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So why should we teach math?

Jerry Tuttle, Univ. of Phoenix

2018

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Math occupations pay well

2018

www.bls.gov/ooh/math/mathematicians-and-statisticians.htm#tab-8

But not everyone wants a math career

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Additional % income for each year of high school math

2018

Regression model, attempts to control for confounding variables; Old data, Calif only.

Math Matters. Heather Rose

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Math is part of culture

2018

“People who enjoy performing an activity don’t feel the need to question its worth.” Stewart.

Movies: Stand and Deliver, Good Will Hunting, A Beautiful Mind, The Imitation Game, Hidden Figures, many more.

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TV show Jeopardy has some math questions

2018

Final Jeopardy: 1930’s movies

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Maybe we should teach logic

2018

  1. What’s the joke? 1a. Is it funny?
  2. Is it logical?

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Think ahead, make a plan, carry it out, check results

2018

Maybe we should teach chess

Paul Morphy vs. Duke of Brunswick & Count Isouard, Paris,1858

Numerous studies correlate chess with problem-solving ability, HS math grades (Ferguson). “Chess is genuine math” (Hardy).

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We need to be able to evaluate the logic of news media, politicians, marketers, lawyers’ arguments

  • Logical fallacies seem persuasive because PR specialists research how to persuade us.
  • Examples: Appeals to popularity, emotion, ignorance. Hasty generalization. Circular reasoning.
  • Confusion of inverse: P(A|B) ≠ P(B|A).
  • Prosecutor’s Fallacy: If P(evidence | innocence) small, then P(I | E) small.

2018

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Math is about “expressing relationships in numerical, graphical, symbolic, verbal, and pictorial forms. … Math is the study of patterns.” Jo Boaler

Who studies patterns?

Art critic

Book, movie critic

Doctor

Math guy/gal

Police detective

Everyone else

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Patterns: In a movie, when an actor crosses a bridge, his life is about to make a major change. Fellner (movie critic)

2018

https://www.army.mil/article/198019/1st_sfg_a_bridging_the_gap

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Math patterns

  • Inductive reasoning: draw general conclusion from specific examples – sometimes how new math is created.
  • A Polya problem solving strategy.
  • Many patterns in Pascal’s Tri; ex: prime row no. divides every no. in row.
  • Online sequence encyclopedia oeis.org
  • Much of workplace involves searching for patterns in work numbers.

2018

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What do the numbers show?

  • News media, politicians, businesses quote lots of data, make charts.
  • “Students must comprehend others’ quantitative arguments in text, chart, and table, … discern differences in source quality, … and navigate ambiguities of incomplete information and contradictory evidence.” N. Grawe
  • Politicians have been known to misuse data and graphs to mislead. Really?

2018

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Has Student Loan Debt increased sharply in recent years?

2018

1st graph from politician has hard-to-read axes, but is believed to start at 2000, with shaded section as 2010-2014.

2nd graph is same data for 2003-2012.

P. Bump, Washington Post, 2016

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It’s so easy to create charts, do regressions, calculate correlations

2018

Tyler Vigen, Spurious Correlations, Tylerigen.com/iew_correlation?id=97

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Workers “need to reason and problem solve, flexibly applying methods to new situations.” Boaler

Too many ridiculous problems, no real-world value.

Too many ‘plug and chug’.

2018

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Summary of Book/Movie Moneyball

2018

Much more data, computing power than ever

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Math is used more places than ever; the non-math person needs to understand it, make decisions.

Math models are used to predict:

What you’ll buy next

Movie profit before movie is released

Quality of wine vintage before it is aged

Your auto insurance claim from your credit score; is this fair?

2018

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Here is the math surprise from my 42 year actuarial career:

The complexity of the math I needed rose dramatically over the years, as my career and my profession advanced. But,

The complexity of the math needed by my non-math major co-workers rose too, because they had to understand and make decisions from my work.

2018

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So why do we make you take math?

2018

20 of 20

Bibliography

  • Boaler, J. (2008). What’s math got to do with it? Viking Penguin. NY.
  • Bump, P. (June 3, 2016). The Washington Post. https://www.washingtonpost.com/news/the-fix/wp/2016/06/03/fact-checking-donald-trumps-nine-graph-tweet-proving-that-obama-has-failed/?utm-term=.16516a9ba44e
  • Fellner, A.C. (Apr. 9, 2018). Private conversation.
  • Ferguson, R.C. (nd.) Teacher’s guide: research and benefits of chess. http://www.shatranj.us/files/BenefitsofChess.pdf
  • Grawe, N. (2011). Beyond math skills: Measuring quantitative reasoning in context. New Directions for Institutional Research, 2011 (149), 41-52.
  • Hardy, G.H. A mathematician’s apology. (2005). http://www.math.ualberta.ca/~mss/misc/A%20Mathematician's%20Apology.pdf
  • Rose, H. and Betts, J.R. (2001). The links between high school curriculum, college graduation, and earnings. Public Policy Institute of California.
  • Stewart, I. (2006). Letters to a young mathematician. Basic Books. NY, NY.

2018