Teaching Mathematics What the Research Says: A Sample or Three

1. Teaching MathematicsWhat the Research Says:A Sample or Three

2. Expert Panel Reports • 30 Years of Research • The Same Message at all levels: K-12 • Drives the training, the resources • Summary provided (by me)

4. Teaching Through Problem Solving • the reason for math to exist • nobody does a sheet of math for fun • 3 part lesson • pose & discuss problem • students solve the problem • debrief • See New Curriculum Sample

5. Problem solving … mainstay of mathematical instruction.

6. Creating a Learning Environment • 50% of the population suffer from math anxiety or math avoidance • teachers teach as they have been taught • mistakes are opportunities to discuss & learn (see communication) • take risks (see above) • arithmetic has one answer but mathematics has multiple solutions

7. Creating a Learning Environment • children come to school as natural mathematicians – we beat it out of them • equity means each child has the right to be taught with methods that are most effective for them • at risk students learn best in a problem solving environment full of talk and communication

8. Promoting Communication • students must speak to learn • a predominately silent math classroom is one where learning has been minimized • students can only write if they have been in a classroom where they have talked and listened • a math problem is the most complex text to read • math is where hands-on learners are successful – the perfect place to start reading & writing

9. Establishing the Big Ideas of Mathematics • teaching mathematics around central concepts – not as a checklist of skills • understanding to create proficiency • Big Ideas of Number Sense counting quantity operational sense (relationships) (representation) proportional reasoning (Junior +) • See New Curriculum Sample

10. Using Manipulatives • modeling mathematics through concrete materials and digital technology • an effective method to create understanding for all students – nothing to do with ability • essential for some learners • count the references to concrete materials in the Grade 3 number sense

11. Assessing Effectively • main purpose of assessment to create learning (formative & feedback) • focused observation is the most effective tool and is the predominate tool for assessment and evaluation in the primary division • variety of tools (observations, performance tasks, journals, portfolios, investigations, self-assessment, tests (Gr. 3 & up) • only assign a grade or mark for summative tasks – grades do not increase learning

12. Positive Learning Environment the learner the classroom environment equity home connections special needs/at risk scheduling teachers Problem Solving Process problem solving making connections lesson design Expert Panel Reports Summary • All Learning Involves Communication • communication • language • The Big Ideas of Math • Big Ideas • Algorithms & Formulas • Learning Tools • concrete material • digital technology • Assessment for Learning • assessment

14. Sample Lesson Think-Pair-Share Think: How would you add these numbers? 24 36 48 72 Pair: 1. With your partner (group), discuss how you added the numbers. 2. Record the different methods in your group journal. (Pictures, numbers, words)

15. Sample Lesson Think-Pair-Share Share: Go to the front and share your groups solutions with the class. In you journal: Describe your favourite method and one other person’s method of adding these numbers.

16. Look to the Numbers!

17. Early Primary Samples

18. Tell me what you know about 5.(Diagnostic – Week 1 Grade 1) 5

20. Tell Me About “5”

24. One More Than/Two More Than Facts This strategy covers 36 basic facts. They have either an addend of 1 or 2. 8 + 2 more 3 + 1 more

25. How many squares?

26. How Many?

27. How many squares?

28. How Many?

29. How many squares?

30. How many squares?

31. How Many?

32. 5 One More Than

36. Two More Than Let’s try two more for the following dot plates.

40. + 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 6 6 7 8 9 10 11 12 13 14 15 7 7 8 9 10 11 12 13 14 15 16 8 8 9 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 18 One-More Than/Two-More Than *36 Facts*

41. Facts to 10 • Use 10 Two-Colour Counters • Shake them in your hand • Drop them • Place them on the 10-Frame • Write a number sentence to represent this • remove the reds from yours and your partner’s. Add the yellows using the frames • You can do this for any number

43. How Would You Add These?How Would You Subtract These? How many dots in all?What is the difference between the number of dots on these two plates?

44. Morgan has 7 apples. Jesse has 9 apples. How da ya like dem apples? • show using counters and no frames • show using counters with frames • show using a numberless number line • show using abstract numbers • show using distributive property to demonstrate strategies • Why did I choose 7 and 9?

45. Hundreds Chart

46. A Better Hundreds Chart

47. De-Brief – Grade 2 Last time for Pizza Day we ordered 37 slices of pizza. This time we need to order 13 more slices. How many pieces of pizza do we need to order?

48. Late Primary/ Early Junior Samples

49. Race to 100 Race to 0

50. Why is this space here?