are formulated and may even want to intentionally set up situations in which students will likely formulate conjectures that turn out to be false. In this article, the authors share a task in a mathematical context that affords children opportunities to make conjectures and prove (or disprove) them. They also offer insights on teaching a 50-minute lesson centered on this task and suggest ways to extend the task to afford even more prospects for children to engage in reasoning and proof. They invite readers to consider how they might use or adapt the task and the enactment we describe for use with their own students.
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: Reports - Descriptive; Journal Articles
Education Level: Elementary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A