Responsiveness To Instruction: Mathematical Understanding

1. Responsiveness To Instruction: Mathematical Understanding Rowan-Salisbury Schools RtI Foundations Training August 2010 Erin Banks & Sarah Brown, School Psychologist and Program Specialist

2. When you need help with math…… • Call Somebody!!! • http://blutube.policeone.com/Clip.aspx?key=9A7EF76E53A5E67C

3. It’s not MY Fault!!!

4. How Our Students Feel About Numbers. . . . .

5. The Ultimate Test Anxiety. . .

6. And Why It’s All Worth It. . . . .

7. What’s Going on With Math? • NAEP 2009 results were released in March 2010 • How do you think NC math results compare to: • United States norms? • Reading results?

8. NAEP (2009) Math Results:

9. In 2009, the average score in North Carolina was • lower than those in 4 states/jurisdictions • higher than those in 29 states/jurisdictions • not significantly different from those in 18 states/jurisdictions • (www.nces.ed.gov)

10. Test Yourself! • Sample 4th grade NAEP Math test question It takes Mrs. Wylie 15 minutes to drive from her house to the store. What is the best estimate of the distance from her house to the store? • 5 feet • 5 miles • 20 feet • 200 miles

11. Are You Smarter than an 8th Grader? Which point is the solution to both equations in the graph? (0,0) (0,4) (1,1) (2,2) (4,0)

12. National Mathematics Panel Report 2008: What do students need for success in Algebra? • Major Findings: • Proficiency with whole numbers, fractions and certain aspects of geometry and measurement are the critical foundations of algebra • Explicit instruction for students with disabilities shows positive effects. • Students need both explicit instruction and conceptual development to succeed in math. • http://www.ed.gov/about/bdscomm/list/mathpanel/index.html

13. Math Basics International Research

14. TIMSS from Improving Mathematics Instruction (Ed Leadership 2/2004) 1995 Video Study Largest and most carefully designed study of teacher instruction and mathematics More than 500,000 students (33,000 in US) Grades 4, 8, 12 41 nations participated Results = 4th grade students scored ABOVE international average; BELOW average in measurement, estimation, and number sense! 8th grade students scored BELOW international average overall, including: Measurement, geometry, and proportionality Outperformed by 20 countries 12th grade students scored WELL BELOW international average (outperformed Cyprus and South Africa)

15. TIMSS from Improving Mathematics Instruction (Ed Leadership 2/2004) 1999 Follow-up Study Examined lessons in Grade 8 in United States, Germany, and Japan US teachers teach student HOW to get answers while Japanese teachers teach for UNDERSTANDING US teachers usually don’t develop math concepts and ideas US teachers taught material with low-level math content vs. other teachers using high-level math content

16. What Do We Need to Do Differently? • Help students develop understanding of math concepts • Teach lessons to challenge students (using high level content)

17. TIMSS (2007) Study • U.S. students' average mathematics score was • 529 for 4th-graders (500 is average) • 508 for 8th-graders (500 is average) • Fourth-graders in 8 of the 35 other countries that participated in 2007 (Hong Kong, Singapore, Chinese Taipei, Japan, Kazakhstan, Russian Federation, England, and Latvia) scored ABOVE their U.S. peers • Among the 16 countries that participated in both the first TIMSS in 1995 and the most recent TIMSS in 2007, at grade 4, the average mathematics score increased in 8 countries, including in the United States, and decreased in 4 countries. Higher than 1995!

18. Style vs.. Implementation High Achieving countries use a variety of styles to teach (calculator vs.. no calculator, ‘real-life’ problems vs.. ‘naked’ problems) High Achieving countries all implement connections problems as connections problems U.S. implements connection problems as a set of procedures NCDPI RtI Foundations Training

19. Exponents and Geometry What is 42 ? Why is it 4 x 4 when it looks like 4 x 2? It means ‘make a square out of your 4 unit side’ Making Connections. . . NCDPI RtI Foundations Training

20. Exponents and Geometry What is 42 ? --4 units-- 1 1 1 1 You’d get how many little 1 by 1 inch squares? 42 = 16 NCDPI RtI Foundations Training

21. Some words about “Key Words” They don’t work… NCDPI RtI Foundations Training

22. We tell them—more means add Erin has 46 comic books. She has 18 more comic books than Jason has. How many comic books does Jason have. But is our answer really 64 which is 46 + 18? NCDPI RtI Foundations Training

23. Sense-Making We need to notice if we are making sense of the math for our students, or if our discussion of the math contributes to --- “The suspension of sense-making” Schoenfeld (1991) NCDPI RtI Foundations Training

24. Just Do It! NCDPI RtI Foundations Training

25. Content Standards • Number & Operations • Algebra • Geometry • Measurement • Data Analysis & Probability • Process Standards • Problem Solving • Reasoning & Proof • Communication • Connections • Representation www.nctm.org

26. What does NC SCOS tell us? • Number and Operations • Measurement • Data Analysis & Probability • Algebra • Problem-Solving (uses the same 5 strands as NCTM Principles)

27. What do researchers tell us? Use Direct and Explicit Instruction to focus upon: • Number Sense • Basic math operations • Problem-solving skills (Kroesbergen & Van Luit, 2003)

28. Why Intervention in Math? • Students have difficulty with: • Mastering math computation skills or • Application of math • Speed and Accuracy are IMPORTANT! • Students who cannot master basic computational skills are very unlikely to succeed at application of those skills. (Shapiro, 2004)

29. Number Sense Number Sense Prerequisite Computation ……in the same way as……… Reading Fluency Phonemic Awareness Prerequisite

30. What is Number Sense? • Manipulate Numbers • Adding on • Counting up • Skip counting • One-to-One correspondence • Counting steps as they walk down/up • Understanding of how number systems work

31. NCTM Strands Without Number Sense Measurement Number & Operations Data Analysis and Probability Geometry Algebra

32. NCTM Strands With Number Sense Measurement Number & Operations Data Analysis and Probability Geometry Algebra

33. Fluency (Automaticity) • Strong correlation (relationship) between poor retrieval of arithmetic combinations (math facts) and global math delays • Automatic recall of arithmetic combinations frees up student ‘cognitive capacity’ to allow for understanding of higher-level problem-solving • Working memory!!!!

34. How to Increase Fluency • PRACTICE!!!!!!!! • However, practice alone may not be sufficient

35. Language in Mathematics NCDPI RtI Foundations Training

36. Are these the same? NCDPI RtI Foundations Training

37. Break • During the break, read the article: “ Early Identification and Interventions for Students With Mathematics Difficulties” (Gersten, Jordan & Flojo, 2005) • Discussion upon returning to group

38. Early Identification • Describe the nature of math difficulties. • How are mathematical difficulties and reading difficulties related? • What is number sense as operationalized by Kalchman, Moss and Case in this article? • What are the two distinct factors in mathematics proficiency in kindergartners? • What is the role of socioeconomic status as stated by Griffin, Case and Sigler in 1994? • What are the instructional implications for the findings? NCDPI RtI Foundations Training

39. How Does Math Fit into the RtI Model? Tier IV IEP Consideration Tier III Student Study Team Tier II Consultation With Other • Intensive Interventions 1-7% • Strategic Interventions 5-15% • Core Curriculum 80-90% Resources Tier I Consultation AMOUNT OF RESOURCES Between Teachers - REQUIRED TO MEET THE Parents STUDENT’S NEEDS INTENSITY OF NEEDS Nds - circles - pub NCDPI RtI Foundations Training

40. What Works Clearinghouse

42. Tier I - Math Characteristics: • Classroom teacher • Core Math instructional time (60 minutes recommended) • Benchmarks - Fall, Winter, Spring Instruction: • Quality Lesson Design • Research-Based Strategies • Differentiated Instruction • Explicit Instruction • Questioning • Connections

43. Assessment At Tier I • Universal Screening/Benchmarking • Fall, Winter, Spring • Investigating Further. . . . • Number Knowledge test (handout) • Money test (handout) • Use Data to: • Develop groups for differentiation • Groups for supplemental intervention/instruction • Groups for enriched instruction http://clarku.edu/numberworlds

44. Differentiated Instruction in Math

45. What is Differentiated Instruction? A teaching theory based on the premise that instructional approaches…. …should vary and be adapted… …in relation to individual and diverse students in classrooms.

47. Ways to Differentiate in Math: • Manipulate Content/Topic • Manipulate Process/Activities • Manipulate Product • Manipulate Environment How have you been successful using these techniques in your classroom?

48. Manipulation of Content Multiple Options for Taking in Information Classroom Objective: All students will subtract using renaming. Manipulation: Some students may learn to subtract two-digit numbers, while others learn to subtract larger numbers in the context of word problems. (Tomlinson, 1999)

49. Manipulation of Process Multiple Options in which a Student Accesses Material One student may explore a learning center, while another student collects information from the web. (Tomlinson, 1999)

50. Manipulation of Project Multiple Options for Expressing What They Know To demonstrate understanding of a geometric concept, one student may solve a problem set, while another builds a model. Tomlinson, 1999