Introduction to Key Shifts in Math Instruction in the Common Core Standards: Introduction to Key Shifts in Math Instruction in the Common Core Standards
Criteria for CCSS : Criteria for CCSS Fewer (focused), clearer, and higher Alignment with college and career expectations Inclusion of rigorous content and application of knowledge through high-order thinking Consideration of strengths of and lessons learned from current state standards Internationally benchmarked, so that all students are prepared to succeed in our global economy and society Evidence and/or research-based 2
Changes by Grade Bands: Grades K-5: Numeration and operation intensified and introduced earlier Early place value foundations in Kindergarten Regrouping as composing/decomposing in Gr. 2 Decimals to hundredths in Gr. 4 All 3 types of measurement introduced simultaneously (Non-standard, English, and Metric) Emphasis on fractions as numbers Emphasis on number line as visualization and structure Changes by Grade Bands: Grades K-5
Shifts in the Mathematics Standards: Shifts in the Mathematics Standards If we just swap out the old standards and put the new CCSS in the old boxes into old systems and procedures into the old relationships i nto old instructional materials and formats i nto old assessment tools, Then nothing will change
Key Shifts in Mathematics Standards: Key Shifts in Mathematics Standards Focus strongly where the standards focus Narrow and deepen the work of each grade level Switch to a curriculum that is a mile deep and an inch wide so that students gain strong foundations Shift 1 FOCUS
The Importance of Focus : The Importance of Focus TIMSS and other international comparisons suggest that the U.S. curriculum is ‘a mile wide and an inch deep.’ “On average, the U.S. curriculum omits only 17% of the TIMSS grade 4 topics compared with an average omission rate of 40% for the 11 comparison countries. U.S. covers all but 2% of the TIMSS topics through grade 8 compared with a 25% non-coverage rate in the other countries. High-scoring Hong Kong’s curriculum omits 48% of the TIMSS items through grade 4, and 18% through grade 8. Less topic coverage can be associated with higher scores on those topics covered because students have more time to master the content that is taught.
Key Shifts in Mathematics Standards: Key Shifts in Mathematics Standards Connect major topics within grades and across grades Build new understanding onto foundations built in previous years Shift 2 COHERENCE 7/28/2012 7
PowerPoint Presentation: Flow Between Domains K 1 2 3 4 5 6 7 8 High School Algebra The Number System Expressions & Equations Operations and Algebraic Thinking Number and Operations- Base Ten Number & Operations- Fractions
PowerPoint Presentation: Modeling K-12 Mathematics Streams Built Upon Learning Progressions Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC K 1 2 3 4 5 6 7 8 9 10 11 12
PowerPoint Presentation: Modeling K-12 Mathematics Streams Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Counting and Cardinality (K) Know number names and the count sequence Count to tell the number of objects Compare numbers © Copyright 2011 Institute for Mathematics and Education K 1 2 3 4 5 6 7 8 9 10 11 12
PowerPoint Presentation: Modeling K-12 Mathematics Streams Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Stream 2: Algebraic Thinking K 1 2 3 4 5 6 7 8 9 10 11 12
PowerPoint Presentation: Modeling K-12 Mathematics Streams Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Stream 3: Number and Quantity K 1 2 3 4 5 6 7 8 9 10 11 12
PowerPoint Presentation: Modeling K-12 Mathematics Streams Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Stream 4: Geometry K 1 2 3 4 5 6 7 8 9 10 11 12
PowerPoint Presentation: Modeling K-12 Mathematics Streams Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Stream 5: Functions K 1 2 3 4 5 6 7 8 9 10 11 12
PowerPoint Presentation: Modeling K-12 Mathematics Streams Geometry Measurement and Data The Number System Number and Operations in Base Ten Operations and Algebraic Thinking Geometry Number and Operations Fractions Expressions and Equations Statistics and Probability Algebra Number and Quantity Functions Statistics and Probability Ratios and Proportional Relationships F CC Stream 6: Statistics and Probability K 1 2 3 4 5 6 7 8 9 10 11 12
Key Shifts in Mathematics Standards: Key Shifts in Mathematics Standards Pursue conceptual understanding, procedural skill and fluency, and application with equal intensity Emphasize conceptual understanding of key concepts Support speed and accuracy in calculation Use mathematics flexibly for application Shift 3 RIGOR
How do these two fraction items differ? : How do these two fraction items differ? 4/5 is closer to 1 than 5/4. Show why this is true on a number line. Which is closer to 1? 5/4 4/5 ¾ 7/10 With your partner, discuss how these items differ . What do they demand from students?