Report

Fluency is More Than a Race Developing Fluency with Understanding It is All About the Problem Using Rich Problems to Develop Mathematical Understanding TERESA HAMMOND, WVDE LYNN BAKER, NBCT [email protected] [email protected] Session Goals Share evidence of student understanding related to place value. Examine strategies to help students develop fluency with basic facts and standard algorithms. Review problems that engage students in the problem solving experience. Linda Gojack Evidence of Student Learning 5 minutes/teacher Summarize mathematical task Share evidence of student learning Seek input from fellow teachers Respect student privacy What is Computational Fluency? Adding It Up The National Academies Press “Procedural Fluency-skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.” Key Fluencies Grade K 1 Required Fluency Add/subtract within 5 Add/subtract within 10 Add/subtract within 20 (using mental strategies) 2 (by end of Grade 2, know from memory all sums of two one-digit numbers) Add/subtract within 100 (pencil and paper) (using strategies based on place value, properties of operations and/or the relationship between addition and subtraction) Multiply/divide within 100 (using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations) 3 (by the end of Grade 3, know from memory all products of two one-digit numbers) Add/subtract within 1000 (using strategies and algorithms based on place value, properties of operations and/or the relationship between addition and subtraction) 4 5 Add/subtract within 1,000,000 (using the standard algorithm) Multi-digit multiplication (using standard algorithm) Key Fluencies (6-8) 6 Multi-digit division (using standards algorithm) Multi-digit decimal operations (add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation) 7 Solve px + q = r, p(x + q) = r 8 Solve simple 22 systems by inspection Developing Fluency 1. Help children develop a strong understanding of number relationships of the operations 2. Develop efficient strategies for fact retrieval through practice. 3. Then provide drill in the use and selection of those strategies once they have been developed. John A. Van de Walle & LouAnn H. Lovin From Memory ≠ Memorize Develop Meaningful Understanding Practice Fluency Timed Tests and the Development of Math Anxiety By Jo Boaler Group Discussion: What challenges your thinking? How will this article impact your thinking? What questions did this article raise? Strategy-Personalized Flashcards Characteristics: 26 cards 10 cards that students know 8 cards that students know but need continued practice 8 cards that students need to learn: 4 cards related to one fact family 4 cards related to one fact family Teaching Basic Facts WHAT TO DO--- WHAT NOT TO DO--- Ask students to self-monitor Don’t use lengthy timed tests Focus on self-improvement Don’t use public comparisons of mastery Drill in short time segments Work on facts over time Involve families Make drill enjoyable Use technology Emphasize the importance of quick recall of facts Don’t proceed through all facts all at once Don’t move to memorization to soon Don’t use facts as a barrier to good mathematics Don’t use fact mastery as a prerequisite for calculator use Fluency-Standard Algorithms Standard Algorithms in the Common Core Karen C. Fuson & Sybilla Beckmann Introduction Strategy, Standard Algorithm, and Written Method Criteria for Emphasized Written Method It is All About the Problem Using Rich Problems to Develop Mathematical Understanding Kathy Seeley Inside Mathematics http://www.insidemathematics.org Parking Cars rd (3 Grade Illustrative Mathematics http://www.illustrativemathematics.org Next Steps Focus on developing fluency and engaging students with problems. Bring evidence of student learning Thursday, May 7, 2015—Fractions--More Than Apples and Pizzas