Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

1. Do not worry if you have built your castles in the air. They are where they should be. Now put the foundations under them. - Henry David Thoreau Building Stronger Math StudentsBy Building a Stronger FoundationMCPS Adoption of New Internationally-driven Standards

2. Icebreaker • Do you consider yourself a “math person?” • Do you consider yourself a reader?

3. Goals of the MCPS Mathematics Program • Develop students who love math and see it as sensible and useful to solving problems and making sense of the world. • All students will reach proficiency in math – Understanding, Computing, Applying, Reasoning, and Engaging (UCARE).

4. Building a Strong Foundation Success in Advanced Math Proficiency in Number Concepts

5. Why internationally-driven standards? Programme of International Student Assessment (PISA) Results Rankings are for the 26 OECD countries participating in PISA in 2000, 2003, and 2006. Slide Credit: EdTrust.org Data Source: Organization for Economic Cooperation and Development (OECD), PISA 2006 Results, http://www.oecd.org/

6. Why internationally-driven standards? OECD Average U.S.A. Slide Credit: EdTrust.org Data Source: Organization for Economic Cooperation and Development (OECD), PISA 2006 Results, http://www.oecd.org/

7. What nations are consistently near the top in math? Why internationally-driven standards? Finland Korea Netherlands Switzerland Canada Japan New Zealand Belgium Australia China has not taken PISA as a nation. Certain cities such as Shanghai have joined and are ranking near the top.

8. What are the Internationally-driven Standards? The Common Core State Standards: • Include rigorous content and application of knowledge through high-order skills • Build upon strengths and lessons of current state standards • Internationally benchmarked so that all students are prepared to succeed in our global economy and society • Based on evidence and research • Learn more: http://www.corestandards.org/

9. Building a Strong Foundation What is needed in curriculum and instruction to help build a strong foundation?

10. Rigor, Coherence, and Focus Source: Achieve – CCSS Rigorrefers to the degree that sets of standards address key content that prepare students for success beyond high school.

11. Rigor, Coherence, and Focus Source: Achieve – CCSS Focusrefers to whether the standards create an appropriate balance among: • conceptual understanding • procedural skill • problem solving with an emphasis on application and modeling

12. MCPS and CCS Strand Comparison

13. Building a stronger foundation • The CCSS recommend that elementary schools focus on building a strong foundation in number concepts – before accelerating into advanced math. • MCPS Math teachers in advanced level courses in middle school and high school have requested a stronger foundation in number concepts for ALL students, even the most advanced. So what does this look like?

14. Going Deep in Mathematics 2001 Curriculum and CCSS Comprehending Concepts, Operations, & Relations Understanding Seeing math as sensible, useful, and doable Carrying out procedures Computing Engaging Applying Reasoning Formulating and solving mathematical problems Using logic to explain a solution

15. MathematicAL Proficiency: Learning A Concept in Depth 1½ ÷ ½ = ½ ¾ 3 1 Write this problem as a question using words and not symbols. COMPUTING How many halves are in one and one half? UNDERSTANDING REASONING

16. MathematicAL Proficiency: Learning A Concept in Depth 1½ ÷ ½ = 3 Describe a situation requiring use of this concept. You have a yard and a half of ribbon to make bows. Each bow requires ½ yard. How many bows can you make? APPLYING REASONING

17. MathematicAL Proficiency: Learning A Concept in Depth Complete the number sentence with <, >, or = 360 114 113 < COMPUTING > Same Problems, but requiring Understanding, Computing, Application, and Reasoning

18. MathematicAL Proficiency: Learning A Concept in Depth ENGAGEMENT When might we need to compare three digit numbers? Which type of milk will give you the most energy per serving? Reduced Fat Milk Chocolate Milk Whole Milk Fat Free Milk

19. Building a Stronger Foundation What Makes The EIC Foundation Stronger?

20. Building a Stronger Foundation Comparing Standards on One Topic in Grade 2: Using Place Value to Add and Subtract

21. Building a Stronger Foundation How Do We Plan To Reach ALL Students? • What do students need to know and be able to do? • How will we know they have learned it? • What will we do when they haven’t? • What will we do when they already know it? Critical Questions For Instructional Planning

22. Building a Stronger Foundation Enriched and Accelerated Instruction in Elementary Math All Students – In the grade level EIC/CCSS Curriculum • Grade level expectations are at a higher level • Fewer topics per grade level • Enrichment–mastery of the 5 UCARE strands requires greater depth for all students Many Students – who consistently master all five UCARE strands for a topic • Additional Enrichment • MCPS Acceleration in mastered topics - Who consistently demonstrate strong mastery in all five strands for an indicator Few Students – grade level advancement

23. Building a Stronger Foundation Enrichment and Acceleration Implementation Plan

24. Building a Strong Number Foundation - Kindergarten:Learning progressions are the basis for deeper enrichment and acceleration beyond the marking period or grade level Number & Operations Base Ten Learning Progressions Enrichment and Acceleration in Kindergarten Foundations for place value: numbers 11-19 are ten ones and some more ones (KMP4) Apply place value concepts: Extend counting sequence to 120 starting at any number (G1MP1) Foundations for place value: Ten ones is a unit called a “ten” Tens can be counted (G1MP1) Operations and Algebraic Thinking Addition and subtraction problems unknowns in all positions within 10 (G1MP1) Addition – putting together and adding to problems within 10. Subtraction – taking apart and taking from problems within 10 (KMP4) Decompose numbers less than or equal to 10 into pairs in more than one way (KMP2) Decompose numbers less than or equal to 10 into more than two parts (KMP2) Decompose numbers less than or equal to 20 into pairs in more than one way (KMP2) Fluency within 5 (KMP4) Counting & Cardinality Know number names and the count sequence to 100 (KMP1) Count forward from a given number Compare numbers (KMP4) Count to tell the number of objects Compare numbers (KMP2) Learning Progression Acceleration Learning Progression Enrichment UCARE Enrichment

25. Opportunities for Enrichment/Acceleration (Grade K)

26. Building a Strong Number Foundation – Grade 1:Learning progressions are the basis for deeper enrichment and acceleration beyond the marking period or grade level Number & Operations Base Ten Concrete Models: Add 2-digit to 1-digit, 2-digit to multiple of 10 Subtract multiples of 10 (G1MP3) Written Methods: Add 2-digit to 1-digit, 2-digit to multiple of 10 Subtract multiples of 10 (G1MP4) Written Methods: Add 2-digit numbers (G2MP2) Operations and Algebraic Thinking Addition and subtraction problems unknowns in all positions within 10 (G1MP1) Addition and subtraction problems with 3 addends (G1MP2) Addition and subtraction problems unknowns in all positions within 20 (G1MP2) Add and subtract within 10 (G1MP1) Add and subtract within 20 (G1MP2) Fluently add and subtract within 10 (G1MP3) Fluently add and subtract within 20 (G2MP1) Add 3 whole numbers within 10 (G1MP1) Number & Operations Base Ten Foundations for place value: 10 ones is a unit called a “ten” Tens can be counted (G1MP1) Compare relative positions of three 2-digit numbers (G1MP1) Count to 120 starting at any number Compare 2-digit numbers (G1MP1) Learning Progression Acceleration Learning Progression Enrichment UCARE Enrichment

27. Opportunities for Enrichment/Acceleration (Grade 1) * moves students to Number and Operations in Base Ten

28. Building a Strong Number Foundation – Grade 2:Learning progressions are the basis for deeper enrichment and acceleration beyond the marking period or grade level Number & Operations Base Ten Two step +/- word problems – 1-digit addends (G2MP2) Two digit addends (G2MP3) More complex two step +/- problem types (G2MP3) One step +/- word problems (G2MP1) Include compare problems (G2MP2) Learning Progressions Enrichment and Acceleration in Kindergarten Learning Progressions Enrichment and Acceleration in Kindergarten Add & subtract 2-digit numbers models- drawings- number lines – place value strategies (G2MP2) Add & subtract 3-digit numbers models- drawings- number lines – place value strategies (G2MP4) Fluently add & subtract 2-digit numbers (G2MP2) Fluently add & subtract 3-digit numbers (G3) Mentally add & subtract within 100 Add four 2-digit numbers within 100 (G2MP2) Generate compare problems (G2MP2) Operations and Algebraic Thinking Add & subtract within 20 – mental strategies (G2MP1) Fluently add and subtract within 20 (G2MP2) Add 1-digit addends from memory (G2MP3) Repeated addition & rectangular arrays (G2MP3) Repeated addition & multiple representations (G2MP3) Number & Operations Base Ten Meaning of a “hundred” Count by 1s, 10s, 100s to 1000 Numerals and expanded form (G2MP1) Count by 5s to 1000 from a given number (G2MP1) Mentally add & subtract 10 or 100 Compare using symbols (G2MP1) Acceleration Enrichment UCARE Enrichment

29. Opportunities for Enrichment/Acceleration (Grade 2)

30. Why internationally-driven standards? But is it fair to compare the U.S. to less diverse nations?

31. Why internationally-driven standards? Immigrants? The U.S. does have a larger percentage of immigrants and children of immigrants than most OECD countries These four nations are in the top ten U.S.A. Source: OECD, PISA 2006 Results, table 4.2c,http://www.oecd.org/

32. Why internationally-driven standards? But, isn’t U.S. performance skewed by the high amount of poverty in the U.S.?

33. Why internationally-driven standards? Math Performance of Wealthiest Students (2003 PISA) U.S.A. Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results, data available at http://www.oecd.org/