Ho How to o Giv Give e Student udents a a Strategic gic Adv - PowerPoint PPT Presentation

Ho How to o Giv Give e Student udents a a Strategic gic Adv dvant antage ge in in Math h Clas lass and and Bey eyond ond Dr. . Jennif ennifer er Bay ay-W -Williams illiams, , Univ Univer ersit ity of of Louis Louisville ille @JBayWilliams 1

What is a Strategic Advantage? “If you don't know where you are going, you'll end up someplace else.” Yogi Berra 2

Strategic Advantage A way of doing things that makes it more successful than others. --Cambridge English Dictionary 3

What is going on here? Van de Walle, Karp, K , Lovin, L. & Bay Williams, J., (2014). Teaching Student-Centered 4 Mathematics – Grades 3-5 . New York: Pearson.

Strands of Mathematical Proficiency National Research Council 2001 5

Str Strate tegy- y- Us Use e 1. 404 – 385 = Solve using a 2. 67 – 39 = strategy of choice 3. 1900 – 58 =

Which proficiencies did you demonstrate? 7

404 – 385 = What story problem ‘fits’ this equation? q Subtraction as ‘take away’ q Subtraction as comparison 8

404 – 385 = q Subtraction as ‘take away’ 300 80 5 19 0 100 200 300 400 9

404 – 385 = q Subtraction as comparison 15 15 + 4 = 19 4 400 385 404 10

“Context has a vital influence on comprehension and understanding. Although most teachers emphasize context in reading, they often fail to see its importance in learning mathematics symbolism and terms.” Lelon Capps Arithmetic Teacher 1993 11

Take away or compare? 1. 404 – 385 = 2. 67 – 39 = 3. 1900 – 58 = 12

Ho How to o Giv Give e Student udents a a Strategic gic Adv dvant antage ge #1: 1: Connect onnect Concept oncepts to o Procedur ocedures es 13

Relational Understanding Continuum of Understanding Relational Instrumental Understanding Understanding Skemp, 1978, as illustrated in Van de Walle, Bay-Williams, Lovin, & Karp, 2018 14

Take away or compare? 1. 404 – 385 = 2. 67 – 39 = 3. 1900 – 58 = 15

Procedural fluency is… “skill in carrying out procedures flexibly , accurately , efficiently and appropriately ” #4fluency (CCSSO, 2010; NCTM, 2014; NRC, 2001)

Effective Mathematics Teaching Practices Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems. Principles to Actions (NCTM, 2014) 17

Bay-Williams, J. M., & Stokes Levine, A. (2017). The Role of Concepts and Procedures in Developing Fluency. In D. Spangler & J. Wanko (Eds.) Enhancing Classroom Practice with Research behind PtA . Reston, VA: NCTM. @ JBayWilliams 18

Developing Procedural Fluency ≠ Fluency Automaticity Facility with Fluency ≠ Algorithms

Developing Procedural Fluency 20

Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems. Principles to Actions (NCTM, 2014) 21

Whic hich h Pie ie Char hart? A B Strategy Selection Flexibility Strategy Accuracy Selection Efficiency Flexibility Efficiency Accuracy 22

Ho How to o Giv Give e Student udents a a Strategic gic Adv dvant antage ge #2: 2: Be e #4F 4Fluenc luency 23

Thoughts? • What’s the goal? • What’s the message to the student? • What’s the message to the parent(s)?

StrategY- Disadvantage

Basic Facts Learning Progression Phase 1: Counting (counts with objects or mentally) Phase 2: Deriving (uses reasoning strategies ) Phase 3: Mastery (efficient production of answers) Based on Baroody, 2006 26

Addition Fact Fluency Chart

Ten FrameS How many dots?

Quick Images: Addition How many dots?

Quick Images: Addition What equation do you see? 9 + 6 How did you think about it? 9 + 1 + 5 10 + 6 – 1

Addition Fact Fluency Chart

Bas asic ic Fact acts Res esear earch h Strategy Groups Outperform Non- strategy Groups • Baroody, Purpura, Eiland, Read, & Paliwal, 2016 • Locuniak & Jordan, 2008 • Purpura, Baroody, Eiland, & Reid, 2016 • Tournaki, 2003

Bas asic ic Fact acts Res esear earch h Strategy Groups RETAIN facts better than non-strategy groups • Baroody, Bajwa, & Eiland, 2009 • Henry & Brown, 2008 • Hiebert & Carpenter, 1992 • Hiebert & Lefevre, 1986 • Jordan, Kaplan, Olah, & Locuniak, 2006

Bas asic ic Fact acts Res esear earch h Strategy use predicts success in math achievement in general . • Geary, 2011 • Jordan, Kaplan, Ramineni, & Locuniak, 2009 • Jordan, Kaplan, Locuniak, & Ramineni, 2007 • Vasilyeva, Laski, & Shen, 2015

Str Strate tegy- y- Us Use e 1. 6 + 9 = Try-out Making 2. 26 + 39 = 10 and Pretend- a-10 on These Problems 3. 7.9 + 5.6 =

Ho How to o Giv Give e Student udents a a Strategic gic Adv dvant antage ge #3: 3: Star art from om the he Beginning ginning 36

Which proficiencies did you demonstrate? 37

How much does each ball weigh? 2.4 lbs. 1.7 lbs. 1.3 lbs.

Which proficiencies did you demonstrate? 39

Ho How to o Giv Give e Student udents a a Strategic gic Adv dvant antage ge #4: 4: Emphas mphasiz ize e the he na natur ural al pr proces ocess of of mult multiple iple attempt empts 41

Ho How to o Giv Give e Student udents a a Strategic gic Adv dvant antage ge Talk Less, Smile More Don’t Let them Know what you’re against Or what you’re for… 42

¡ 4 + 4 ¡ 4 + 6 Video of second grader using a ¡ 9 + 4 variety of strategies to show her ways of thinking about basic ¡ 2 + 9 addition facts. ¡ 6 + 7 ¡ 6 + 6 ¡ 8 + 7

Talk Less, Smile more The use of manipulatives and verbal discussion during instruction affords an invaluable opportunity for assessment of student understanding. Lelon Capps Arithmetic Teacher 1993 (emphasis added) 44

How might you solve these problems? 1. Sammy bought 3 widgets for $2.40. At the same price, how much would 10 widgets cost? 2. Tammy bought 4 widgets for $3.75. How much would a dozen widgets cost? 45

Reasoning about Ratios

Ho How to o Giv Give e Student udents a a Strategic gic Adv dvant antage ge #6: 6: Ask k “ When… hen… 47

Make a 180º turn on this question!

When hen will ill you ou us use e a a 1. 404 – 385 = … … …take-away 2. 67 – 39 = strategy? …a compare 3. 1900 – 58 = strategy?

How might you solve these problems? 1. Sammy bought 3 widgets for $2.40. At the same price, how much would 10 widgets cost? 2. Tammy bought 4 widgets for $3.75. How much would a dozen widgets cost? 50

Bloom’s Levels and Mathematics Level of Thought Bloom’s Fluency with Algorithms (Fan & Bokhove, 2014) Levels Create • comparing different algorithms Level 3: Evaluation and Evaluate • judging efficiency of an Construction algorithm When…? • constructing new algorithms (strategies) • generalizing Analyze • describing why a procedure Level 2: Understanding Apply works Why…? and Comprehension Understand • applying procedure in a complex situation Level 1: Knowledge Remember • telling the steps of a procedure What…? and Skills • carrying out steps in a straightforward situation

Ho How to o Giv Give e Student udents a a Strategic gic Adv dvant antage ge #7: 7: Stop op attac aching hing ma math h to o genet genetics ics 52

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Ho How Will ill You ou Giv Give e Student udents a a Strategic gic Adv dvant antage? ge? 1. Connect concepts and procedures 2. Be #4Fluency 3. Start early 4. Ask (don’t tell) how 5. Emphasize the natural process of multiple attempts 6. Ask “When…” 7. Stop attaching math to genetics 54