1. Technology

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

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

4. 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.

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

6. Electromechanical Calculators
Early 1960’s
Large machines, small displays and simple keyboards.
For detailed information on slide rules to eletromechanical calculators:

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

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

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

10. 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.

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

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

13. 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.

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

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

16. 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?

17. What technology? What can it do?

18. 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

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

20. Distance Learning
Teleconference
Web Pages
Videos

21. Let’s Get Started!