"Play is often talked about as if it were a relief from serious learning. But for children, play is serious learning."
- Mr. Rogers
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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 for the purpose of this blog post, we have chosen to focus on investigating the affordances and constraints of the virtual manipulative section of the website. On Toy Theater's website, there are virtual 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 tools, such as a Timer, Stopwatch, Coin Flip, Spinner, Dice, and Playing Cards. Throughout this blog post, we will be exploring virtual manipulatives as they compare to concrete manipulatives and the affects of virtual manipulatives on academic learning.
When examining the affordances and constraints of Toy Theater's virtual manipulatives, it was important for us to relate these tools to the TPACK Framework, a framework that identifies three types of knowledge instructors need to combine for successful edtech integration—technological, pedagogical, and content knowledge (PowerSchool, 2022). Toy Theater directly relates to the TPACK Framework through the interconnectedness between technology (the tool itself), pedagogy (we know manipulatives are helpful to learn concrete and abstract concepts), and content (what it is we are teaching) (ISTE, 2009). Through our Team Teaching with Toy Teacher we utilize each of the three knowledge domains within TPACK (ISTE, 2009). The teachings of Pestalozzi, Piaget, and Froebel we discussed from “An Insanely Brief and Incomplete History of Making,” written by Sylvia Libow Martinez and Gary Stager in 2013, express the importance of learning through playing and tinkering. Froebel’s “gifts,” or educational toys, are tangential with physical and virtual manipulatives used in schools (Libow Martinez et. al., 2013). Stager and Libow Martinez state that “like Piaget more than a century later, Pestazolli believed that learning resulted from the learner’s first-hand experiences and self activity” (Martinez et. al., 2013).
In determining the affordances and constraints of the product, it felt important to do some research into using virtual manipulatives. Through our research, we found two different studies: “Learning Mathematics with Technology: The Influence of Virtual Manipulatives on Different Achievement Groups,” (Moyer, 2012), and “Virtual Versus Concrete: A Comparison of Mathematics Manipulatives for Three Elementary Students With Autism” (Shurr et al., 2021).
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 applications of virtual manipulatives allows students to benefit in different ways. Academically 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. Academically 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.
In Shurr’s research, 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 and 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 the graph below). The students were then given training in the usage of both concrete manipulatives, which was a set of base10 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 virtual manipulative 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). Overall, it can be concluded that virtual manipulatives seem to fare better over concrete manipulatives for students with Autism Spectrum Disorder when working with addition operations.
Using this research and our own experiences, we were able to come up with a list of the affordances and the constraints of this tool. The affordances are as follows:
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.
The constraints are as follows:
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.
Overall, there are immense benefits to using virtual manipulatives when teaching most students. There is never a one size fits all, but the options available on Toy Theater seems to have something that would fit most. If students are given the freedom to use the platform as it fits their needs, they will be able to visualize and represent their thinking in new ways to better connect with the concepts. When looking for a platform to use for virtual manipulatives, Toy Theater is a free, easy to use interface that students will be able to interact with independently.
Written by Mary Verberg, Jessica Fleis and Stephanie Saska
References
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/32552888utm_source=pdf&utm_medium=banner&utm_
campaign=pdf-decoration-v1
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
Koehler, M. J., & Mishra, P. (2009). Too cool for school? No way! Using the TPACK framework:
You can have your hot tools and teach with them, too. Learning and Leading with Technology,
36(7), 14-18
Martinez, S. L., & Stager, G. (2013). Invent to learn: Making, tinkering, and engineering in the
classroom.
The TPACK Framework Explained (2022, April 20). PowerSchool.
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