Calc Co-evolution

Calc Co-evolution - The Co-Evolution of Calculators and...

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Unformatted text preview: The Co-Evolution of Calculators and High School Mathematics Dan Kennedy Baylor School Chattanooga, TN Change makes everyone less comfortable ..but we change because we must. Calculators have changed quite a bit in the last 20 years. And so has high school mathematics. Some people seem to think that pre-college mathematics is timeless. If it was important for our parents, how can it be unimportant today? But technology has been rendering our parents mathematics obsolete for decades. For example, consider log tables. Here is a 1928 College Board mathematics achievement exam. It looks a lot like todays college placement tests. But that is another talk. Notice that problem #7 is from the 1928 version of the Real World. You must find the angle of elevation of a balloon by using logarithms. In the old days (e.g. 1970 ), any good algebra book had a table of 5-place logarithms to solve problems like #7 which was posed in 1928 . log 1613 = log (1.613 10^3) = 3.20763 log 2871 = log (2.781 10^3) = 3.45803 ( 29 = =- 1613 Tan , so log tan 2871 log1613 log 2871-- 3.20763 3.45803 0.25040 = 9.74959 10 So log (tan ) = 9.74959 10. Now we go to a log trig table and look for 9.74959 in the L Tan column. We find some success on the 29 page. Since 9.74959 is two-thirds of the way between 9.74939 and 9.74969, we conclude that = 29 19 ' 40 " But that was then. This is now: And speaking of logarithms And do any surviving Algebra I teachers remember these? Theorem: ( b + c ) + ( c ) = b Statement Reason 1. b and c are real numbers Hypothesis 2. b + c is a real number Axiom of closure for addition 3. c is a real number Axiom of additive inverses 4. ( b + c ) + ( c ) = b + [ c + ( c )] Associative axiom of addition 5. c + c = 0 Axiom of additive inverses 6. b + [ c + ( c )] = b + 0 Substitution principle 7. b + 0 = b Additive axiom of 0 8. b + [ c + ( c )] = b Transitive property of equality 9. ( b + c ) + ( c ) = b Transitive property of equality A sobering thought: There are people walking the streets of your town right now who became convinced years ago that they could not do math -- because they could not do some things that we no longer teach today! And who defines what it means to do math? MATH TEACHERS! This a big difference between the ability to do mathematics and the ability to read! Someone who can read this sentence knows how to read. How about this sentence: Ontogeny recapitulates phylogeny. What does it mean to do mathematics?...
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Calc Co-evolution - The Co-Evolution of Calculators and...

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