Interventions for Fractions based on Critical Point Assessments Grades 3-5

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DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Interventions for Fractions based on Critical Point Assessments Grades 3-5 DeAnn Huinker & Judy Winn University of Wisconsin- Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil Hi-Mount Community School Milwaukee Public Schools Wisconsin Mathematics Council Annual Meeting, May 4, 2012 Green Lake, Wisconsin

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Interventions for Fractions based on Critical Point Assessments Grades 3-5. DeAnn Huinker & Judy Winn University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil Hi-Mount Community School Milwaukee Public Schools Wisconsin Mathematics Council - PowerPoint PPT Presentation

Transcript of Interventions for Fractions based on Critical Point Assessments Grades 3-5

Page 1: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Interventions for Fractions based on Critical Point AssessmentsGrades 3-5

DeAnn Huinker & Judy WinnUniversity of Wisconsin-Milwaukee

Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’NeilHi-Mount Community SchoolMilwaukee Public Schools

Wisconsin Mathematics CouncilAnnual Meeting, May 4, 2012Green Lake, Wisconsin

Page 2: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Our Purpose

Share our experiences in designing and implementing an intervention for fractions with students in Grades 4 and 5, including students with and without Individual Evaluation Plans (IEPs) in mathematics.

Page 3: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Agenda

• Background

• Screener

• Intervention

• Impact on Student Learning

• Classroom Carryover

Page 4: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

BackgroundRtI, DWW, CCSSM

Page 5: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

CulturallyResponsive

Practices

CulturallyResponsive

Practices

Page 6: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Wisconsin Response to Intervention RoadmapA Model for Academic and Behavioral Success for All Students Using Culturally Responsive

Page 7: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

URL: dww.ed.gov• US Department of Education

• Research-based education practices

IES Practice GuideDeveloping Effective Fractions Instruction for Kindergarten Through 8th Grade

Page 8: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Page 9: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Grades 1-2 FractionsDomain: Geometry•Standards 1.G.3 and 2.G.3

Grades 3-5 FractionsDomain: Number and Operations – Fractions•Standards 3.NF.1, 3.NF.2, 3.NF.3

Page 10: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

2.G.3.

•Partition circles and rectangles into two, three, or four equal shares,

•describe the shares using the words halves, thirds, half of, a third of, etc., and

•describe the whole as two halves, three thirds, four fourths.

•Recognize that equal shares of identical wholes need not have the same shape.

Fractions in Grade 2 (Geometry Domain)

Page 11: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Screener

Page 12: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Developing the Screener

• Reviewed IES, CCSSM, research on fractions, curriculum materials.

• Developed framework of 5 key understandings.• Created a draft of a screener: 13 items.• Piloted with a range of students.• Reviewed student work.• Selected items that differentiated students

and fraction ideas.• Revised the screener: 7 items.

Page 13: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Screener Framework: Key Understandings (KU) to Assess

KU1. Partitioning and fair shares

KU2. Comparing, ordering, and equivalence

KU3. Fraction symbols and landmarks

KU4. Fractions as a point on the number line

KU5. Informal use of operations in context

Page 14: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Study the Screener - Work in pairs

Identify which key understanding from the framework is being assessed in each item.

KU1. Partitioning and fair shares

KU2. Comparing, ordering. and equivalence

KU3. Fraction symbols and landmarks

KU4. Fractions as a point on the number line

KU5. Informal use of operations in context

Page 15: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Screener Items & Key Understandings (KU)

Item 1: KU1 Partitioning

Item 2: KU1 Partitioning

Item 3: KU5 Operations in context

Item 4: KU2 Comparing, ordering, equivalence

Item 5: KU3 Symbols and landmarks

Item 6: KU5 Operations in context

Item 7: KU4 Point on a number line

Page 16: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Selecting Students for the Intervention

Page 17: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Analysis of Student Work

Non-FractionalReasoning

TransitionalStrategy

FractionalStrategy

Early FractionalStrategy

Adapted from OGAP Fraction Framework (VMP, 2009http://margepetit.com/FractionFrameworkSept2011V19.pdf)

- Whole number reasoning

- Rule based- No or very little

evidence of fraction ideas

- Semi-appropriate model or idea

- Misconception or error

- Some notion of partitioning to build upon

- Generate a model

- Strategy works but not efficient

- Some gaps in fraction understanding

- Fraction sense- Correct models- Efficient strategies- Reasoning with

benchmarks, equivalence, and relative magnitude

Page 18: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Nathan has of a pan of brownies. Amber has of a pan of brownies. Who has more and why?

Non-FractionalReasoning

Page 19: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Nathan has of a pan of brownies. Amber has of a pan of brownies. Who has more and why?

TransitionalStrategy

Early FractionalStrategy

Page 20: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Analysis of Student Work

Non-FractionalReasoning

TransitionalStrategy

FractionalStrategy

Early FractionalStrategy

Adapted from OGAP Fraction Framework (VMP, 2009)

- Whole number reasoning

- Rule based- No or very little

evidence of fraction ideas

- Semi-appropriate model or idea

- Misconception or error

- Some notion of partitioning to build upon

- Generate a model

- Strategy works but not efficient

- Some gaps in fraction understanding

- Fraction sense- Correct models- Efficient strategies- Reasoning with

benchmarks, equivalence, and relative magnitude

Page 21: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Design of the Intervention

Page 22: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Intervention Flow

Fair SharesFair Shares HalvesHalvesFourths

Unit Fractions

FourthsUnit

Fractions

FourthsNon-unit

Fractions & Equivalency

FourthsNon-unit

Fractions & Equivalency

Diagrams & SymbolsDiagrams & Symbols

Page 23: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Checklist

Provided…• A frame for the

instructional sequence.• A record of instruction.• A record of students’

understanding.Could be used for a group of students or for individual students.

Page 24: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Key Resource

Extending Children's Mathematics: Fractions & Decimals

Authors: Susan Empson & Linda Levi

Date of Publication: 2011Publisher: Heinemann

Page 25: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

“Nuts and Bolts”of the Intervention

Page 26: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

How it was done…Ms. O’Neil Ms. Le Flore Ms. Schlichtholz

Fourth Grade Fourth/Fifth Grades Special education students

5 students 5 students 5 students (3 in fourth grade and 2 in fifth grade)

8 sessions 10 sessions 8 sessions

Before Fraction unit During Fraction unit Before unit for some; During for others

After school During school During school

In classroom In classroom In resource room

30 minutes over the course of three weeks

20 minutes over the course of a month

30 minutes on consecutive days

Page 27: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Intervention Examples

Page 28: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Page 29: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Task 1: Fair Shares

Jayson has a bag of 10 pieces of licorice. He wants to share the licorice with 4 friends. How much licorice would each friend get?

Page 30: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Page 31: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

• Describe the shares. • Justify why they are fair.

Turn and Talk

Turn and Talk

Page 32: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Task 2: Re-composing Wholes and Equivalent Fractions

Page 33: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Impact on Students

Page 34: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Four children are sharing 3 candy bars. If the children share the candy bars equally, how much can each child have?

Pre-Assessment Post-Assessment

Miracle

Page 35: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Two children are sharing 5 candy bars. If the children share the candy bars equally, how much can each child have?

Achantia

Pre-Assessment Post-Assessment

Page 36: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Four children are sharing 3 candy bars. If the children share the candy bars equally, how much can each child have?

Jordan

Pre-Assessment Post-Assessment

Page 37: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Classroom Carryover

Page 38: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Back in the classroom…

• Students had the fraction language to participate in class discourse.

• Students showed increased confidence, volunteered more – they raised their hands!

• Students had access to the math content.

• Still some struggles with transfer...

Page 39: Interventions for Fractions  based on Critical Point Assessments Grades 3-5

DeAnn Huinker & Judy Winn, University of Wisconsin-MilwaukeeLeah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

Thank you!DeAnn Huinker [email protected]

Judy Winn [email protected]

Leah Schlichtholz [email protected]

Frelesha A LeFlore [email protected]

Jennifer O'Neil [email protected]