Math Strategies That You Can Count On

1. Math Strategies That You Can Count On By: Michelle Flaming and Renee’ Smith ESSDACK

3. Affinity Diagram • Write math strategies you currently use. • One strategy per sticky note. • As a group - sort and label the strategies.

4. Pre-Assessment of Strategies

5. Temporary & Permanent Memory

6. How the Brain Learns Mathematics

7. How the Brain Learns Mathematics

8. Principles of Brain-Compatible Classrooms

9. 3. Metaphors and Analogies “When students connect the new to the known, they fit the new learning into their personal world.” (Caine and Caine, 1994)

10. Analogy • Addition is to sum as multiplication is to ________________. • Five is to pentagon as ________ is to octagon. • Inch is to mile as _______ is to kilometer. • Degree is to temperature as pound is to ___________.

11. 4. Simulations and Role Play “Movement places knowledge at multiple addresses in the brain.”

12. 8. Projects and Problem-Based Learning Collaborative problem solving is one design principle around which all learning should be organized.

13. Websites: • http://www.wested.org/pblnet/other_gp.html • http://ozpk.tripod.com/pbl.html//web.mac.com/khoneycuttessdack/Kevin/21st_Century_Collaborative_Projects.html

14. 9. Mnemonics • Don’t Be Mean Fair Share “The brain is constantly seeking patterns.” (Wolfe, 2001)

15. Keyword Strategy • Visual image for the “2 Family” • 2 x 2 - skateboard with 2 sets of wheels. • 3 x 2 • 4 x 2 • 5 x 2 • 6 x 2 • 7 x 2 • 8 x 2 • 9 x 2

16. Letter Strategy • S earch the word problem • T ranslate the words into a picture form • A nswer the problem • R eview the solution

17. Pegword Strategy

18. 11. Brainstorming and Discussion Prior knowledge is activated during brainstorming because one person’s idea causes others to search their neuronal networks for additional, related ideas. (Tanner 1998)

19. 12. Drawing and Artwork Researchers have used art therapy for people with brain damage because the art causes the brain to rewire itself, allowing it to make more and stronger connections. (Kolb and Whishaw, 1990)

20. 3 1/2 divided by 3/8 = • Estimate an answer • Draw a picture to model this. • Write a real-world problem

21. 14. Games “Play involves the built-in process of challenge, novelty, feedback, coherence, and time, which all enable the brain to mature faster.” (Jensen, 2001)

22. 17. Problem Solving As a Focus - CGI • Built on the belief that learning occurs as new knowledge is linked to existing knowledge, and teaching is most effective when instruction directly builds on what children already know.

23. Solve Roller Coaster Problem: • “At the fair, there are 36 children in line to ride the roller coaster. The roller coaster has 10 cars. Each car holds 4 children. How many children can sit 3 to a car, and how many have to sit 4 to a car?” • Solve in 2 different ways.

24. Rachel’s Problems – Problem Type DifficultyRate each of the following problems from 1 (easy) to 5 (most difficult) • 1. Using a scale - Rate each problem in comparison with each other. - Record under Rating #1. • 2. Working with a partner - directly model each problem, discuss the difficulty if the problem is directly modeled • 3. At your table, discuss a mutual ranking. Think about the rationale - Rating #2.

25. “Justifying and explaining ideas improves students reasoning skills and their conceptual understanding.” • (Maher and Martino 1996)

26. Introduction to Strategies • Direct Modeling • Act out the problem. • Follow sequence of the action in a problem. • Represent sets with materials (unifix cubes, tally marks, etc.) • Counting Strategies • Hold one number in the head. • Derived Facts/Facts • Doubles +1, -1, +2, and -2 • Sums of 10 (8 + 3 = 8 + 2 is 10 plus 1 more = 11) • Invented Approaches

27. Big Ideas on Children’s Solution Strategies • At the most basic level, children use physical objects to directly model the action or relationship in each problem. • As children mature, their strategies become more abstract and efficient. DM is replaced by counting, which in turn are replaced with derived fact and recall of number facts. • Direct Modeling provides a basis for learning of the other strategies. • Children in any class will be at different levels of understanding and will use different strategies to solve the same problems. • Children naturally progress through the levels without direct instruction if children have the opportunity to explain their mathematical understanding.

28. Common Components of CGI Classrooms • Problem solving is the focus on instruction; teachers pose a variety of problems. • Many problem solving strategies are used to solve problems. Children decide how they should solve each problem. • Children communicate to their teachers and peers how they solved the problems. • Teachers understand children’s problem solving strategies and use that knowledge to plan instruction.

29. Principles of Brain-Compatible Classrooms

30. Math Mentors • http://math.essdack.org

31. During the session today, I appreciated: A strategy I would like to try in my classroom is….