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Finding Focus for Mathematics Instruction Grades K-2

Thumb-Area Student Achievement Model and Huron Intermediate School District. Finding Focus for Mathematics Instruction Grades K-2. March 25, 2010 Huron Area Technical Center March 31, 2010 Tuscola Technical Center April 14 and 26, 2010 Huron ISD Central Office. Getting SB-CEUs?.

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Finding Focus for Mathematics Instruction Grades K-2

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  1. Thumb-Area Student Achievement Model and Huron Intermediate School District Finding Focus for Mathematics Instruction Grades K-2 March 25, 2010 Huron Area Technical Center March 31, 2010 Tuscola Technical Center April 14 and 26, 2010 Huron ISD Central Office

  2. Getting SB-CEUs? Online evaluation REQUIRED for credit: • e-mail address • last 4 digits of SS# on sign-in sheet • enter PIC # in profile • Shirley will e-mail

  3. 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

  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 (MEAP assessed in 3rd for 2nd grade): • 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. http://www.corestandards.org/

  11. Common Core Draft

  12. Common Core Standards Initiative Revised DRAFT 3-10-2010 • Match CCSI standards to Focal Points and GLCEs • Make new piles if needed • No GLCE for a CCSI standard? Check another grade.

  13. Common Core (CC) – When??? OLD Race to the Top: • Adopt CC in June and roll out in August • Current MEAP/MME through Spring, 2014 • New test beginning 2014-2015 • Application not approved; MI will re-submit Best Guess: • MI will adopt Common Core • At least 4 more years of Current MEAP likely

  14. MI Participates in Two Multi-state Assessment Collaboratives • 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

  15. Recommendations • Make changes now to reflect Focal Points and core/extended GLCEs • When Common Core is adopted by MI, develop a transition plan for your district

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

  17. 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

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

  19. Base ten number system Count, write, order wholes Working with geometric shapes Work with unit fractions Identify & describe shapes Addition, subtraction fluency Add & subtract whole numbers Measure, add, & subtract length Record, add, & subtract money Solve measurement problems Tell time, solve problems 2009 Grade 3 MEAP (Gr. 2 content)

  20. Focal Points Grades K-2

  21. Mentally • Add 28 + 35

  22. Mental Computation Strategies for 28 + 35 • Compensation – find a “friendly” number • Think: 30 + 35 = 65; take away 2, so 63 • OR: 30 + 33 = 63 • Decomposition – use place value positions • Think: 8 + 5 = 13; 20 + 30 = 50; 50 + 13 = 63 • OR: 20 + 30 = 50; 8 + 5 = 13; 50 + 13 = 63 • Jump – begin with one number • Think: 28 + 5 = 33; 33 + 30 = 63 • OR: 28 + 30 = 58; 58 + 5 = 63

  23. 11 Game • Use place value to add and subtract • Two ways to play: • Bingo - each person has his own card • Connect 4 - share a card

  24. Think - Write • Choose the addition/subtraction focal point for your grade. What are the critical ideas – the mathematics that students must understand – for that topic?

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

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

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

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

  29. Three Sections for Each Focal Point From the 3-10-2010 Revised DRAFT of the Common Core Standards Initiative

  30. 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 addition and subtraction focal point for your grade. What number is it? • Choose any focal point at your grade. Compare the GLCEs for the focal point to the DRAFT CCSI standards.

  31. 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

  32. SILENT Reading • Find the “Big Mathematical Ideas and Understandings” for the 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

  33. Break

  34. 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.

  35. Arithmetic Combinations Should children memorize the basic facts? Yes . . but that is misleading as stated. Knowledge of arithmetic concepts form an organizing framework for storing arithmetic combinations . . . Students with greater conceptual knowledge are more likely to use sophisticated strategies and retrieve combinations accurately. That is one reason we do not prefer the term “fact” – knowing an arithmetic combination well means far more than knowing a simple, isolated “fact.” - Sarama and Clements (2009), pp. 131 – 132

  36. Partial Learning Progression for Arithmetic Combinations • Understand numerals and counting • Understand the structure of the teens numbers • Solve addition and subtraction with totals less than 10 • Find “break-apart” partners (numbers <= 10) • Use the 10s structure to add/subtract with teen numbers: 10 + 2 = 12; 18 – 8 = 10 • Add and subtract with three addends using 10s • 4 + 6 + 3 = 10 + 3 = 13; 15 – 5 – 9 = 10 – 9 = 1 • Develop the “Break-Apart-to-Make-Tens” Strategy

  37. Understand the Structure of Teen Numbers • Nimble Numeracy (Fischer, 2002), p. 7 Verbal Counting – 13 through 19

  38. Place Value for the –teen Numbers

  39. “Break-Apart” Partners for Numbers through 10 • Partner Houses • Math Mountains - Math Expressions Grade 1, Houghton Mifflin Harcourt

  40. Break-Apart-to-Make-Tens (BAMT)Concrete Phase

  41. Break-Apart-to-Make-Tens (BAMT)Representational Phase Clements and Sarama (2009), p. 86

  42. Becoming Fluent with Arithmetic Combinations Guidelines to Achieving Fluency: • Essential core skills only • Concepts and strategies first • Distributed practice • Research-based strategies • software • increasing ratio review • Develop relationships and strategic thinking • 8 = 2 x 4 - Sarama and Clements, pp139-140

  43. What does NOT work Timed tests were negatively correlated with knowledge of basic combinations Flash card use was not correlated with better combination knowledge Basic-combination worksheets were positively correlated, but only weakly - Sarama and Clements, pp. 135-138 What works Break-apart-to-make-tens 7 + 8 = 8 + 2 + 5 15 – 8 = 10 – 8 + 5 Tens complements More predictive than work on doubles or smaller sums n + 1 before doubles Structured discovery Developing Knowledge, Fluency, and Adaptive Expertise Neither memorization without understanding nor unsophisticated counting procedures helps.

  44. Math Vocabulary • Targeted Vocabulary with Focal Points on Page 5 • Suggested Vocabulary at end of document How would you describe each list? How would you use each list?

  45. Importance of Explicit Vocabulary Instruction Find “Targeted Vocabulary” on Page 5

  46. Number Pattern • num-ber pat-tern • nəm-bər pa-tərn

  47. Write the term Outline the term - category or synonym  details Add an example math sentences and personal connections also work

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