Transcript Standards
Are We Ready to Implement the Common Core Standards in Mathematics ? Katy White based on a presentation by DR. WESLEY BIRD [email protected] Criteria for Establishing Common Core Standards Fewer, clearer, and higher Aligned with college and work expectations 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 CCSSO, National Governors Conference, March 2010 Bird Educational Consulting Missouri – 3rd Determine the perimeter of polygons CCS – 3rd Determine the perimeter of polygons Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. (Last part –formerly at grade 6) 19 Missouri Content Standards vs. CCS Emphasis on Relationships Current Math Curricula In many districts, a fragmented mathematics program has been developed There is more emphasis on learning rules - not on conceptual understanding There is a greater focus on specific test items - not necessarily on good mathematics The curricula is not preparing all students for future employment or the global economy An environment has been created where it is impossible to teach to the depth needed for true understanding. Bird Educational Consulting What does it take to make a mathematical mind? Number sense – a sense of numerosity. We recognize that collections may contain different number of objects and which may contain the most. Numerical ability – able to continue number sequences indefinitely and to count large collections Algorithmic ability – can follow a specified sequence of steps that leads to a particular goal The above attributes provide most of the ingredients to do arithmetic. The remaining attributes all contribute to a greater or lesser sense to mathematics (as opposed to arithmetic) ability The Math Gene – Keith Devlin 26 Bird Educational Consulting What does it take to make a mathematical mind? The ability to handle abstractions – the limitation in coping with abstraction presents the greatest barrier to doing mathematics. A sense of cause and effect – humans seem to acquire this sense at a very early age Logical reasoning – ability to construct and follow a step-by-step logical argument Relational reasoning – relationship between (abstract) objects Spatial reasoning – ability to reason about space and view problems in a spatial fashion The Math Gene – Keith Devlin The K-8 Math Standards are organized by Domain, Clusters, and Standards Domain: Overarching ideas that connect topics across the grade levels. Clusters: Demonstrate the grade by grade progression of task complexity. Standards: Define what a student should be able to know and do at that grade level. Organization of Standards Document Bird Educational Consulting Operations and Algebraic Thinking (Domain) • Represent and solve problems involving multiplication and division. (Cluster) • Understand properties of multiplication and the relationship between multiplication and division. (Cluster) • Multiply and divide within 100. (Cluster) • Solve problems involving the four operations, and identify and explain patterns in arithmetic (Cluster) Bird Educational Consulting Represent and solve problems involving multiplication and division. 1. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. 2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?. (Standards) Bird Educational Consulting Eight Standards of Mathematical Practice 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look and make use of structure 8. Look for and express regularity in repeated reasoning Common Core Standards – State Standards Initiative Bird Educational Consulting Standards of Mathematical Content Elementary Counting Operations and Algebraic Thinking Number and Operations in Base Ten Measurement and Data Geometry Middle High School Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability School Ratios and Proportions Number System Expressions and Equations Statistics and Probability Functions Bird Educational Consulting Common Core Standards – State Standards Initiative Dr. Wesley Bird [email protected] 573-864-4880