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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 Do you consider yourself a “math person?” Do you consider yourself a reader? 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). 2000 Rank 2003 Rank 2006 Rank (out of 26) (out of 26) (out of 26) 2009 Rank (out of 26) Math 17th 22nd 22nd Tied 20th Science 13th Tied for 17th 19th 13th n/a Tied 10th Subject Reading 14th 14th 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/ 550 2003 PISA - Math OECD Average U.S.A. 500 450 400 350 300 Slide Credit: EdTrust.org Data Source: Organization for Economic Cooperation and Development (OECD), PISA 2006 Results, http://www.oecd.org/ China has not taken PISA as a nation. Certain cities such as Shanghai have joined and are ranking near the top. Finland Korea Netherlands Switzerland Canada Japan New Zealand Belgium Australia 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/ 2001 MCPS CCSS/EIC Rigor ✔ ✔ Coherence ✔ ✔ Focus ✔ refers to the degree that sets of standards address key content that prepare students for success beyond high school. 2001 MCPS CCSS/EIC Rigor ✔ ✔ Coherence ✔ ✔ Focus ✔ refers to whether the standards create an appropriate balance among: conceptual understanding procedural skill problem solving with an emphasis on application and modeling Percent of Content 2001 MCPS Curriculum Number Algebra Geometry Measurement Statistics Math Math Math Math Math Math Math Math Alg. K 1 2 3 4 5 6 7 Prep Probability Percent of Content Final Common Core Standards Math Math Math Math Math Math Math Math Math K 1 2 3 4 5 6 7 8 Number Algebra Geometry Measurement Statistics Probability 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. 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 1½ ÷ ½ = a. b. c. d. ½ ¾ 3 1 Write this problem as a question using words and not symbols. 3 2 3 2 1 How many halves are in one and one half? 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? Complete the number sentence with <, >, or = 352 < 360 114 > 113 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 What Makes The EIC Foundation Stronger? MCPS 2001 Curriculum Framework EIC / Internationally-driven standards “Spiral” Curriculum – concepts introduced and mastered over several grade levels Concept introduced and mastered in one grade level Grade level standards not sufficiently challenging for most students Many standards are “pulled down” from upper grades. Language of standards was general and not specific – resulting in teaching to test. Fewer, higher, clearer standards provide direction for teaching and learning – not testing. Curriculum developed independently of all other subjects Curriculum integrated with other content areas and thinking and academic skills Comparing Standards on One Topic in Grade 2: Using Place Value to Add and Subtract MCPS 2001 Curriculum EIC / Internationally-driven standards • Add and subtract two- and three-digit numbers using alternative strategies. • Add two- and three-digit numbers with regrouping. • Subtract two-and three-digit numbers with regrouping. * • Model and use the identity and commutative properties for addition…to solve problems. * * From a higher grade level • Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. • Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100– 900. • Explain why addition and subtraction strategies work, using place value and the properties of operations. Critical Questions For Instructional Planning 1. 2. 3. 4. 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? 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 • Additional - Who consistently UCARE strands Enrichment demonstrate strong for a topic • MCPS mastery in all five Acceleration strands for an indicator in mastered Few Students – grade topics level advancement Enrichment and Acceleration Implementation Plan School Year 2011-2012 School Year 2012-2013 Kindergarten, Grade 1, Grade 2 Grade 3, Grade 4, Grade 5 Common Core State Standards/ Elementary Integrated Curriculum Grade Level Math Curriculum with enrichment and acceleration MCPS 2001 Curriculum Continue acceleration within grade level and next grade level up Kindergarten, Grade 1, Grade 2, Grade 3 Common Core State Standards/ Elementary Integrated Curriculum Grade Level Math Curriculum with enrichment and acceleration Grade 4, Grade 5 MCPS 2001 Curriculum Continue acceleration within grade level and next grade level up Number & Counting & Operations and Operations Cardinality Algebraic Thinking Base Ten Foundations for place value: numbers 11-19 are ten ones and some more ones (KMP4) Foundations for place value: Ten ones is a unit called a “ten” Tens can be counted (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) Addition and subtraction problems unknowns in all positions within 10 (G1MP1) Decompose numbers less than or equal to 10 into more than two parts (KMP2) Know number names and the count sequence to 100 (KMP1) UCARE Enrichment Apply place value concepts: Extend counting sequence to 120 starting at any number (G1MP1) Decompose numbers less than or equal to 20 into pairs in more than one way (KMP2) Count to tell the number of objects Compare numbers (KMP2) Learning Progression Enrichment Fluency within 5 (KMP4) Count forward from a given number Compare numbers (KMP4) Learning Progression Acceleration 1 2 2 2 3 3 3 4 4 4 5 5 Accel.: Counting 6 and Cardinality 5 6 Acceleration: Counting and Cardinality Enrich/ Accel.: Oper. and Alg. Thinking Accel.: Counting 6 and Cardinality 7 Marking Period 4 1 Accel.: Accel.: Operations Counting and 3 and Cardinality Algebraic 4 Thinking Enrichment: Meas. and Data 2 5 Weeks 1 Weeks 1 Weeks Weeks Marking Period 1 Opportunities for Enrichment/Acceleration (Kindergarten) Marking Period 2 Marking Period 3 Enrichment: Geometry 6 7 7 7 8 8 8 8 9 9 9 9 Accel.: Number and Operations in Base Ten Number & Number & Operations and Operations Algebraic Thinking Operations Base Ten Base Ten Concrete Models: Add 2-digit to 1-digit, 2-digit to multiple of 10 Subtract multiples of 10 (G1MP3) Addition and subtraction problems unknowns in all positions within 10 (G1MP1) Add and subtract within 10 (G1MP1) Add 3 whole numbers within 10 (G1MP1) Foundations for place value: 10 ones is a unit called a “ten” Tens can be counted (G1MP1) UCARE Enrichment 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) Addition and subtraction problems unknowns in all positions within 20 (G1MP2) Add and subtract within 20 (G1MP2) Addition and subtraction problems with 3 addends (G1MP2) Fluently add and subtract within 10 (G1MP3) Count to 120 starting at any number Compare 2-digit numbers (G1MP1) Learning Progression Enrichment Fluently add and subtract within 20 (G2MP1) Compare relative positions of three 2-digit numbers (G1MP1) Learning Progression Acceleration Marking Period 2 Acceleration: Number and Operations 2 in Base Ten 1 Enrichment: Number and Operations 2 in Base Ten 1 Enrichment: Number and Operations 4 in Base Ten 3 3 5 5 3 Weeks Enrichment/Acceleration: Operations and 6 Algebraic Thinking 4 6 7 7 8 8 9 9 Enrichment: Operations and Algebraic Thinking Acceleration: Operations and Algebraic Thinking Marking Period 4 Acceleration: Operations and Algebraic 2 Thinking/ Number and 3 Operations in Base Ten 1 2 Enrichment: Measurement and Data 4 Weeks 1 Weeks Marking Period 3 5 6 4 Acceleration: Operations and Algebraic Thinking* Weeks Marking Period 1 5 6 7 7 8 8 Acceleration: Number and Operations in Base Ten 9 * moves students to Number and Operations in Base Ten 9 Enrichment: Geometry Number & Operations Base Ten Number & Operations and Operations Algebraic Thinking Base Ten Add & subtract 3-digit numbers models- drawings- number lines – place value strategies (G2MP4) Add & subtract 2-digit numbers models- drawings- number lines – place value strategies (G2MP2) One step +/- word problems (G2MP1) Include compare problems (G2MP2) Add & subtract within 20 – mental strategies (G2MP1) Generate compare problems (G2MP2) Fluently add and subtract within 20 (G2MP2) Meaning of a “hundred” Count by 1s, 10s, 100s to 1000 Numerals and expanded form (G2MP1) UCARE Enrichment 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) Two step +/- word problems – 1-digit addends (G2MP2) Two digit addends (G2MP3) Add 1-digit addends from memory (G2MP3) Mentally add & subtract 10 or 100 Compare using symbols (G2MP1) Enrichment Repeated addition & rectangular arrays (G2MP3) More complex two step +/problem types (G2MP3) Repeated addition & multiple representations (G2MP3) Count by 5s to 1000 from a given number (G2MP1) Acceleration Opportunities for Enrichment/Acceleration (Grade 2) Marking Period 2 Marking Period 3 1 Acceleration: 1 5 Enrichment: Number and Operations in Base Ten 6 7 7 8 9 Weeks Weeks 4 Accel.: Oper. and 2 Algebraic Enrich.: Number 3 Thinking and Op. in Base Ten 4 Enrich.: Oper. 5 and Accel.: Algebraic Oper. Thinking and 6 Algebraic Thinking Acceleration: Oper. and Algebraic Thinking 1 1 2 2 3 Accel.: Num. & Op. in Base Ten Enrich.: Num. & Op. in Base Ten Enrichment: Measurement and Data 5 4 Enrichment: Oper. and Algebraic Thinking 5 6 6 7 7 8 8 9 9 Enrichment: Geometry Enrichment: Oper. and Algebraic Thinking Marking Period 4 3 4 Weeks Oper. and Acceleration: 2 Alg. Thinking Number and Operations 3 in Base Ten Weeks Marking Period 1 8 9 Acceleration: Number and Operations in Base Ten These four nations are in the top ten U.S.A. Source: OECD, PISA 2006 Results, table 4.2c, http://www.oecd.org/ 600 550 500 450 400 350 300 Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results, data available at http://www.oecd.org/ U.S.A.