Finding Focus for Mathematics Instruction Grades 6-8

1. Thumb-Area Student Achievement Model and Huron Intermediate School District Finding Focus for Mathematics Instruction Grades 6-8 March 8, 2010 Tuscola ISD Administrative Building March 16, 2010 Huron Area Technical Center March 10 and 16, 2010 Huron ISD; HATC

2. Today’s Goals • Become familiar with Mathematics Curriculum • Deepen understanding of Big Math Ideas • Use strategies for explicit vocabulary instruction • Understand instructional implications of research • Use assessment in a 3-tier process • Support instruction for intervention and enrichment

3. Be Thinking About • What is one idea you will try in the next week? • What are 2-3 items you will share or discuss with your colleagues? • How will that happen?

4. What Are the Focal Points?

5. What Do the Focal Points Look Like? • Work in grade-level teams. • Find the focal points for your grade. • Sort the GLCE topics according to focal point. Make a separate pile for “leftover topics.” Compare your sort to MDE list. Re-arrange if necessary.

6. How Should the Focal Points Impact Instruction? • Based on nationally-recognized topics • Related to GLCEs and MEAP: • Core expectations • Must be related to a focal point • No more than 20 per grade • Assessed with two items, all students • Extended core expectations • Not related to a focal point • Assessed with no more than one item (sampled)

7. Discussion • 70-80% of instruction should focus on GLCEs related to focal points. Use your textbook to think about your instruction. What topics should be emphasized more? Less?

8. Useful Documents • Math GLCEs Assessed with NC Designations • www.mi.gov/mathematics • Mathematics Focal Points K-8 Alignment (11-11-09 from SAM) • http://www.hisd.k12.mi.us/SAM/main.html

9. Common Core Standards Initiative • Coalition of states who have all agreed to adopt the same state standards • 48 states, 2 territories (Puerto Rico and the U.S. Virgin Islands), and the District of Columbia • Who’s missing? • Alaska and Texas

10. Common Core Standards Initiative DRAFT 1-13-2010 • Match CCSI standards to Focal Points and GLCEs • Make new piles if needed • No GLCE for a CCSI standard? Check another grade.

14. Common Core (CC) – When??? From Michigan’s Race to the Top application (January 19, 2010): • Adopt the CC Readiness Standards (CCRS) and K-12 Standards (CCK-12) by June, 2010 (p. 51) • Roll-out sessions in August, 2010 (dates to be announced June, 2010) (p. 58) • Revise and update the Michigan Curriculum Framework to be consistent with CCRS, CCK-12 anticipated by May 2011 (p. 59)

15. What about testing? • “Use of the existing assessment system . . . from spring 2010 through spring 2014.” (p. 64) • “Move to common annual summative assessment provided by the common assessment consortium that Michigan joins when those assessments are available and validated for such use beginning in Fall 2014.” (p. 64) • Competitive grants to consortia of ISDs to develop annual summative assessments in subject/grade combinations not currently tested at the state level beginning in fall 2011 (pp. 64-65): • Develop specifications by spring 2012 • Develop review procedures by spring 2014

16. Multi-state Assessment • SMARTER (p. 52) • Summative Multi-state Assessment Resources for Teachers and Educational Researchers • MI is a lead state • Develop summative assessments based on the CCK-12 Standards in ELA and mathematics • MOSAIC (p. 52) • Multiple Options for Student Assessment and Instruction Consortium • “Interim benchmark and formative assessments . . . designed to complement a summative assessment system” (i.e., SMARTER) • Also collaboratively develop a curriculum framework and instructional support and integration materials

17. But . . . • It was announced Friday morning that MI did not get any money for the first round of grants. • MI will reapply when applications are accepted in June.

18. What does it take to pass the Math MEAP?

19. What does this mean? • Percent Proficient is meaningless • Cut scores are low because of the composition of the test • Look at Item Analysis: • Not reliable to item or GLCE level • Look at groups of items – by Focal Point or Topic

20. Looking at your item analysis • 80% or better • 60-79% • 59% or lower • Prioritize by topic or focal point • Track multi-year trends

21. Grade 7 MEAP (Grade 6 content): Rational number operations: Multiply and divide fractions Integers and rationals: +,- Decimal, %, and rational numbers Expressions and equations: Variables, combine like terms Solve equations Properties of 3D shapes Convert in measurement systems Grade 8 MEAP (Grade 7 content): Proportionality and similarity Rates, ratios, & proportions Directly proportional, linear Similar polygons Functions, linear equations Represent linear functions Expressions & equations Compute with rational numbers Represent & interpret data Analysis of Several Local Districts

22. Focal Points Grades 6-8

23. Rational Number Projecthttp://www.cehd.umn.edu/rationalnumberproject/ • From the home page, scroll down and choose “publications in chronological order” • Two documents released 2009: • RNP1 – “Initial Fraction Ideas” • RNP2 – “Fraction Operations and Initial Decimal Ideas”

27. Correct Notation Examples of multiplicative language: • If I double the total parts then the shaded parts double. • If the total number of parts is multiplied by 3, then the shaded parts are three times as many too. • If the number of shaded parts is multiplied by 4 then total number of parts is multiplied by 4.

28. FREE: Fractions Model I from Illuminations Factor Tree from National Library of Virtual Manipulatives Chapter 6 Templates from MMPI (www.michiganmathematics.org) Available for purchase from Scholastic: FASTTMath Fraction Nation Visual and Mental Models for Fractions

29. Think - Write • Choose an algebra focal point for your grade. What are the critical ideas – the mathematics that students must understand – for that topic?

30. Read the introduction. • Share with a neighbor.

31. How many focal points are at your grade level? • The GLCE topics are the same as the Core and Extended Designations document from MDE

32. National Math Panel Benchmarks are checkpoints • Benchmarks are often a grade or two past where the topic is typically taught

33. Find this chart for each focal point at your grade. • The columns are the same as the 11” x 17” K-8 Alignment chart

34. Three Sections for Each Focal Point From the 1-13-2010 DRAFT of the Common Core Standards Initiative

35. Explore the Finding Focus Document • There are two places in this document to find the list of GLCE topics for focal a point. Where are those two places? • Find the “leftover” GLCEs for your grade. Compare the chart to the 11” x 17” K-8 Alignment. • Find the fractions focal point for your grade. What number is it? • How many “Extended Core” expectations are related to the fraction focal point? • Choose any focal point at your grade. Compare the GLCEs for the focal point to the DRAFT CCSI standards.

36. The Big Ideas are NOT Topics for instructional planning GLCEs for assessing students The Big Ideas ARE The mathematics YOU should keep in mind as you plan instruction Critical ideas that are true at all grade levels Big Mathematical Ideas and Understandings

37. SILENT Reading • Find the “Big Mathematical Ideas and Understandings” for the algebra focal point you brainstormed about earlier • Read, re-read, highlight, and take notes • Add to the list you brainstormed of critical ideas for your grade

38. Break

39. Big Ideas With your grade level, discuss • What stood out to you from the Big Ideas? • What questions do you still have? • Revise your notes.

40. Children’s Difficulties in Beginning Algebra Using Variables: • Do #1, 3, 4, 6, 7, 9, 12 • What misconceptions so students have?

41. Student Misconceptions from “Using Variables” l

42. Students struggle with . . . • The focus of algebraic activity and the nature of “answers” • The use of notation and convention in algebra • The meaning of letters and variables • The kinds of relationships and methods used in arithmetic

43. The Nature of “Answer”

44. 14-year-old Wendy

45. 16-year-old Marie

46. 14-year-old Michael

47. Student Misconceptions from “Using Variables” 14x

48. Notation and Convention in Algebra15-year-old Wayne

49. Implications • “2+3” means “add 3 to 2” but it also means “the number that is 3 more than 2” • Students think that 3n means 3+n. Consider delaying conjoined terms (3n) and use the full product (3 x n). • The “2 apples plus 5 bananas” approach to 2a + 5b may not be helpful. Students use this to justify that 2a + 5b = 7ab because 2 apples plus 5 bananas is 7 apples-and-bananas.

50. Letters in Algebra with 15-year-old Peter And what does the y mean, in a question like that [Add 3 to 5y]? Does it mean anything, does it stand for anything, or is it just a letter, or what?