1. Session 6 Thursday Aug 21 st, 2008 7:00 – 8:30

2. Teaching through the Mathematical Processes Session 6: Connecting the MP to Differentiated Instruction

3. PLACE MAT TASK

4. Individually in your space, answer the question: “How does teaching through the mathematical processes support DI?” (3 minutes) As a group, share your ideas and collectively complete the centre area with ideas that are common or that everyone agrees answers the question. (3 minutes) REPORT PLACE MAT TASK

5. Curriculum tells us what to teach; differentiation tells us how.” Tomlinson 2000

6. Brainstorm Brainstorm ideas of how to remember and present some of your learning.

7. Develop and Create….. ….using available resources

8. Share…. …your product

9. Outside circle faces in, inside circle faces out. Outside circle answers: As a result of Math Camppp I will share with a colleague ________ Inside circle answers: As a result of Math Camppp My teaching will _________ because……, My students will ____________ because…. Inside/Outside Circle: Outside circle ROTATES one place, answer opposite statement to your new partner... And Again...

10. Why am I an educator...... it’s about the culture of learning.

11. Thank you ! Anne & Rod

13. Other Ideas and Goodies

14. The Evolution of Mathematics Teaching  1960s: A peasant sells a bag of potatoes for $10. His costs are 4/5 of his selling price. What is his profit?  1970s: A farmer sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price, that is, $8. What is his profit?  1980s (New Math): A farmer exchanges a set P of potatoes with set M of money. The cardinality of the set M is equal to 10, and each element of M is worth $1. Set C represents production costs. What is the cardinality of the set of profits?

15. The Evolution of Mathematics Teaching  1990s: A farmer sells a bag of potatoes for $10. His production costs are $8, and his profit is $2. Underline the word “potatoes” and discuss with your classmates.  2000s: A farmer sells a bag of potatoes for $10. His or her production costs are 80% of his or her revenue. On your calculator, graph Revenue vs. Costs. Run the POTATO program to determine the profit. Discuss the results with the students in your group. Write a brief essay that analyses this example in the real world of economics. Anon. Adapted from The American Mathematical Monthly Vol 101 No. 3 May 1994

16. Graphical Representation Numerical Representation Algebraic Representation Concrete Representation f(x) = 2x - 1 Problem Solving: Multiple Strategies

17. Learning Profile “ Balance instructional strategies to attend to all learning styles – and ensure that the teacher’s own preferred learning style does not dominate instruction.” Leading Math Success – p52

18. “Explicitly engaging students in the creation of non-linguistic representation actually stimulates and increases activity in the brain.” Gerlic & Jausovec, 1999

19. “Necessary for Some But Good for All Students”. Anne & Rod Yeager 2000

20. Remember: If students do not learn the way we teach...... then we must teach the way they learn. Anne & Rod Yeager 2000

21. “Every student can learn, just not on the same day, or in the same way.” George Evans

22. Brain research demonstrates that when more senses are involved the memory pathways are enhanced and consequently there is better retrieval, and students are more likely to remember and connect. Loring Coes NCTM 2002 remember and connect.

23. We Learn…  10% of what we read  20% of what we hear  30% of what we see  50% of what we both hear and see  70% of what is discussed with others  80% of what we experience personally  95% of what we teach to someone else William Glasser

24. CHINESE PROVERB  I DO AND I UNDERSTAND  I SEE AND I REMEMBER  I HEAR AND I FORGET

25. Each student has unique strengths and diverse learning needs. Anne and Rod Yeager 2001

26. Minds On Math Flash Mind Reader e.g. “47” 47 – (4 + 7) = 36

27. Flash Mind Reader Any two digit number: i.e.10x + y Subtract the digits: i.e.subtract x and y Therefore, 10x + y – (x + y) = 9x A multiple of nine!!! 9 18 72 63 54 45 36 27 99 90 81 0