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

Ho How to

• Giv

Give e Student udents a a Strategic gic Adv dvant antage ge in in Math h Clas lass and and Bey eyond

• nd

Dr. . Jennif ennifer er Bay ay-W

• Williams

illiams, ,

Univ Univer ersit ity of

• f Louis

Louisville ille

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@JBayWilliams

What is a Strategic Advantage?

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“If you don't know where you are going, you'll end up someplace else.”

Yogi Berra

Strategic Advantage A way of doing things that makes it more successful than others.

• -Cambridge English Dictionary

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What is going on here?

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

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Strands of Mathematical Proficiency

National Research Council 2001

Str Strate tegy- y- Us Use e

• 1. 404 – 385 =
• 2. 67 – 39 =
• 3. 1900 – 58 =

Solve using a strategy of choice

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Which proficiencies did you demonstrate?

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404 – 385 =

What story problem ‘fits’ this equation?

q Subtraction as ‘take away’ q Subtraction as comparison

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q Subtraction as ‘take away’

400 100 200 300 300 80 5

404 – 385 =

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10

385 400 404

q Subtraction as comparison

15 4

404 – 385 =

15 + 4 = 19

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“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

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

Ho How to

• Giv

Give e Student udents a a Strategic gic Adv dvant antage ge

#1: 1: Connect

• nnect Concept
• ncepts

to

• Procedur
• cedures

es

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Relational Understanding

Skemp, 1978, as illustrated in Van de Walle, Bay-Williams, Lovin, & Karp, 2018

Instrumental Understanding Relational Understanding Continuum of Understanding

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

Procedural fluency is… “skill in carrying out procedures flexibly, accurately, efficiently and appropriately”

#4fluency

(CCSSO, 2010; NCTM, 2014; NRC, 2001)

Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students,

• ver time, become skillful in using procedures

flexibly as they solve contextual and mathematical problems.

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Principles to Actions (NCTM, 2014)

Effective Mathematics Teaching Practices

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. 18

@JBayWilliams

Developing Procedural Fluency

Automaticity

≠

Fluency Facility with Algorithms

≠

Fluency

Developing Procedural Fluency

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Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students,

• ver time, become skillful in using

procedures flexibly as they solve contextual and mathematical problems.

Principles to Actions (NCTM, 2014)

Whic hich h Pie ie Char hart?

A

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Accuracy Accuracy Efficiency Efficiency Strategy Selection Strategy Selection Flexibility Flexibility

B

Ho How to

• Giv

Give e Student udents a a Strategic gic Adv dvant antage ge

#2: 2: Be e #4F 4Fluenc luency

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Thoughts?

• What’s the goal?
• What’s the message

to the student?

• What’s the message

to the parent(s)?

StrategY- Disadvantage

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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

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 9 + 1 + 5 10 + 6 – 1

How did you think about it?

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

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

Bas asic ic Fact acts Res esear earch h

Str Strate tegy- y- Us Use e

Try-out Making 10 and Pretend- a-10 on These Problems

• 1. 6 + 9 =
• 2. 26 + 39 =
• 3. 7.9 + 5.6 =

Ho How to

• Giv

Give e Student udents a a Strategic gic Adv dvant antage ge

#3: 3: Star art from

• m the

he Beginning ginning

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Which proficiencies did you demonstrate?

2.4 lbs. 1.7 lbs. 1.3 lbs.

How much does each ball weigh?

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Which proficiencies did you demonstrate?

Ho How to

• 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

• cess of
• f mult

multiple iple attempt empts

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Ho How to

• Giv

Give e Student udents a a Strategic gic Adv dvant antage ge

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Talk Less, Smile More Don’t Let them Know what you’re against Or what you’re for…

¡ 4 + 4 ¡ 4 + 6 ¡ 9 + 4 ¡ 2 + 9 ¡ 6 + 7 ¡ 6 + 6 ¡ 8 + 7

Video of second grader using a variety of strategies to show her ways of thinking about basic addition facts.

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)

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How might you solve these problems?

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• 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?

Reasoning about Ratios

Ho How to

• Giv

Give e Student udents a a Strategic gic Adv dvant antage ge

#6: 6: Ask k “When… hen…

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Make a 180º turn on this question!

When hen will ill you

• u us

use e a a … …

• 1. 404 – 385 =
• 2. 67 – 39 =
• 3. 1900 – 58 =

…take-away strategy? …a compare strategy?

How might you solve these problems?

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• 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?

Bloom’s Levels and Mathematics

Level of Thought (Fan & Bokhove, 2014) Bloom’s Levels Fluency with Algorithms

Level 3: Evaluation and Construction Create Evaluate

• comparing different algorithms
• judging efficiency of an

algorithm

• constructing new algorithms

(strategies)

• generalizing

Level 2: Understanding and Comprehension Analyze Apply Understand

• describing why a procedure

works

• applying procedure in a

complex situation Level 1: Knowledge and Skills Remember

• telling the steps of a procedure
• carrying out steps in a

straightforward situation

What…? Why…? When…?

Ho How to

• Giv

Give e Student udents a a Strategic gic Adv dvant antage ge

#7: 7: Stop

• p attac

aching hing ma math h to

• genet

genetics ics

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Ho How Will ill You

• u 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

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