Manipulatives

Apart from my work as a teaching assistant at University, I also tutor an elementary student in math and a high school student in history. On Thursday I helped my math student review division, and I realized I needed to bring in some math manipulatives. Manipulatives are physical objects you can use to help demonstrate a concept. In this case, I think I am going to bring in some pasta and cups, so we can practice dividing different amounts of pasta into equal groups. We were using Lego, but Lego is so diverse and has so many interesting properties that it can be distracting. 

In my Early Childhood Education training and practica, much of curriculum design revolved around introducing objects that would demonstrate ideas as children experimented wih them. For example, I created an infant toy that was a blanket with patches. The only variable that changed on each patch was texture, because the blanket was designed to teach tactile and visual sensory integration (what we experience as something 'looking bumpy' or 'looking smooth'). I've always thought this subtle education, where the environment is set up in such a way to teach the student from experience, was very clever and also very effective. After all, the way we learn outside the classroom is by interacting with our environment and forming ideas based on experience.

What I would like to be able to do, if possible, is create objects to demonstrate philosophical concepts. But philosophy is very abstract, and the world itself is (supposedly) the thing from which philosophy is derived. I think perhaps thought experiments are a kind of way of creating pedagogical objects, a way of manipulating and experimenting with ideas. 

I remember once a friend and I used a bulletin board, pieces of paper, pins and yarn to map out the axioms and propositions of Spinoza's ethics. It took forever, but just working with the yarn and touching each piece of paper helped me feel closer and closer to understanding what Spinoza was about. Maybe creating art can be the pedagogical object of philosophy.