Manipul8: An Interactive Experience to Inspire Pattern-based Algebraic Thinking and Representational Fluency

Boles, K. L., Macedo, L., Proctor, C., & Blikstein, P. (2018). Manipul8: an interactive experience to inspire pattern-based algebraic thinking and representational fluency. Proceedings of the 17th ACM Conference on Interaction Design and Children (pp. 501–504). New York, NY, USA: ACM. doi:10.1145/3202185.3210763

Transitioning students from arithmetic to algebraic thinking is a primary challenge in mathematics education. Visual patterns and physical manipulatives can be helpful, but students often struggle to see the connections between different representations. Manipul8 combines visual patterns with physical manipulatives and provides digital scaffoldingto help students develop representational fluency. Using a tabletop tangible user interface, students manipulate equation frames with cutouts for quadratic, linear, and constant terms. Tangible, interchangeable terms are represented either traditionally or as quantities of shapes. The projected digital image provides real-time feedback showing algebraicgrowth patterns generated from the user-chosen equation structure and terms. Color provides scaffolding for noticing the connections between the equation’s terms and visual-pattern-based representations.

Cite this paper

@inproceedings{boles_2018_manipul8,
    author = "Boles, Kelly L. and Macedo, Livia and Proctor, Chris and Blikstein, Paulo",
    title = "Manipul8: An Interactive Experience to Inspire Pattern-based Algebraic Thinking and Representational Fluency",
    abstract = "Transitioning students from arithmetic to algebraic thinking is a primary challenge in mathematics education. Visual patterns and physical manipulatives can be helpful, but students often struggle to see the connections between different representations. Manipul8 combines visual patterns with physical manipulatives and provides digital scaffoldingto help students develop representational fluency. Using a tabletop tangible user interface, students manipulate equation frames with cutouts for quadratic, linear, and constant terms. Tangible, interchangeable terms are represented either traditionally or as quantities of shapes. The projected digital image provides real-time feedback showing algebraicgrowth patterns generated from the user-chosen equation structure and terms. Color provides scaffolding for noticing the connections between the equation’s terms and visual-pattern-based representations.",
    booktitle = "Proceedings of the 17th ACM Conference on Interaction Design and Children",
    series = "IDC '18",
    year = "2018",
    isbn = "978-1-4503-5152-2",
    location = "Trondheim, Norway",
    pages = "501--504",
    numpages = "4",
    doi = "10.1145/3202185.3210763",
    acmid = "3210763",
    publisher = "ACM",
    address = "New York, NY, USA",
    keywords = "algebra, functions, math, multiple representations, representational fluency, tangible user interfaces, visual patterns",
    url = "http://chrisproctor.net/publications/boles\_2018\_manipul8",
    pdf = "http://chrisproctor.net/media/publications/boles\_2018\_manipul8.pdf"
}

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