Differentiating Math Instruction

Challenge the Stars, Reach the StrugglersNCTM Annual Meeting 2006

Susan PhillipsMeadow Lane Elementary

Lee’s Summit, MO

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Successful learners who find math rewarding and enjoyable

Our Goal

Our Reality

Different Personalities

Different Mathematical Backgrounds

Different Abilities

Meet the diverse needs of the students in your classroom

by implementing

Curriculum Compacting

Flexible Grouping

Curriculum Compacting

Curriculum CompactingAn instructional technique for modifying the curriculum for above average ability students

(Reis, Burns, &

Renzulli, 1992)

Purposes of Curriculum Compacting

To facilitate learning experiences that are rewarding and enjoyable for all studentsTo relieve students of the repetition of work in areas they have already masteredTo provide time for in-depth learning or enrichment activities

Rationale Findings of Curriculum compacting study

by Renzulli:Ninety-five percent of teachers were able to identify high ability students in their classes and document students’ strengthsApproximately 40-50% of traditional classroom material could be eliminated for targeted students

These student behaviors may suggest that compacting is needed:

Consistently finishing tasks earlyExpressing interest in pursuing alternate or advanced topicsConsistent high performance or motivationBuilding a complete replica of a human skeleton out of paper clips, pencils, and rulers while raising his hand to answer a question in class

Every person is gifted in some area. We just have to find out in what.

Evelyn Blose Holman

The Compacting Process

Determine the learning objectives of the regular curriculum for a single unit

Assess students for previous mastery of these objectives

Substitute more appropriate learning options for the students who show mastery

Step 1

• Select a learning unit, chapter, or topic in one content area

AveragesMean

Median

Mode

Step 2Develop a pre-test (and post-test) to assess the learning objectives for that unitDetermine criteria for “mastery” of the concept using the pretest

AveragesMean

Median

Mode

Pretest

Step 3Develop an enrichment activity or in-depth learning opportunity for the compacted topicDevelop a “compacting contract” for the project or another way of identifying student expectations

AveragesMean

Median

Mode

Pretest

Step 4Administer the pretestIdentify compacting students for this unit

Identify

Students

AveragesMean

Median

Mode

Pretest

Step 5Introduce the compacting project to the identified students

•Review student responsibilities and identify student expectations (contract, scoring guide, check list)

•Let them get to work!

Flexible Grouping

Flexible Grouping

Allowing students to work in differently mixed groups depending on the goal of the learning task at hand.

Michael Opitz

Flexible GroupingRoots in the “One-Room Schoolhouse”Students are grouped and regrouped according to specific goals, activities, or individual needsTends to make teacher’s job easier and students more productiveAllows teacher to work in small groups, taking all students to a higher-level of thinking about the learning experience

Flexible Grouping

Specific Performance

Ability Grouping

General Achievement

Fluid Static

All groups are given higher-level thinking activities

Different groups receive different instruction – “low” group is given lower-level activities

Flexible Grouping

Pre-test gives information needed to group students

Non-compacting group can be split into two sections to better meet the needs of the students:

Facilitated by the Curriculum Compacting process

The “I’ve almost got it” groupThe rest of the class

Two small groups for more individualized instructionor

Ideas for Differentiating Instruction for Groups

PowerPoint LessonsStudents work through “book lesson” in small groupsOne group “teaches” other groupOne group writes problems for other groupGroups working more quickly can take topic further enriching the learning

Curriculum Compacting and Flexible Grouping

Adjusting the presentation of the curriculum to fit the learners rather than expecting students to modify themselves for the curriculum

The challenge for educators is to begin to see students in inclusive ways and to value diversity in their classrooms so that those students who

have become a “ghost”… can become contributors.

C. Dudley-Marling and S. Stires