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Reasoning Activities Using 0.999... = 1 in Developmental Mathematics Chris L. Yuen, CLYUEN@buffalo.edu SUNY University at Buffalo November 13, 2014

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Cross Examination O Inherent the Wind (1960) https://www.youtube.com/watch?v=l5Kdc0 LLSW8 O Witness for the Prosecution (1957) https://www.youtube.com/watch?v=Fq3UK 04pNrY https://www.youtube.com/watch?v=Fq3UK 04pNrY O Legally Blonde (2001) Start the clip at 3:14 https://www.youtube.com/watch?v=ytWGiO uzpe4

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.999… as an Object of Interest O Why use.999…? Yopp et al. (2011) studied in-service teachers’ perception toward.999…

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Another Finding…

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More findings from Yopp

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And More… O Some teachers modify “truth” to fit their subjective beliefs. O Some teachers dismiss conflict as unimportant or uninteresting as it relates to their teaching. O Some teachers teach that approximations are good enough and “small” does not matter.

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Developmental Math O Much instruction directed to development math is pedagogically delivered differently from higher math. O Emphasis of procedures O Emphasis of formulas O Emphasis of performing well on traditional tests and exams

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Proving.999… = 1

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A Multiplication Proof

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An algebraic proof

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Proof by Limit

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How to Engage Students? O The proofs alone are not going to motivate students. O Developmental students often do not know much about the concepts of “limits.” O One can show an application of proof in legal arguments – Reductio ad absurdum O So, involving a trial for the students to craft arguments may be a productive alternative.

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What is Reductio ad absurdum? O Big Bang Theory https://www.youtube.com/watch?v=ytWGiOuz pe4 https://www.youtube.com/watch?v=ytWGiOuz pe4

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Reductio ad absurdum O Reduction to absurdity O To demonstrate a statement is true by showing that a false, untenable, or absurd result follows from its denial O This sounds very much like “Proof by Contradiction

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The Trial

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Analysis of the Activity O The trial encompasses all the proofs that a developmental mathematics student could comprehend. O The trial co-create mathematical discourse with students in a social manner, as opposed to proving a mathematical fact in a solitary setting. O Mathematics can be system/postulate specific, and the court room setting is analogous to a specific system.

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Application

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Questions/Comments Contact Information: Chris L. Yuen, Ed.D., CLYUEN@buffalo.eduCLYUEN@buffalo.edu EOC Assistant Professor of Mathematics University at Buffalo Educational Opportunity Center 555 Ellicott Street Buffalo, NY 14203

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MENTAL MATH Adding Facts to 5 1 + 1 = 2 - 1 = 1 + 2 =

MENTAL MATH Adding Facts to 5 1 + 1 = 2 - 1 = 1 + 2 =

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