NCIDA 2009 Helping Students Stay Connected in Math

1. NCIDA 2009Helping Students Stay Connected in Math Joanie Gerken, M.Ed. Fellow, A.O.G.P.E.

2. Dyscalculia • Dyscalculia = “difficulty in learning or comprehending mathematics” dyscalculia.org • Identified in patients suffering brain trauma resulting in math problems • Arithmetic difficulties in calculation and number memory deficits “dys” = Greek, “badly” “calculia” = Latin, “calculare”, “to count”

3. Dyslexia/ Dyscalculia • Are they related? DYSLEXIA DYSCALCULIA

4. Characteristics of Dyscalculia • Confusing signs, +, -, x, ÷ • Inability to tell which is larger • Rely on ‘counting on’ strategies • Difficulty with mental math, tables • Inability to remember concepts, rules, sequences, formulas • Rotate numbers, 56 as 65 • Difficulty estimating everyday time, money, comparisons in amount and measurement • Difficulty with score keeping, rhythm-sequential processing; dance, cheerleading

5. Simulation How does it feel to many children in math class! Errors often occur when students don’t know basic facts fluently Project Access, web.utk.edu/~access/mathdisabilities.html

6. Addition Sometimes charts are used to assist poor recall

7. Multiplication Used to help with multiplying and dividing

8. Use the chart to work the problems in your folder

9. Answers: 21 42 314 32143 +12+13+222+22334 33 121 1202 121203 44213 12 23 413 +22314x 3x14x 4 133133 102 210 4130 230 1100

10. Factors Influencing All Learning • Language disorders • Reading difficulty • Accuracy • Rate • Repetition • Learning Style Attention difficulties Processing deficits Memory deficits Motor skills difficulty

11. Critical Factors Affecting Math Learning style Math language Cognitive level Prerequisite skills Levels of Learning mastery

12. 7 Prerequisite Skills • Inductive reasoning/ easily seeing patterns in generalizations 6. Deductive reasoning/ draw conclusions 5. Estimation skills 4. Visualization/ picture what’s going on in your head 3. Recognize patterns and continue it 2. Sense of directionality, spatial orientation and organization 1. Follow a sequence

13. What made this task difficult? 21 42 314 32143 +12+13+222+22334 33 121 1202 121203 44213 12 23 413 +22314x 3x14x 4 133133 102 210 4130 230 1100

14. What made this task difficult? Pattern Recognition Not knowing basic facts/ with all information new skills Fluency

15. Best Practices in Math • Choose fewer topics to teach at each grade level • Be diagnostic and prescriptive/individualize to match needs • Guide to success is pacing and vice versa • Be mindful of learning style/ moving from simple to complex • Give feedback and clues to help scaffold learning • Teach concepts and promote fact fluency • Focus on applying problem solving skills

16. 1/3 of US students are at or above grade level in math National Center for Educational Statistics, 2005

17. US Ranking in World Math reading 24th 20th Science 15th

18. www.symphonylearning.com

19. NCTM recommends • Develop problem solving and critical thinking skills • Understand and generalize information • Fluency

20. Best Practices in Math • Choose fewer topics to teach at each grade level • Be diagnostic and prescriptive/individualize to match needs • Guide to success is pacing and vice versa • Be mindful of learning style/ moving from simple to complex • Give feedback and clues to help scaffold learning • Teach concepts and promote fact fluency • Focus on applying problem solving skills

21. Focus on what makes most tasks difficult Pattern Recognition Not knowing basic facts/ with all concept or process information new skills Fluency

22. Informal Inventory and error analysis Doesn’t have to be long Sampling of problems testing Number sense Sequencing Pattern recognition Computation Problem solving

23. 3 Focal pts of NC standards • Use math to solve problems • Apply logic/reasoning to justify solution • Connect and communicate ideas of math in and out of school environment http://community.learnnc.org/dpi/math/archives/2005/06/grade_two_assess.php

24. Sample inventory Number sense Cotton balls Paper clips Sequencing 37 38 ___ ____ 41 = Pattern recognition + - =

25. Recognizing number patterns 16 24 32 _ _ 56

26. Computation • Single skill blocks for younger students • Mixed skills for older 23 345 28 34 236 + 25+296- 14- 17-178 27 32 234 X 5x 24x 67

27. Problem solving Molly collects stamps. She has 17 new stamps to put in her stamp book. If she can fit 6 stamps on each page, how many pages will she need? Show your work with pictures, words or numbers

28. Error Analysis • Find the pattern for common errors • Find the reason for the error • memory for facts/sign confusion • sequence of steps • understanding of process • visualization • inference • carelessness or lack of attention to detail

29. Find the common errors 64 32 76 81 + 27 - 25+33- 56 102 13 109 35

30. Samples of errors/What do the errors mean? Refer to prerequisite skills needed! 10 4 • 3 1 • - 2 8 + Get out the manipulatives! Next draw pictures

31. Practice the steps in renaming • After the concept is solid -gradually move to abstract 5 12 2 14 6 2 3 4

32. < > Sign confusion 23 52 reversal Visualize numerousness

33. How much is 5 5 what $

34. Number sense! An awareness or sense of quantity

35. Number sense/ numerosity • Innate sense of numbers/quantity

36. count

37. Guessing Jar

38. Recognizing number

39. Counting slows down speed!

40. Touch math • 5 3 14 + 6+7- 8

41. Best Practices in Math • Choose fewer topics to teach at each grade level • Be diagnostic and prescriptive/individualize to match needs • Be mindful of learning style/ moving from simple to complex • Teach concepts and promote fact fluency • Success guided by pacing and vice versa • Give feedback and clues to help scaffold learning • Focus on applying problem solving skills

42. Games to teach pattern recognition improve fluency Matching pattern to pattern concrete semi - concrete Matching pattern to number concrete/ semi-abstract/ semi-concrete abstract Matching pattern to process

43. Games Matching pattern to pattern concrete/ semi - concrete Capable of being perceived by the senses; not abstract or imaginary Wordweb

44. games Matching pattern to number concrete/ semi-abstract/ semi-concrete abstract

46. Connect concrete to semi – concrete with gallon man Music , movement & visual aids help memory bridge hands- on learning to visual cue

47. Gallon Man song: to the tune of “Alice the Camel”Susan Simon, 3rd Grade Teacher, Fayetteville, NC • Four quarts equal a gallon, • Four quarts equal a gallon, • Four quarts equal a gallon, • So roll, baby, roll (roll hands)! • Boom, boom, boom (hips go side to side) . . . • Eight pints equal a gallon, • Eight pints equal a gallon, • Eight pints equal a gallon, • So roll, baby, roll! • Boom, boom, boom . . . • Sixteen cups equal a gallon, • Sixteen cups equal a gallon, • Sixteen cups equal a gallon, • So roll, baby, roll! • Boom, boom, boom!

48. Best Practices in Math • Choose fewer topics to teach at each grade level • Be diagnostic and prescriptive/individualize to match needs • Be mindful of learning style/ moving from simple to complex • Teach concepts and promote fact fluency • Success guided by pacing and vice versa • Give feedback and clues to help scaffold learning • Focus on applying problem solving skills

49. All concepts have 3 key ingredients Linguistics Idea Skills Concepts

50. spaghetti estimation Focus on concept without pencil paper • Volunteers use uncooked spaghetti to guesstimate height, length