Specially Designed Instruction in Math PDU Session One

1. Specially Designed Instruction in Math PDU Session One Oct 9, 2012 4:30-6:30

2. PDU Goal To build the capacity of special educators to provide quality specialized instruction for students with disabilities in the area of math, by building content knowledge of mathematics, assessing students using diagnostic tools, creating lesson based on a scope and sequence and progress monitoring growth

3. PDU Requirements • Attend ten sessions (20 hours) • 11 hours of professional development using the How the Brain Learns Mathematics by David A. Sousa and Teaching Learners Who Struggle with Mathematics by Sherman, Richardson, and Yandl • 9 hours of small group lesson writing and reflection using the “Lesson Study” protocol • If a session is missed then you will be responsible for doing a self study of the missing content and complete the corresponding exit slip and “Lesson Study” Protocol

4. PDU Requirements • Complete a Diagnostic Math assessment on the targeted student (assessment provided in class)(1 hour) • Complete progress monitoring tool after 5-10 hours of instruction (progress monitoring tool provided in class) (1.5 hours) • IEP meeting for the targeted student sometime during the PDU (annual, eligibility or special request) where writing is discussed (2 hours including planning and meeting)

5. PDU Requirements • Math lesson plans (10+ hours) • Direct instruction in mathematics for the targeted student (15+ hours) • Reflection Essay (1 hour) • Complete a portfolio (1 hour) • 9 Lesson Plans with “Lesson Study” Protocol • Copy of Diagnostic Assessment • Copy of IEP with names crossed out • Copy of Progress Monitoring with Interpretation • Copy of Reflection Essay • Attend Final PDU peer review process (2 hours)

6. Text

7. Outcomes for Session One Participants will have a basic knowledge of the National Math Panel report of 2008 Participants will have a foundational knowledge of the psychological processes of mathematics

8. Math basics quiz • T F The brain comprehends numerals first as words, then as quantities. • T F Learning to multiple, like learning spoken language, is a natural ability • T F It is easier to tell which is the greater of two larger numbers than of two smaller numbers • T F the maximum capacity of seven items in working memory is valid for all cultures • T F Gender differences in mathematics are more likely due to genetics that to cultural factors

9. Math basics quiz • T F Practicing mathematics procedures makes perfect • T F Using technology for routine calculations leads to greater understanding and achievement in mathematics • T F Symbolic number operations are strongly linked to the brain’s language areas

10. Manipulative make it concrete • We are going to add polynomials using Algeblocks • After learning how to use the Algeblocks you will be able to add and subtract these polynomials in less than 10 seconds • Before we can use the concrete manipulative we need to build some background knowledge. • You need a set of Algeblocks and Algeblocks Basic Mat 3x2 – 2y + 8 – 2x2 + 5y

11. CRA Algebra- using Algeblocks 1 unit 1 square unit 1 unit The greens don’t match up so this means the yellow rod is a variable 1 unit = X X

12. CRA Algebra- using Algeblocks 1 unit =Y Y X = X2 X

13. CRA Algebra- using Algeblocks =Y2 Y Y

14. CRA Algebra- using Algeblocks =XY X Y

15. Algeblocks Key 1 sq unit Y2 X Y x2 XY

16. Basic Mat: -3+2 - +

17. Basic Mat: -3+2 (Make 0 pairs) -3+ 2= -1 - +

18. Basic Mat: 3x-5 + (2-X) - +

19. Basic Mat: 3x-5 + (2-X) (0 pairs) Solution is 2x -3 - +

20. Basic Mat: (3y +5) + (y-3) - +

21. Basic Mat: (3y +5) + (y-3) (0 Pairs) Solution is 4y +2 - +

22. You try lets add these polynomials 3x2 – 2y + 8 – 2x2 + 5y

23. Basic Mat: 3x2 – 2y + 8 – 2x2 + 5yconcrete - +

24. Basic Mat: 3x2 – 2y + 8 – 2x2 + 5y Solution is 8 +x2+3y - +

25. Basic Mat: 3x2 – 2y + 8 – 2x2 + 5yrepresentational Solution is 8 +x2+3y - +

26. Basic Mat: 3x2 – 2y + 8 – 2x2 + 5yabstract 3x2- 2x2=x2 -2y + 5y=3y 8 8+x2+3y

27. 2006 National Math Panel President Bush Commissioned the National Math Panel “To help keep America competitive, support American talent and creativity, encourage innovation throughout the American economy, and help State, local, territorial and tribal governments give the Nation’s children and youth the education they need to succeed, it shall be the policy of the United States to foster greater knowledge of and improve performance in mathematics among American students.”

28. 2006 Panel • 30 members • 20 independent • 10 employees of the Department of Education • Their task is to make recommendations to the Secretary of Education and the President on the state of math instruction and best practices based on research • Research includes • Scientific Study • Comparison study with other countries who have strong math education programs

29. 2008 Recommendations Algebra is the most important topic in math al-jebr (Arabic) “reunion of broken parts” -study of the rules of operations and relations

30. 2008 Recommendations All elementary math leads to Algebraic mastery

31. Elementary Math Focus- by end of 5th grade Automatic recall of facts Mastered standard algorithms Robust sense of number Estimation Fluency

32. Middle School Math Focus- by end of 8th grade Positive and negative fractions Fractions and Decimals Fluency with Fractions Percentages

33. A need for Coherence • High Performing Countries • Fewer Topics/ grade level • In-depth study • Mastery of topics before proceeding • United States • Many Topics/ grade level • Shallow study • Review and extension of topics (spiral) “ Any approach that continually revisits topics year after year without closure is to be avoided.” -NMP

34. Interactive verses Single Subject Approach … topics of high school mathematics are presented in some order other than the customary sequence of a yearlong courses in Algebra 1, Algebra II, Geometry, and Pre-Calculus …customary sequence of a yearlong courses in Algebra 1, Algebra II, Geometry, and Pre-Calculus No research supports one approach over another approach at the secondary level. Spiraling may work at the secondary level. Research is not conclusive .

35. Math Wars Conceptual Understanding verses Standard Algorithm verses Fact Fluency “Debates regarding the relative importance of conceptual knowledge, procedural skills, and the commitment of ….facts to long term memory are misguided.” -NMP You need all three and not in a particular order “Few curricula in the United States provide sufficient practice to ensure fast and efficient solving of basic fact combinations and execution of the standard algorithms.” -NMP

36. Number Sense

37. Fractions “Difficulty with learning fractions is pervasive and is an obstacle to further progress in mathematics and other domains dependent on mathematics, including algebra.” -Use fraction names the demarcate parts and wholes -Use bar fractions not circle fractions -Link common fraction representations to locations on a number line -Start working on negative numbers early and often

38. Developmental Appropriateness is challenged “What is developmentally appropriate is not a simple function of age or grade, but rather is largely contingent on prior opportunities to learn.” NRP Piaget Vygotsky

39. Social, Motivational, and Affective Influences • Motivation improves math grades • Teacher attitudes towards math have a direct correlation to math achievement • Math anxiety is real and influences math performance

40. Teacher directed verses Student directed Only 8 studies inconclusive - rescind recommendation that instruction should be one or the other

41. Formative Assessment “The average gain in learning provided by teachers’ use of formative assessments is marginally significant. Results suggest that use of formative assessments benefited students at all levels.”

42. Low Achieving and MLD

43. Real World Math

44. Everyone Can Do Math Number Sense is Innate Numerosity to count perform simple addition and subtraction Number of objects You don’t’ need to teach these skills. We are born with them and will develop them with out instruction. It is a survival skill. Babies can count

45. Why do children struggle with 23x42? This is not natural … not a survival skill!

46. Numerosity Activation in the brain during arithmetic Parietal lobe Motor cortex involved with movement of fingers

47. Which has more?

48. Prerequisite to counting Recognizing the number of objects in a small collection is a part of innate number sense. It requires no counting because numerosity is identified in an instant. When the number exceeds the limit of subitizing, counting becomes necessary Subitizing (latin for instant)

49. Subitizing

50. Counting