Teachers’ Uses of Virtual Manipulatives in K-8 Mathematics Lessons

Patricia S. Moyer-Packenham, Gwenanne Salkind,& Johnna J. Bolyard

George Mason UniversityOctober 26, 2007

29th Annual Meeting of PME-NALake Tahoe, Nevada, USA

Goals of the Presentation

• Identify the virtual manipulatives teachers use

• Describe the mathematics content taught with virtual manipulatives

• Classify the ways teachers and students use virtual manipulatives

Examine teachers’ uses of virtual manipulatives in mathematics lessons across Grades K-8

What are Virtual Manipulatives?

• Interactive

• Web-based

• Visual representation of a dynamic object

• Presents opportunities for constructing mathematical knowledge

Moyer, Bolyard, & Spikell (2002)

Review of Research

• Representations are signs, characters, icons, or objects that stand for, or “represent” something else (Goldin, 2003).

• Dual Coding Theory: Information for memory is processed and stored by two interconnected systems: verbal codes and visual codes. When learners are presented with both visual and verbal codes, there is an additive effect on their recall of information (Clark & Paivio, 1991).

• Virtual manipulatives include verbal codes (i.e., letters, numbers, and words) and visual codes (i.e., pictures) presented simultaneously.

Research Questions

• What virtual manipulatives are used by teachers in mathematics lessons?

• How are they used?

Participants

• 116 teachers• Kindergarten through Grade 8• Same school district• Teaching experience

• Range: 1-32 years• Average: 12 years

• Teaching Level• 67% at Elementary• 33% at Secondary

Mathematics Institutes

• One-week during the summer (40 hours)

• Followed by 4 formal meetings during the school year (8 hours)

• 4 grade bands (K-2, 3-4, 5-6, 7-8)

• 2 sections of each group for a total of 8 groups

• Taught by 4 instructors

• Readings, discussions, hands-on experiences including the use of virtual manipulatives

Data Sources

• Each teacher developed 5 lessons

• Lessons were taught in their classrooms

• Written lesson plans were collected

• 95 lesson plans included virtual manipulatives• 28% Grades K-2• 16% Grades 3-4• 32% Grades 5-6• 24% Grades 7-8

Analyses

• Mathematics content

• Types of virtual manipulatives used within grade-specific groups

• Categories describing how the virtual manipulatives were used

• Connections between virtual and physical manipulatives

Mathematics Content

• Number & Operations (35%)

• Geometry (32%)

• Algebra (13%)

• Measurement (13%)

• Data Analysis & Probability (7%)

Virtual Manipulatives Used

Angles

Arrays

Attribute Blocks

Balance

Balls in Bags

Base-Ten Blocks

Box Plots

Clocks

Color Chips

Color Tiles

Factor Trees

Fractals

Fraction Bars

Fraction Circles

Fraction Squares

Geoblocks

Geometric Solids

Histograms

Let’s Make a Deal

Money

Number Lines

Pattern Blocks

Peg Puzzles

Pentominoes

Percent Bars

Protractors

Quilt

Spinners

Tangrams

Triangles

Virtual Manipulatives Used Most Frequently

• Geoboards (11%)

• Pattern Blocks (11%)

• Tangrams (9%)

• Base-ten Blocks (8%)

VMs Used Across Grade-Specific Groups

Grade-Specific Groups

Virtual ManipulativesK-2

(N=27)

3-4(N=15)

5-6(N=30)

7-8(N=23)

All(N=95)

Base-Ten Blocks 11% 20% 7% 0% 8%

Fraction Circles 0 7 10 4 5

Fraction Squares 4 0 7 4 4

Geoboards 4 0 17 17 11

Geometric Solids 0 7 3 4 3

Number Lines 0 7 3 4 3

Pattern Blocks 22 13 0 9 11

Tangrams 19 7 10 0 9

How Virtual Manipulatives Were Used

Grade-Specific Groups

CategoryK-2

(N=27)

3-4(N=15)

5-6(N=30)

7-8(N=23)

All(N=95)

Investigate 52% 33% 47% 43% 45%

Understand 29 47 33 43 37

Intro 11 20 13 13 14

Game 4 0 3 0 2

Other(Aide, Model, Extend)

4 0 3 0 2

How Virtual Manipulatives Were Used

Grade-Specific Groups

CategoryK-2

(N=27)

3-4(N=15)

5-6(N=30)

7-8(N=23)

All(N=95)

Used Only VM 37% 40% 77% 44% 52%

Used PM, Then VM 59 53 17 52 42

Used VM, Then PM 0 0 7 0 2

Simultaneous Use 4 7 0 4 3

Key Findings and Implications

• A variety of virtual manipulatives were used by teachers for mathematics instruction across Grades K through 8.

• The majority of lessons were in the Number & Operations and Geometry Standards

• We were not surprised that geoboards, pattern blocks, base-ten blocks, and tangrams were the most frequently used virtual manipulatives as these are commonly used physical manipulatives.

Key Findings and Implications

• Virtual manipulatives were frequently used to investigate mathematical ideas or develop understandings of mathematical concepts.

• An approximately equal number of lessons used virtual manipulatives alone as used virtual manipulatives together with physical manipulatives.

• When there was a combination of virtual manipulatives and physical manipulatives, teachers used the physical manipulative first.

Patricia S. Moyer-Packenhampmoyer@gmu.edu

Gwenanne Salkindgsalkind@gmu.edu

Johnna J. Bolyardjohnna.bolyard@mail.wvu.edu