Quotes 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 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.
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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 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.
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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 if one does not know it nor help one if one does know it.
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Fran Lebowitz, Social Studies, Tips for Teens, 1981.
Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.
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R. P. Boas, Jr., If This Be Treason..., American Math Monthly, 64(1957), 247-249.
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 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.
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E. T. Bell, MATHEMATICS: Queen & Servant of Science, MAA Spectrum, 1987
Only one person in hundreds ever actually uses the common algebra he learned.
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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, sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more of mathematics.
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DeSoto Custom Sedan
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Table of Contents
• Real Numbers
• Fundamental Operations
• Factoring
• Fractions
• Linear Equations in One Unknown
• 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
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• Logarithms
• Binomial Theorem
• Mathematical Induction
• Inequalities
• Complex Numbers
• Complex Numbers
• Theory of Equations
• Permutations and Combinations
• Probability
• Determinants
• Infinite Series
• Partial Fractions
• The Mathematics of Investment
• Curve Fitting and Least Squares
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Table of Contents
• Algebraic Expressions, Models, Real Numbers
• Exponents and Scientific Notation
• Radical and Rational Exponents
• Polynomials
• 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
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• Linear Functions and Slope
• More on Slope
• Transformations of Functions
• Combinations and Composite Functions
• Inverse 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
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• Exponential Functions
• Logarithmic Functions
• Properties of Logarithms
• Exponential and Logarithmic Equations
• Exponential Growth and Decay
• 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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Approximating Roots Approximating Roots 39 6 3 6.2308
≈ + 13 ≈
Approximating Roots
Approximating Roots
Teaching Mathematics Teaching Mathematics
Historically
Historically
Discussion 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?
teach but you question why?
• What topics/procedures/ideas do you predict will someday no longer be taught…like square root algorithms?
What else?
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 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!
