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

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Interventions for Fractions based on Critical
Point AssessmentsGrades 3-5

• DeAnn Huinker Judy Winn
• University of Wisconsin-Milwaukee
• Leah Schlichtholz,
• Frelesha LeFlore, Jennifer ONeil
• Hi-Mount Community SchoolMilwaukee Public
  Schools
• Wisconsin Mathematics Council
• Annual Meeting, May 4, 2012
• Green Lake, Wisconsin

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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.

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Agenda

• Background
• Screener
• Intervention
• Impact on Student Learning
• Classroom Carryover

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BackgroundRtI, DWW, CCSSM
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Wisconsin Model of RtIWisconsin Response to
Intervention A Guiding Document
Balanced Assessment
Collaboration
Culturally Responsive Practices
High Quality Instruction
MULTI-LEVEL SYSTEM OF SUPPORT
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Wisconsin Response to Intervention Roadmap A
Model for Academic and Behavioral Success for All
Students Using Culturally Responsive
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URL dww.ed.gov

• US Department of Education
• Research-based education practices

IES Practice Guide Developing Effective Fractions
Instruction for Kindergarten Through 8th Grade
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(No Transcript)
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• Grades 1-2 Fractions
• Domain Geometry
• Standards 1.G.3 and 2.G.3
• Grades 3-5 Fractions
• Domain Number and Operations Fractions
• Standards 3.NF.1, 3.NF.2, 3.NF.3

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Fractions in Grade 2 (Geometry Domain)

• 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.

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Screener
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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.

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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

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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
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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

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Selecting Students for the Intervention
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Analysis of Student Work
Non-Fractional Reasoning
Early Fractional Strategy
Transitional Strategy
Fractional Strategy
- Generate a model - Strategy works but not
efficient - Some gaps in fraction understanding
- 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
- Fraction sense - Correct models - Efficient
strategies - Reasoning with benchmarks,
equivalence, and relative magnitude
Adapted from OGAP Fraction Framework (VMP,
2009 http//margepetit.com/FractionFrameworkSept20
11V19.pdf)
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Nathan has of a pan of brownies. Amber has
of a pan of brownies. Who has more and why?
Non-Fractional Reasoning
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Nathan has of a pan of brownies. Amber has
of a pan of brownies. Who has more and why?
Transitional Strategy
Early Fractional Strategy
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Analysis of Student Work
Non-Fractional Reasoning
Early Fractional Strategy
Transitional Strategy
Fractional Strategy
- Generate a model - Strategy works but not
efficient - Some gaps in fraction understanding
- 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
- Fraction sense - Correct models - Efficient
strategies - Reasoning with benchmarks,
equivalence, and relative magnitude
Adapted from OGAP Fraction Framework (VMP, 2009)
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Design of the Intervention
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Intervention Flow
Fair Shares
Halves
Fourths Unit Fractions
Diagrams Symbols
Fourths Non-unit Fractions Equivalency
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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.

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Key Resource

• Extending Children's Mathematics Fractions
  Decimals
• Authors Susan Empson Linda Levi
• Date of Publication 2011?
• Publisher Heinemann

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Nuts and Boltsof the Intervention
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How it was done
Ms. ONeil 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
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Intervention Examples
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(No Transcript)
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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?

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(No Transcript)
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Turn and Talk

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

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Task 2 Re-composing Wholes and Equivalent
Fractions
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Impact on Students
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Four children are sharing 3 candy bars. If the
children share the candy bars equally, how much
can each child have?
Miracle

• Pre-Assessment

• Post-Assessment

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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
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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
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Classroom Carryover
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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...

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Thank you!
DeAnn Huinker huinker_at_uwm.edu Judy
Winn jwinn_at_uwm.edu Leah Schlichtholz schlicle_at_milw
aukee.k12.wi.us Frelesha A LeFlore
parkerfa_at_milwaukee.k12.wi.us Jennifer O'Neil
oneiljs_at_milwaukee.k12.wi.us