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


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.


Agenda

• Background

• Screener

• Intervention

• Impact on Student Learning

• Classroom Carryover


BackgroundRtI, DWW, CCSSM


CulturallyResponsive

Practices

CulturallyResponsive

Practices


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


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

• Research-based education practices

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


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


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)


Screener


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.


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


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


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


Selecting Students for the Intervention


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


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



Analysis of Student Work



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


Design of the Intervention


Intervention Flow

Fair SharesFair Shares HalvesHalvesFourths

Unit Fractions

FourthsUnit

Fractions

FourthsNon-unit

Fractions & Equivalency

FourthsNon-unit

Fractions & Equivalency

Diagrams & SymbolsDiagrams & Symbols


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.


Key Resource

Extending Children's Mathematics: Fractions & Decimals

Authors: Susan Empson & Linda Levi

Date of Publication: 2011Publisher: Heinemann


“Nuts and Bolts”of the Intervention


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


Intervention Examples


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?


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

Turn and Talk

Turn and Talk


Task 2: Re-composing Wholes and Equivalent Fractions


Impact on Students


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


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

Achantia



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

Jordan



Classroom Carryover


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...


Thank you!DeAnn Huinker [email protected]

Judy Winn [email protected]

Leah Schlichtholz [email protected]

Frelesha A LeFlore [email protected]

Jennifer O'Neil [email protected]

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

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