assess basic facts like they are important...5 fundamentals of fact fluency #1: mastery must focus...

Assess Basic Facts Like They are Important

Alaska Webinar Series, Session #3

@JBayWilliams

Jennifer Bay-Williams University of Louisville

Becoming Fluent with Teaching and Assessing Fact Fluency Webinar Series

2007

5 Fundamentals of Fact Fluency #1: Mastery must focus on fluency

#2: Fluency develops in three phases.

#3: Knowing foundational facts must precede derived facts.

#4: Timed tests do not assess fluency

#5: Students need substantial and enjoyable practice.

Bay-Williams, J. M. & Kling, G. G. (2019). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

#4FLUENCY

5

Where is each student on this learning progression? Phase 1: Counting Counts with objects or mentally

Phase 2: Deriving Uses reasoning strategies based on known facts

Phase 3: Mastery Efficient production of answers

Based on Baroody, 2006

Bay-Williams, J. M. & Kling, G. G. (in press). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

Addition Facts Flexible Learning Progression

Bay-Williams, J. M. & Kling, G. G. (in press). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

Multiplication Facts Flexible Learning Progression

Timed Tests

q  Flexibility q  Accuracy q  Efficiency q  Appropriate

Strategy Use

Aspects of Fluency

Timed Tests

q  Flexibility q  Accuracy q  Efficiency q  Appropriate

Strategy Use

Aspects of Fluency

Timed Tests

q  Flexibility q  Accuracy q  Efficiency q  Appropriate

Strategy Use

Aspects of Fluency

Tests: Extended q  Flexibility q  Accuracy q  Efficiency q  Appropriate

Strategy Use

Aspects of Fluency

80%

50%

100%

Timed tests…

In addition to the powerful negative emotions that timed tests cause, they give students a strong message about math—that it is a performance subject, the main purpose of which is to order and categorize students, rather than a rich and diverse subject that students should enjoy. In too many math classrooms, students believe that their role is to perform—to show they know math and can answer questions correctly—rather than to learn.

-Jo Boaler, 2014

JOURNAL WRITING

Assessing Basic Fact

Fluency Strategy #1

Journal Writing q  Flexibility q  Accuracy q  Efficiency q  Appropriate

Strategy Use

Aspects of Fluency

If your friend didn’t know the answer to 4 + 5, how would you tell him to figure it out?

Journal Writing

q  Flexibility q  Accuracy q  Efficiency q  Appropriate

Strategy Use

Aspects of Fluency

Review the four student responses: What might you infer about each child’s level of fluency?

Journal Writing

q  Flexibility q  Accuracy q  Efficiency q  Appropriate Strategy Use

Aspects of Fluency

Journal Writing

22 Writing Prompts: What might you add?

Flexibility Accuracy Explain how you think through these problems: • 8 + 7 • 5 + 9

What is the answer to 9 × 4 ? How do you know it is correct?

Efficiency Appropriate Strategy Selection

Which facts do you just know? Which facts doyou use a strategy? [Give a list]

Emily solved 6 + 8 by changing it in her mind to 4 + 10. What did she do? Is this a good strategy? Tell why or why not.

OBSERVATIONS

Assessing Basic Fact

Fluency Strategy #2

Observation Checklist

q Flexibility q  Accuracy q  Efficiency q  Appropriate Strategy Use

Asp

ects

of

Flu

ency

Observation Checklist: “Top” of the Flexible Learning Progression

Observation Checklist: “Top” of the Flexible Learning Progression

Observation Checklists: Foundational Facts

What will students be doing in order to see what they know? What might you record in the cells?

Observation Tool: One Fact Set

Observation Tool: One Fact Set [5s]

Observation Tool: Diagnostic Analysis

Observation Tools: Class Strategy Use

Observation Checklists: Derived Facts

CODE: I = Inefficient method used (e.g., Phase 1) S = (efficient) Strategy used K = Just knew (recall) A = Automatic (< 3 seconds)

INTERVIEWS

Assessing Basic Fact

Fluency Strategy #3

INTERVIEWS q  Flexibility q  Accuracy q  Efficiency q  Appropriate

Strategy Use

Aspects of Fluency

Which of the aspects of fluency can be assessed with informal interviews? Which of the aspects of fluency can be assessed with more formal interviews?

Observation Time! Observers: For which facts are your ‘students’ counting? using strategies? automatic?

Game

Strategy Games

AdditionFactsMasteryChartFlexibleLearningProgression

+/-0,1,2

Doubles Combosof10 10+___

NearDoubles Making10Pretend-a-10

AdditionFactsMasteryChart

FlexibleLearningProgression:FoundationalFacts

+/-0,1,2

Doubles Combosof10 10+___

FoundationalFactSets

DerivedFactStrategies

Multiplication Games: •  Squares Bingo •  Trios •  Rectangle Fit •  Crossed Wires •  Product Pile-Up •  The Factor Game •  Right Price Game •  Salute

Addition Games: •  Lucky 13 •  Finding 5s •  One More Cover It •  Fishing for 10s •  Double to Connect 4 •  Fixed Addend War •  Subtraction Stacks •  Salute

Strategy Games Multiplication Games: •  Squares Bingo •  Trios •  Rectangle Fit •  Crossed Wires •  Product Pile-Up •  The Factor Game •  Right Price Game •  Salute

Addition Games: •  Lucky 13 •  Finding 5s •  One More Cover It •  Fishing for 10s •  Double to Connect 4 •  Fixed Addend War •  Subtraction Stacks •  Salute

Interviews: Just the Facts

¡ First (in any order)[+0,1,2]:

0 + 7 2 + 3 1 + 6

¡ Middle (in any order)[Doubles w/10; C-10]

3 + 3 3 + 7 6 + 4 4 + 4 5 + 5 9 + 1

¡ Last (in any order)[Within-10 toughies]

4 + 5 5 + 3 3 + 4

Interview #2 In order, for each ask, “How did you think about it?”

Which strategies do you think Grade 2 students might use to solve these facts?

¡ 4 + 4

¡ 4 + 6

¡ 9 + 4

¡ 2 + 9

¡ 6 + 7

¡ 6 + 6

¡ 8 + 7

Four Facts Interview Protocol

Multiplication:

6 × 4

7 × 6

9 × 6

4 × 9

Reflecting on Interviews

¡ Number of questions?

¡ How much time?

¡ Teach or don’t teach?

¡ How do you ‘create the space’?

¡ How many children do you interview?

¡ Other questions?

•  What do you notice about this interview protocol?

•  How might you use such a tool?

ADAPTED TESTS

Assessing Basic Fact

Fluency Strategy #4

Tests: Alternatives

Adapting Tests

Circle the ones you ‘just know’. Star the ones where you used a strategy

Just Knew

JUST KNEW

Counting Near Doubles

Make 10 Pretend-a-10

Bay-Williams, J. M. & Kling, G. G. (2019). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

Just Knew

Used a Strategy

Counted On

Automatic! Working on It

SNOW BALL FIGHT!

SNOW BALL FIGHT!

8 × 7 Solve your fact. Tell your partner how you thought about it.

What ideas might you implement to adapt

facts tests so that they de-emphasize time and

emphasize personal improvement and

strategy-use?

PROGRESS CHARTS

Assessing Basic Fact

Fluency Strategy #5

PROGRESS CHART

FOUNDATIONAL FACTS

Promising Results! Kling (2013) followed 30 children from 2 different schools, 4 different classrooms, in Kalamazoo, MI.; 21 had no exposure to timed testing or drill in the classroom in either 1st or 2nd grade. By the end of 2nd grade all 21 children demonstrated:

¡ automaticity with addition facts (solved within 3 seconds) 95% of the time.

¡ Strategy use (e.g., making ten) so quickly that it was impossible to distinguish between strategy use and “knowing from memory.”

…and RETENTION

18 of the children were interviewed once more in the first week of 3rd grade prior to any fact strategy review. All 18:

¡ Children demonstrated automaticity 91% of the time.

¡ Were accurate and used strategies (not counting) 99.99% of the time.

NCTM Teaching Children Mathematics April 2014 Two Complementary Articles

What assessment strategies might you implement?

What other steps might you

take to ensure that we use the most effective assessment

strategies for our most important topic?

Bibliography

Bay-Williams, J. M. & Kling, G. G. (2019). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD. Bay-Williams,J.andG.Kling(2014).EnrichingAddi>onandSubtrac>onFactMasterythroughGames.TeachingChildrenMathema1cs,21(4),238–247.Baroody,A.(2006).WhyChildrenHaveDifficul>esMasteringtheBasicNumberCombina>onsandHowtoHelpThem.TeachingChildrenMathema1cs13(1):22-31.Baroody,A.(1985).MasteryofBasicNumberCombina>ons:Internaliza>onofRela>onshipsorFacts?JournalforResearchinMathema1csEduca1on,16(2)p.83-98.Boaler,Jo.2012.“TimedTestsandtheDevelopmentofMathAnxiety”Educa1onWeek,onlineJuly3,2012.Henry,V.andR.Brown(2008).First-GradeBasicFacts:AnInves>ga>onIntoTeachingandLearningofanAccelerated,High-DemandMemoriza>onStandards.JournalforResearchinMathema1csEduca1on:39(2)p.153-183.Kling,GinaandJenniferBay-Williams(2014).AssessingBasicFactFluency.TeachingChildrenMathema1cs.20(8),488-497.Kling,Gina(2011).FluencywithBasicAddi>on.TeachingChildrenMathema1cs18(2),80-88.Kling,G.,&Bay-Williams,J.M.(2015).Threestepstomasteringmul>plica>onfacts.TeachingChildrenMathema1cs,21(9),548-559.

Bibliography (Con’t)

Mokros, J., S. Russell, & K. Economopoulos (1995). Shouldn’t Students Memorize the Basic Math Facts? Beyond Arithmetic. White Plains, NY: Dale Seymour Publications. National Council of Teacher of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc. National Research Council (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. Ramirez, Gerardo, Elizabeth A. Gunderson, Susan C. Levine, and Sian L. Beilock. 2013. “Math Anxiety, Working Memory, and Math Achievement in Early Elementary School.” Journal of Cognition and Development, 14(2): 187-202. Steinberg, R. (1985). Instruction on Derived Facts Strategies in Addition and Subtraction. Journal for Research in Mathematics Education, 16(5), p. 337-355. Thornton, C. (1978). Emphasizing Thinking Strategies in Basic Fact Instruction. Journal for Research in Mathematics Education: 9(3), 214-227. Wheatley, G. and A. Reynolds (1999). Thinking in Units. Coming to Know Number: A Mathematics Activity Resource for Elementary Teachers. Bethany Beach, DE: Mathematical Learning.