Embedded Files
Polypad is a collection of 25+ various interactive digital manipulatives designed to be used by both teachers and students for the purposes of mathematics learning. Created by the company Mathigon, these digital manipulatives provide classrooms with an alternative to physical manipulatives, which may not be afforded by all establishments or persons. Some digital manipulatives even provide opportunities which were not previously available through physical manipulatives (for example, prime factor circles, which do not have a physical equivalent!).
Some digital manipulatives offered through Polypad include:
Geometry
Polygons
Tangrams
3D Solids
Measurement Tools (Ruler, Compass, Protractor, Set Triangle)
Numbers
Number Tiles
Number Bars
Number Frames
Number Lines
Prime Factor Circles
Number Grids
Fractions
Fraction Bars
Fraction Circles
Algebra
Algebra Tiles
Balance Scales
Function Machines
Cartesian Graphs
Probability and Dice
Coins
Dice
Spinners
Tables
Cards
Games and Applications
Keyboard (Instrument)
Logic Gates
Chess
Currencies
Clocks
Dominos
Polypad - The Mathematical Playground (Mathigon, 2021)
Implementation in the Classroom:
The Mathigon webpage "Puzzles, Activities, and Lesson Plans" (Puzzles, Activities, and Lesson Plans, 2023) outlines many tutorials, games, and lesson plans for Polypad.
Their Youtube (Mathigon, 2023) also hosts a series of tutorials and PD [Professional Development] videos towards using Polypad.
An example implementaiton of Polypad in the classroom is to give students "representational worksheets" to demonstrate their learning. Polypad allows instructors to share premade workspaces with students, so using this feature, we can create a series of algebra questions through the algebra tiles and and balance scales, then have students solve for the value of unknown weights. In the example below, we have students solve the equation of "14=2x", without having them explicitly be told that this pictorial representation is that of "14=2x". In order for students to answer this question, they would have to manipulate the digital scale. For example, they could remove one 'x' from the right side, and remove 1-tiles from the left side until the scale balances. Once they have the scale balanced, they would send it to the teacher by taking a screenshot of their entire Polypad workspace and upload it to a Google Classroom assignment submission page, for example.
Impact on Student Learning:
A popular style of teaching in Education is the CRA method, which stands for Concrete-Representational-Abstract (Concrete-Representational-Abstract: Instructional Sequence for Mathematics, 2020). this is a progressive style of teaching where the same concept is first introduced to students using concrete, physical manipulatives, then through representational means (2D images), and finally through abstract means (symbolic, means such as "4+5"). Polypad is considered something which is between a physical manipulative and a pictoral representation of an object.
What makes the concrete stage so important is that it engages multiple senses of the learner, such that they encode their new information through kinesthetic, visual, auditory, and tactile senses, i.e. a variety of cognitive abilities. Although the tactile sense is not as strongly engaged as when we work with physical manipulatives, Polypad still does a strong job of allowing students to interact and explore different ideas with the digital manipulatives through the other senses.
Witzel et. al.'s (2008) write that CRA is particularly helpful for learners with learning disabilities. They provide four reasons why CRA teaching is effective. Knowing that digital manipulatives can behave as both the concrete and representational stages, Polypad seems to be a great vehicle for this teaching!
Allows for multimodal learning (through seeing, hearing, muscle movement, and touch)
Allows students with various learning preferences to engage with the material in multiple ways
Intentional manipulations of materials in the concrete and representational phases allow students to found procedures in the abstract phase
Generalization through the CRA approach may lead to a more deep understanding of mathematics than rote memorization of algorithms
References
Concrete-Representational-Abstract: Instructional Sequence for Mathematics. (2020). Pattan.net; Pennsylvania Training and Technical Assistance Network.
methods3920wba.pdf&hash=4ee5add68a50b35ac1279a 143a522196d018c407445282aea1244a31c1039575&ext=.pdf
Mathigon. (2021). Polypad - the mathematical playground. [Video]. Youtube. https://www.youtube.com/watch?v=jZp4G-8EHhE
Mathigon. (2023). Mathigon - Youtube. Youtube. https://www.youtube.com/@Mathigon
Puzzles, Activities, and Lesson Plans. (2023, November 6). Mathigon. Retrieved November 6, 2023, from https://mathigon.org/tasks
Witzel, B. S., Riccomini, P. J., & Schneider, E. (2008). Implementing CRA with secondary students with learning disabilities in mathematics. Intervention in
School and Clinic, 43(5), 270–276. https://doi.org/10.1177/1053451208314734
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