During the three years which I spent at

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2 Quotes Ron Aharoni, a math professor at Technion, Israel, in the Forward to Arithmetic for Parents (2007), admits that most of the adults make do without mathematics: Most adults have long buried their memories of studying mathematics. All they really want is to forget the trauma. They accept their past incomprehension as a tolerable, albeit painful, fact. "You don't really need to know mathematics," they console themselves. Until one day the need does arise and the old anxieties resurface. This happens when their child begins dealing with the same experiences.

3 Quotes In autobiographical recollections that he wrote in 1876 for his children, Charles Darwin expressed himself (Dr. Euler's Fabulous Formula, p. 11) as follows: During the three years which I spent at Cambridge my time was wasted, as far as academical studies were concerned... I attempted mathematics, and even went during the summer of 1828 with a private tutor... but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.

4 Quotes J. B. Mencken, De Chralataneria eruditorium, 1715 (quoted in C. Fadiman, The Mathematical Magpie, p. 256): Mathematics contains much that will neither hurt one if one does not know it nor help one if one does know it.

5 Quotes Fran Lebowitz, Social Studies, Tips for Teens, Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.

6 Quotes R. P. Boas, Jr., If This Be Treason..., American Math Monthly, 64(1957), When I was teaching mathematics to future naval officers during the war, I was told that the Navy had found that the men who had studied calculus made better line officers than men who had not studied calculus. Nothing is clearer (it was clear even to the Navy) than that a line officer never has the slightest use for calculus.

7 Quotes E. T. Bell, MATHEMATICS: Queen & Servant of Science, MAA Spectrum, 1987 Only one person in hundreds ever actually uses the common algebra he learned.

8 Quotes B. Russell, Autobiography, v1, G.Allen & Unwin, LTD, 1967, p 43 There was a footpath leading across fields to New Southgate, and I used to go there alone to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more of mathematics.

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13 DeSoto Custom Sedan 1951

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15 1951 Table of Contents Real Numbers Fundamental Operations Factoring Fractions Linear Equations in One Unknown Functions and Their Graphs Linear Functions and Their Graphs Systems of Linear Equations Exponents and Radicals Quadratic Equations Quadratic Equations in Two Unknowns Variation, Ratio, and Proportion Progressions

16 1951 Table of Contents Logarithms Binomial Theorem Mathematical Induction Inequalities Complex Numbers Theory of Equations Permutations and Combinations Probability Determinants Infinite Series Partial Fractions The Mathematics of Investment Curve Fitting and Least Squares

17 2011 Table of Contents Algebraic Expressions, Models, Real Numbers Exponents and Scientific Notation Radical and Rational Exponents Polynomials Factoring Polynomials Rational Expressions Graphs and Graphing Utilities Linear and Rational Equations Models and Applications Complex Numbers Quadratic Equations Linear and Absolute Value Inequalities Basic Functions and Graphs More on Functions and Graphs

18 2011 Table of Contents Linear Functions and Slope More on Slope Transformations of Functions Combinations and Composite Functions Inverse Functions Distance and Midpoint Formulas Quadratic Functions Polynomial Functions and Graphs Dividing Polynomials: Remainder and Factor Theorems Zeros of Polynomial Functions Rational Functions and Graphs Polynomial and Rational Inequalities Modeling using Variation

19 2011 Table of Contents Exponential Functions Logarithmic Functions Properties of Logarithms Exponential and Logarithmic Equations Exponential Growth and Decay Systems of Linear Equations 2 Variables Systems of Linear Equations 3 Variables Partial Fractions Systems of Inequalities Linear Programming Matrices and Determinants Conic Sections Sequences, Induction, Probability

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22 Approximating Roots

23 Approximating Roots

24 Teaching Mathematics Historically

25 Discussion Discuss with a partner and be prepared to share What topics/procedures/ideas did you used to teach that you no longer teach? What topics/procedures/ideas do you currently teach but you question why? What topics/procedures/ideas do you predict will someday no longer be taught like square root algorithms?

26 What else? What sacred ground can we trample on? o Finding roots? o Graphing functions by hand? o Simplifying derivatives? o Computing derivatives? o Computing integrals? o Simplifying expressions? o Solving equations? Note that the availability of CAS is ubiquitous and free! o Handheld calculators o wolframalpha.com o Smart phones o More!

27 The Bottom Line is it 1951?

28 or 2011?