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

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

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.

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

6. 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 Participants

7. 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 Mathematics Institutes

8. 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 Data Sources

9. 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 Analyses

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

11. 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 Virtual Manipulatives Used Pattern Blocks Peg Puzzles Pentominoes Percent Bars Protractors Quilt Spinners Tangrams Triangles

12. Geoboards (11%) Pattern Blocks (11%) Tangrams (9%) Base-ten Blocks (8%) Virtual Manipulatives Used Most Frequently

13. VMs Used Across Grade-Specific Groups

14. How Virtual Manipulatives Were Used

15. How Virtual Manipulatives Were Used

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.

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-Packenhampmoyer@gmu.edu • Gwenanne Salkindgsalkind@gmu.edu • Johnna J. Bolyardjohnna.bolyard@mail.wvu.edu