Hey! What's the Deal with Virtual Manipulatives?
July 7, 2022
"Learn ● Create ● Play"
-- Toy Theater
"Learn ● Create ● Play"
When we moved to virtual instruction during the pandemic, we felt anxious about so many things, but one thing at the forefront was, "Are kids even able to learn this way?" We were forced to shift many of our standard pedagogical practices and teaching strategies. For many, teaching math online felt like a struggle, especially without the use of manipulatives and hands-on instruction in class. Teachers and schools were forced to make the shift to virtual manipulatives (through a variety of platforms and tools), but at the back of our mind, we were all thinking, "Is this really working?" And the short answer is yes.
However, in order to fully answer this question, we have to consult some research. First, we have to consult TPACK. TPACK is the interconnectedness between technology (the tool itself), pedagogy (how we teach it), and content (what it is we are teaching). Here's a great introduction to TPACK if it's a new concept for you. Virtual manipulatives fit perfectly into the cross section of technology, pedagogy, and content. We have to teach math at our varying levels; this is the content. We know that manipulatives are helpful for students learning math concepts; this is the pedagogy that has been standard practice for years. The only thing we are shifting here is the technology. The technology used to be a physical manipulative - such as a counting bear - and is not a virtual manipulative - such an interactive image of a counting bear on a Chromebook. Does switching from physical to virtual affect students ability to understand the content?
We found a research study that studied, “Learning Mathematics with Technology: The Influence of Virtual Manipulatives on Different Achievement Groups,” (Moyer, 2012). In Moyer’s research, they found that the use of manipulatives in general (physical or virtual) significantly increased students’ mathematical knowledge. These manipulatives provide an externalized representation of mathematical processes and reflect mathematical properties and conventions. By using and viewing the virtual manipulatives, user’s strategic choices were visually represented while engaged in the mathematical activity. While virtual manipulatives appeared to be beneficial for all students, students at different levels benefitted differently from the virtual manipulatives. “Further examination of the individual gains of each achievement group (low-, average-, and high-achieving) using virtual manipulatives indicated that the low-achieving group had statistically significant pre- to post-test gains, while the average- and high-achieving groups did not,” (Moyer, 2012, p. 52). However, this isn’t to say that virtual manipulatives aren’t helpful for these high-achieving groups. Having choices within the apps of virtual manipulatives allows students to benefit in different ways. Higher students work well with focused constraint, meaning that it was beneficial for them to only have exactly what they need in front of them. Even if they did not need it, they had to use it, which caused them to focus their thinking. Lower students work well with efficient precision. On Toy Theater, they have the exact equipment and the right amount of it, keeping them from getting bogged down by things around them.
It's important not only to think about our general education students, we must think about those with different abilities. In the study, “Virtual Versus Concrete: A Comparison of Mathematics Manipulatives for Three Elementary Students With Autism” (Shurr et al., 2021), they conducted a study in which 3 male students, ages 9, 9, and 10, all diagnosed with Autism Spectrum Disorder and having difficulty with addition operations, were given a series of addition problems to solve with various manipulatives, both virtual manipulatives (VM) and concrete manipulatives (CM). The first series of problems included a set of unique double digit addition problems were administered to the three students without the use of manipulatives. Students were graded on accuracy of the addition problems, and all scored relatively low (see graph). The students were then given training in the usage of both concrete manipulatives, which was a set of base 10 blocks and a place value mat, as well as training in a virtual manipulatives application on an iPad. Students were then administered the remaining question sets, and were allowed to use one of the manipulatives at a time per question.
It was found that “while both [virtual manipulatives and concrete manipulatives] were significantly more effective at producing independent and accurate performance on the mathematics tasks than baseline conditions, the VM condition fared slightly better in terms of independence and accuracy” (Shurr et al., 2021). Max was found to be 93% accurate when using virtual manipulatives, whereas he accurately solved 69% of the problems using concrete manipulatives (Shurr et al., 2021). Henry scored 92% accuracy using VM compared to 81% accuracy using CM (Shurr et al.,). Finally, Dane scored 100% accuracy using virtual manipulatives compared to 97% accuracy when using concrete manipulatives (Shurr et al., 2021). This study suggests that virtual manipulatives could be a valuable option for students with Autism Spectrum Disorder when working with addition operations.
So, now that you know about virtual manipulatives, where do you go to use them? Toy Theater is an interactive program that uses educational games and virtual manipulatives to engage students in their learning. There are many games to play on the site, as well as assessment tools for teachers, but we have chosen to focus on the virtual manipulatives. There are manipulatives available for both math and literacy. The math virtual manipulatives are divided in the following categories: Fractions, Time, Number Chart, Geometry, Counters, Graph, Place Value, Probability, and Money. The literacy virtual manipulatives are also divided into categories, as follows: Alphabet tiles/cards, Digraph and Trigraph tiles/cards, Word Family tiles/cards, and Elkonin boxes. Additionally, there are other helpful tool, such as a Timer, Stopwatch, Coin Flip, Spinner, Dice, and Playing Cards.
Free! Accessible to all with internet access and is affordable to teachers with limited budgets and resources.
No distribution or clean-up needed.
Option for students to choose the tool that works for them.
VM were more successful for students with ASD (Shurr et al., 2021) - more equitable than CM
Focused constraint - precise representations allowing accurate and efficient use.
Efficient precision - constrain student attention on mathematical objects and processes.
Working at their own pace.
“Unlimited” amount of material.
Students with visual impairments and/or sensory impairments might benefit more from physical manipulatives.
May limit the ability for teachers to observe students’ thinking.
Can force a student to think more abstractly than if they were using concrete manipulatives.
A learning curve for those students less comfortable with technology.
As with all technology, more unsupervised distractions are available.
Constraints with specific tools.
My teammates - Mary and Jess - and I worked together to synthesize this research and teach about the tool Toy Theater to our classmates in the MAET program. We spent a week going through what we learned and organizing it into a lesson plan to teach our peers. Below you will see the slide deck from that presentation.
The team teaching went well; our classmates seemed to love learning about the tool and the implications of it for their contexts. We talked through the above slide deck and gave time for exploration at the end of the lesson. Our peers added their thoughts to a Jamboard, as well as sharing out their thoughts. You can see artifacts from this team teaching below.
Moyer-Packenham, P. S., & Suh, J. (2012). Learning mathematics with technology: The influence of virtual manipulatives on different achievement groups. Retrieved 5 July 2022, from https://core.ac.uk/display/32552888?utm_source=pdf&utm_medium=banner&utm_campaign=pdf-decoration-v1
R, C. (2013, April 16). TPACK in 2 Minutes. https://www.youtube.com/watch?v=FagVSQlZELY
Shurr, J., Bouck, E. C., Bassette, L., & Park, J. (2021). Virtual versus concrete: A comparison of mathematics manipulatives for three elementary students with autism. Focus on Autism and Other Developmental Disabilities, 36(2), 71–82. https://doi.org/10.1177/1088357620986944