This week I learned that alternate interior angles (from a bisected parallel line) are equal to each other. I was lead to draw this conclusion by the use of a simple paper manipulative. Folding the points of a square in on themselves to form another square, and then folding in half to create parallel lines and perpendicular bisectors. I was asked to prove what I know through open class conversation. According to Marshall (2000), “Saying out loud what one has just learned is an excellent reflective strategy to improve learning.” Whole class discussion solidified this Math manipulative experience.
There is no substitute for direct experience. Yet, when might a mathematical manipulative not be appropriate as a teaching tool?
According to Freerweiss, when we use manipulatives we can reach up to 10% more students who naturally gravitate toward kinesthetic and tactile learning. Indeed, anytime I incorporate a wider range of teaching with the senses I routinely see greater engagement. In addition, manipulatives lower anxiety in a historically anxiety rich content area that is frequently plagued with memorizing facts and formulas.
Learning through experience first, and teaching for conceptual understanding can help students to solve problems they have never seen before. To successfully take a mathematical formula out of a text book, requires a teaching strategy that incorporates real world context. If I introduce a tactile experience along the way, and connect this to prior learning, I can help students’ understanding take hold with permanence.
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