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Mysterious Subtraction



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 toreasoning 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.


Reprinted with permission from Mathematics Teacher: Learning and Teaching PK-12, copyright 2014, by the National Council of Teachers of Mathematics. All rights reserved.