In the Classroom

Polypad is highly useful in the classroom to help build those concepts that can be difficult for students to grasp and to really cement math learning. Teachers can create modules within the tool to augment instruction, bringing manipulatives into the classroom without having to worry about managing the quantities of items available to each student. Polypad can also be used as instruction itself, with the teacher guiding the students through a visual representation of a problem or facilitating a student-led exploration of a new concept. Once students are comfortable with both the concepts and the tool, polypad can also be used as an assessment method; students can create visual presentations of solutions with the tool that can be easily shared in a gallery walk format or just privately with the teacher. Smaller modules with limited tool availability for the students can also be used for quick checks on student understanding. This makes polypad an ideal tool for a minds-on, action, or consolidation activity.

Research Connections

Research has proven that interactions with manipulatives significantly enhances student retention of mathematical procedures (Witzel, 2005). This has view been given even more support by recent understandings of the neurological processes that arise around exercising math fluency which have also drawn a close connection between mathematical ability and our brain's visual sense (Boaler, 2016). As a result, the Concrete-Representational-Abstract (CRA) framework has jumped to the forefront of many discussions of effective math education (Hurrell, 2018). In the CRA framework, concepts are built up from a concrete level where students work with manipulatives (physical or virtual) to develop an understanding of the underlying nature of mathematical processes (eg. counting out zeros with algebra tiles or forming squares out of linking cubes to understand square roots). Once the concrete level is understood, the learning is elevated to a representational framework where symbolic stand-ins (eg. multiplication grids or scale drawings) are now used to represent the concrete manipulatives. It is only when these two layers are deeply understood that the mathematics is brought to its abstract layer where the numbers, symbols, variables, and formulae that encompassed all of traditional math education can be found.

References

Witzel. B.S. (2005). Using CRA to Teach Algebra To Students With Math Difficulties in Inclusive Settings. Learning Disabilities: A Contemporary Journal, 3 (2), 49-60.

Boaler, J., Chen, L., Williams, C., & Cordero, M. (2016). Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning. Journal of Applied & Computational Mathematics, 5 (5), 10000325.

Hurrell, D. (2018). I'm proud to be a toy teacher: Using CRA to become an even more effective teacher. Australian Primary Mathematics Classroom, 23 (2), 32-36.

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