A primary component of the AIMM program is the use of Manipulatives in the teaching of Mathematics. My working definition of a Manipulative in Mathematics is any tool (whether physical or digital) that can be used to model the conceptual/concrete knowledge of a topic in mathematics. For example, a teacher could use a set of wooden rods (let’s call them Cuisenaire Rods J) that are cut to different centimeter lengths and each painted with a different color. Students could then explore the concept of fractions through part-whole relationships between the Rods.
I fully believe in Manipulatives in Mathematics, if they are used properly. When I say, “Properly”, I mean they are not just taught as another procedure in a mathematics classroom that students should memorize. Manipulatives should encourage discovery of concepts and inquiry into those concepts. Recently, I had a teacher ask about manipulatives and their effectiveness in the mathematics classroom, particularly the achievement of students. Over my time as both a teacher of mathematics and teacher of teachers of mathematics in higher education, I have read many articles and listened to many presentations related to manipulatives and their effect. I recently read through the following article that has an EXCELLENT review of the literature surrounding manipulatives (positive and negative results) and shares positive findings from their own research on the effectiveness of manipulatives in a geometry classroom (https://files.eric.ed.gov/fulltext/EJ1097429.pdf). Even though this research was conducted in Turkey, the researcher cited many American researchers that have found similar, positive results who have also shared warnings towards the perceived “Magical” properties of manipulatives(see for example Deborah Ball https://www.aft.org/sites/default/files/periodicals/ae_summer1992_ball.pdf) Ball stated in her article, “My main concern about the enormous faith in the power of manipulatives, in their almost magical ability to enlighten, is that we will be misled into thinking that mathematical knowledge will automatically arise from their use.” I fully agree with this statement. One cannot make the statement “If you use manipulatives, they will learn!” Teachers must focus on what Deborah Ball also stated in her article in that teachers must use tools and solicit student thinking through classroom discourse and exploration. If you are to IMPROVE YOUR AIMM, you must think about how you manipulate the concepts you teach. If you are simply teaching procedures (computational and/or physical) then students are not thinking, you are. However, if you are supplementing your procedural instruction with tools that challenge student thinking and encourage classroom discourse, then greater learning can take place in your mathematics classroom. Keep Improving your AIMM, John
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AuthorsJohn Lamb, Ph.D. Archives |
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