Manipul8: an interactive experience to inspire pattern-based algebraic thinking and representational fluency

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 scaffolding to 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 algebraic growth 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.