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Comprehensive School of Mathematics Project (CSMP)

Comprehensive School of Mathematics Project (CSMP). By James Matte, Stephanie Myers Christopher Pollard MED 600- Fall 2013. What is CSMP?. The Project is for both primary and intermediate grades Basic program Harold Jacobs authored many books which brought this project to life.

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Comprehensive School of Mathematics Project (CSMP)

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  1. Comprehensive School of Mathematics Project (CSMP) By James Matte, Stephanie Myers Christopher Pollard MED 600- Fall 2013

  2. What is CSMP? • The Project is for both primary and intermediate grades • Basic program • Harold Jacobs authored many books which brought this project to life.

  3. CSMP History • Established in 1966 under Burt Kaufman • Originally affiliated with Southern Illinois University • First programs for 7-12 called Elements of Mathematics • Focused on highly individualized instruction • Frederque Papy • Mini-computer

  4. Addition with Jacobs • Addition began by demonstrating opposites • Dark circles represented negative numbers, white circles represent positive numbers Positive Numbers:Negative Numbers: • Addition used matching to solve problems • Negative match to positive and whatever is left over would be your answer. • Antiparticles and ordinary particles

  5. Same Sign Addition

  6. Different Sign Addition

  7. Subtraction with Jacobs

  8. Subtraction with Jacobs • Similar to addition • Positive numbers are represented by hollow circles and negative numbers are represented by solid circles • Adding pairs of particles and antiparticles because they cancel each other out.

  9. Let’s Consider the Problem from the Cartoon: Problem: • Thinking in terms of particles: We have 4 positive particles: • This may seem impossible but if we add two pairs of particles and antiparticles to the picture, we’ll have: • Then we take away 6 positive particles and get: • Therefore, the answer is -2

  10. Example of Subtraction

  11. Another Example of Subtraction

  12. Eli the Elephant • Introduction story to Comprehensive School Mathematics Program • Eli had a problem, he liked to have peanuts for lunch. He normally had his Old Favorite peanuts but the supermarket introduced a New Style peanut. • The problem was that when he put them on the same plate they would disappear before he had time to eat them. • He went home and did some experiments to find out what was happening. • He discovered that when an Old Favorite peanut and a New Style peanut were on the same plate they disappeared two by two

  13. Eli’s Conclusions Experiment 1: 6 Old Favorite and 6 New Style. Result: Nothing Left! Experiment 2: 5 Old Favorite and 2 New Style. Result: 3 Old Favorite.

  14. Eli’s Conclusion Experiment 3: 4 Old Favorite and 6 New Style. Result: 2 New Style. • Eli also concluded that peanuts only vanished when they are together on the same plate. So he did a few more experiments.

  15. Eli’s Conclusion Experiment 4: 2 Old Favorite and 6 Old Favorite. Result: 8 Old Favorite. Experiment 5: 3 New Style and 4 New Style. Result: 7 New Style.

  16. Comprehensive School Mathematics Program- Addition • The number line is extremely useful • The first number is where you start on the number line • The second number is how many spaces you move to the left or the right on the number line

  17. CSMP-Addition Continued • If adding a positive integer move to the right on the number line • If adding a negative integer move to the left on the number line • Negative integers are represented by: • Addition can also be represented as ordered pairs:

  18. Addition-Examples

  19. Addition-Examples

  20. Addition- More Examples

  21. Comprehensive School Mathematics Program- Subtraction • The number line is also extremely useful • The first number is where you start on the number line • The second number is how many spaces you move to the left or the right on the number line

  22. CSMP-Subtraction Continued • If subtraction a positive integer move to the left on the number line • If subtraction a negative integer move to the right on the number line • Negative integers are still represented by: • Subtraction is the exact opposite of addition in the Comprehensive School Mathematics Program.

  23. Subtraction-Examples

  24. Jacobs Multiplication • Multiplication represented graphically • Earth and moon are moving apart at a rate of 4 feet each year

  25. Jacobs Multiplication • Multiplication represented graphically

  26. CSMP Multiplication • Also represented multiplication graphically • ^ was used to represent a negative number • Graphing Activity • Examples • 4 x 2 = 8 • 4 x 3 = -12 • 4 x 2 = ? ^ ^ ^

  27. Division • Both CSMP and Jacobs used inverse multiplication to describe division. Let’s try: • -10/2 is the same as: • What must be multiplied by 2 to get -10? • -20/4 is the same as…

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