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The paper explains both inductive and deductive reasoning and focuses on deductive reasoning, also known in mathematics as proof. The paper looks at the most common format for explaining proofs and explores why students can hold incorrect conceptions of proof. Finally, the paper addresses how teachers can teach proofs, particularly in geometry, and describes how a visual system can be utilized.
From the Paper:"There are two basic kinds of reasoning that are important for all people, no matter what they are doing with or in their lives, and that holds true for both education and personal/career experience (Discovering, 2009). These two kinds of reasoning are inductive and deductive. Inductive reasoning is used to identify visual and numerical patterns so that the student can make predictions based on those patterns. Deductive reasoning explains why the patterns are true. In geometry, students learn about angle measurements in both intersecting and parallel lines and make assumptions about the measurements and their relationships to each other. Logical arguments are given so that a student may learn how to explain why these conjectures are true (Discovering, 2009).
"Inductive reasoning involves cause and effect based on personal experiences of the student. For example, every time you go outside in the rain without an umbrella, you get wet. The inductive reasoning used to draw the conclusions from repeated experiences is inductive, however in mathematics the answer is not always so concrete (Discovering, 2009). For this reason, mathematicians can use inductive reasoning to find out what could be true, and because there is an element of possibility involved, inductive reasoning is not foolproof, so mathematicians do not generally use inductive reasoning to explore factual problems."
Sample of Sources Used:
- Discovering Geometry: A Guide for Parents. 2008, Key Curriculum Press. Retrieved October 19, 2009 at http://www.keymath.com/documents/dg4/GP/DG4_GP_02.pdf
- Herbst, Patricio G. Establishing a Custom of Proving in American School Geometry: Evolution of the Two-Column Proof in the Early Twentieth Century, Educational Studies in Mathematics, Vol. 49, No. 3 (2002), pp. 283-312,
Cite this Term Paper:
Geometry Proofs (2012, April 26) Retrieved June 18, 2013, from http://www.academon.com/term-paper/geometry-proofs-150834/
"Geometry Proofs" 26 April 2012. Web. 18 June. 2013. <http://www.academon.com/term-paper/geometry-proofs-150834/>