1. Teachers’ Uses of Virtual Manipulatives in K-8 Mathematics Lessons
Patricia S. Moyer-Packenham, Gwenanne Salkind,
& Johnna J. Bolyard
George Mason University
October 26, 2007
29th Annual Meeting of PME-NA
Lake Tahoe, Nevada, USA

2. Goals of the Presentation
Examine teachers’ uses of virtual manipulatives in mathematics lessons across Grades K-8
Identify the virtual manipulatives teachers use
Describe the mathematics content taught with virtual manipulatives
Classify the ways teachers and students use virtual manipulatives

3. What are Virtual Manipulatives?
Interactive
Web-based
Visual representation of a dynamic object
Presents opportunities for constructing mathematical knowledge
Moyer, Bolyard, & Spikell (2002)

4. 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.
Applying Dual Coding Theory to instruction when virtual manipulatives are used infers that mathematics environments that activate multiple systems of codes have a greater potential for improving learning because two mental representations are available for use, rather than just one.

5. Research Questions
What virtual manipulatives are used by teachers in mathematics lessons?
How are they used?

6. 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

7. 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

8. 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

9. 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

10. Mathematics Content Number & Operations (35%) Geometry (32%)
Algebra (13%)
Measurement (13%)
Data Analysis & Probability (7%)

11. 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

12. Virtual Manipulatives Used Most Frequently
Geoboards (11%)
Pattern Blocks (11%)
Tangrams (9%)
Base-ten Blocks (8%)
Percentage of all 95 lessons
Links to virtual manipulatives – briefly show each one and how it works. What are our time constraints?

13. VMs Used Across Grade-Specific Groups
Virtual Manipulatives
K-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 7 10 4 5
Fraction Squares
Geoboards 17 11
Geometric Solids 3
Number Lines
Pattern Blocks 22 13 9
Tangrams 19
11% of K-2 lessons included Virtual Base-Ten Blocks, etc.
8 Virtual Manipulatives were used in 3 of the 4 grade-specific groups

14. How Virtual Manipulatives Were Used
Grade-Specific Groups
Category
K-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 14
Game 4 3 2
Other
(Aide, Model, Extend)
52% of the K-2 lessons were investigations, etc.
Most of the lessons focused on investigating mathematical ideas or understanding mathematical concepts
Greater number of lessons at K-2 and 5-6 that included investigations
Greater number of lessons at 3-4 were designed to develop mathematical understandings
Equal number of lessons at 7-8 to investigate and develop understandings

15. How Virtual Manipulatives Were Used
Grade-Specific Groups
Category
K-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 7 2
Simultaneous Use 4 3
An approximate equal number of lessons used virtual manipulatives alone (49 lessons) as used VM together with physical manipulatives (46 lessons).
Three grade-specific groups used virtual manipulatives and physical manipulatives together in a larger proportion of lessons than VM alone (59% of lessons at K-2, 60% of lessons at 3-4, and 56% of lessons at 7-8)
A large portion of the lessons in 3 grade-specific groups used PM first, then VM (K-2, 3-4, 7-8)
The majority of lessons in grades 5-6 used VM alone

16. 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.
Number & Operations and Geometry could be because of the number of topics in these standards or because of the availability and usability of the virtual manipulative applets for these standards

17. 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.

18. Patricia S. Moyer-Packenham pmoyer@gmu.edu
Gwenanne Salkind
Johnna J. Bolyard