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, WVDELYNN BAKER, NBCT

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 GradeRequired Fluency KAdd/subtract within 5 1Add/subtract within 10 2 Add/subtract within 20 (using mental strategies) (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) 3 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) (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 Add/subtract within 1,000,000 (using the standard algorithm) 5 Multi-digit multiplication (using standard algorithm)

Key Fluencies (6-8) 6Multi-digit division (using standards algorithm) Multi-digit decimal operations (add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation) 7Solve px + q = r, p(x + q) = r 8 Solve simple 2  2 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 Understanding Meaningful 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

Teaching Basic Facts WHAT TO DO--- Ask students to self-monitor Focus on self-improvement 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 WHAT NOT TO DO--- Don’t use lengthy timed tests Don’t use public comparisons of mastery 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 Parking Cars (3 rd Grade

Illustrative Mathematics g g

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