Technology

The history of mathematics goes a long way back with devices and methods of calculation.

The Ancient Abacus Counting boards -500 B.C. Today’s abacus - 1200 A.D. - China Not a calculator but a recorder

Logarithms and the Slide Rule 1614 John Napier discovered the logarithm Edmund Gunter’s number line William Oughtred takes two Gunter's lines making them slide relative to each other. From the late 17th century, the slide rule was the tool of choice for the next three hundred years.

Mechanical Calculating Machines Adding machines -17th century The comptometer (shown here) Introduced in the 1800’s.

Electromechanical Calculators Early 1960’s Large machines, small displays and simple keyboards. For detailed information on slide rules to eletromechanical calculators: http://www.hpmuseum.org/prehp.htm

Very large computers The Army’s ENIAC- the world's first electronic digital computer 1800 sq. feet of space 18,000 vacuum tubes Popular Mechanics quote March 1949

Then the handheld calculator Late 1960's - electronic four function fixed point calculators were brand new Today’s graphing calculators are mini-math-computers

The electronic computer First mini computers early 1960’s The first microprocessor the Intel 4004 early 1970’s Today’s amazing race

Technology isn’t just machinery From Dialogues Concerning Two New Sciences, Galileo, 17th Century: Theorem 1: If a moving particle, carried uniformly at constant speed, traverses two distances, then the time intervals required are to each other in the ratio of these distances.

In the Early17th Century Galileo required a full page to prove this theorem

Present Day We can state the basic relationships of distance (d) , rate (r), time (t) for two motions as:

Thanks to Algebra We can prove Galileo’s Theorem 1 with one sentence: In the case r1 = r2, the r terms cancel, leaving d1/d2 = t1/t2. Algebra is the technology which gives us the means to do this easy manipulation of symbols to prove the theorem.

But with it comes many questions! Technology is here! But with it comes many questions!

Questions like… Now that we have technology, what do we do with it???? How is technology changing the way mathematics is taught???

And... What is important to include in the curriculum? What skills need to be taught and what can be left behind? Should calculators/computers be allowed for tests? How do we teach problem solving?

What technology? What can it do?

Scientific Calculators Graphing Calculators large and small numbers exponents and roots logarithms sines and cosines Graphing Calculators graphing equations solving equations solving systems derivatives and integrals

Computers Spreadsheets Mathematics computation software Self-directed individualized learning The Internet Web pages and e-mail Presentations

Distance Learning Teleconference Web Pages Videos

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