Problem Solving and Supporting Algebraic Thinking at the Middle and Secondary Grades

1. Problem Solving and Supporting Algebraic Thinking at the Middle and Secondary Grades Amy Barto LDA of Michigan November 14, 2011

2. Food For Thought • “Mathematical know-how is not only one of the most important qualities for workers to possess in the future, it is critical for successful functioning in life”. - Jo Boaler, 2008.

3. Prime Your Circuit

4. Best Practices Tell Us: NEW

5. More Food For Thought “… twenty-first-century citizens need mathematics. But the mathematics that people need is not the sort of math learned in most classrooms. People do not need to regurgitate hundreds of standard methods. They need to reason and problem solve, flexibly applying new methods in new situations. Mathematics is now so critical to American citizens that some have labeled it the ‘new civil right’.” - Jo Boaler, 2008.

6. But WHAT IS MATH?

7. Functions • Graphs • Probability • Statistics Patterns Number Sense Place Value Operations Formulas

8. DO THIS AT HOME! • Concept A: Mathematical Representations Around Us • 5 minute Math Hunt: Examples of Math Around Us • Output: Make a List & Be Able to Defend Mathematical Connection (can be related to most recent unit of instruction)  • Concept B: Number Sense •  5 minute Number Hunt: Representations of • Levels of Difficulty = Differentiation • Whole Numbers; decimals; fractions, exponential numbers • Output: Make a List (must have different types of examples; i.e. not a list of numerals)

9. 5 Minutes – GO!

13. Mathematical Observations

15. Scaffolding Exploration and Effective Application

17. Speaking of…… • “Children need to solve complex problems, to ask many forms of questions, and to use, adapt, and apply standard methods, as well as to make connections between methods and to reason mathematically – and they can engage in such methods at home and (one hopes) at school”. - Jo Boaler, 2008.

18. Say What?!?!?!?!?!

19. 7th and 8th Grade Students

20. Some Structures for Assessment

21. Some Less-Traditional Sources for Exploring

24. Sarah’s father is 60 years old. Sarah is ¼ as old her father. How many years older than Sarah is her father? At what age will Sarah be 1/10 her father’s age?

25. Mathematical Know-How

26. Good Problem Solvers Solve Problems Based on Common Structures

27. Solve It!

28. READ • READ the problem. Decoding the Text Decoding the Math

29. Identify the important information. More than key words. Mathematical Concepts Put it into (your own) words. LANGUAGE gives meaning.

30. Diagram Graph Chart A Schematic: A MAP or math blueprint MUST RELATE TO THE PARAPHRASE.

31. Make a plan Choose operations Putting together the puzzle…. Setting up your mathematical experiment/notation Pattern and Logic in Mathematical Language

32. Create a realistic target. The Goal is the 2nd Ring – not a bullseye. Relies on Comprehension of Mathematical Concept/Operations.

33. Computation Supports Multiplication Chart Calculator Tactile Materials Visualization & Hypothesis Self-Made Supports Self-talk & routine Developing Algorithms

34. Using the Inverse “Am I right?” “I am right AND I can prove it.” Meta-cognition.

35. Solve It = Math Power!

37. Teacher’s Role

38. Math HW Goal

39. Some Math Lab Staples

40. Other Barto Staples

41. Back to The Fun Stuff!!!!! Sarah’s father is 60 years old. Sarah is ¼ as old her father. How many years older than Sarah is her father? At what age will Sarah be 1/10 her father’s age?

43. The ultimate goal of mathematics education is for all students to develop mathematical power to participate fully as a citizen and worker in our contemporary world.

44. Montague, Marjorie. Math Problem Solving for Middle School Students with Disabilities http://www.k8accesscenter.org/training_resources/MathProblemSolving.asp Curriculum Resource available from Exceptional Innovations at http://www.exinn.net/solve-it.html

45. Barto’s Gurus Montague, M. (2003). Solve It!: A mathematical problem-solving instructional program. Reston, VA: Exceptional Innovations.Montague, M., Warger, C., & Morgan, H. (2000) Solve it! Strategy instruction to improve mathematical problem solving. Learning Disabilities Research and Practice, 15, 110-116.Wong, B.Y, Harris, K.R., Graham, S., & Butler, D.L. (2003). Cognitive strategies instruction research in learning disabilities. In H.L. Swanson, K.R. Harris, & S. Graham (Eds.). Handbook of learning disabilities (pp. 273-292). New York: Guilford. Sousa, David. How the Brain Learns Mathematics. 2007. The Van de Walle Professional Mathematics Series

46. Material Resources.. ETA Cuiseniare http://www.etacuisenaire.com/ Exceptional Innovations Solve It!: A Practical Approach to Teaching Mathematical Problem Solving Skills http://www.exinn.net/solve-it.html Pearson AGS Globe http://www.pearsonschool.com/index.cfm?locator=PSZ1Ai Key Curriculum Press http://www.keypress.com/ Corwin Press http://www.corwin.com/corwinSearch.nav?&_requestid=2043573

47. Some Resources Boaler, Jo. What’s Math Got to Do With It?. 2008. Brown, C. A Roadmap for Math Achievement for All Students. Center for Comprehensive School Reform and Instruction. Enzensberger, Hans. The Number Devil. 1997 VanDerHeyden, A. RTI and Math Instruction. RTI Action Network.

48. Some On-Line Resources National Math Panel Reports, Jan. 2007. Math Laboratory Blog http://www.mrsbsmathlaboratory.blogspot.com LDA of America http://www.ldaamerica.us/ National Library of Virtual Manipulatives http://nlvm.usu.edu/ The Algebra Project www.algebra.org Funbrain http://www.funbrain.com/math/index.html National Council for Teachers of Mathematics http://illuminations.nctm.org

49. Yeah, I Can Keep Going • http://www.spotthedifference.com/explorer.asp • Basher Books • Math Practice Guides – What Works! • http://www.lumosity.com/ • Common Core for Math • Facebook/Mindjolt Games

50. Contact Information Amy Barto tchrqueen1@gmail.com www.bartosworld.blogspot.com My Class: www.mrsbmathlab.blogspot.com