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Making Learning Meaningful Through Self-Discovery, Part III

As I said earlier in Part II, letting students discover laws and properties for themselves, particularly in STEM classes, is an important part of their learning process. It is a student’s way of learning the how in addition to the what. In this conclusion of this three-part article, I will cover the two examples I touched on briefly in Part II in greater detail. Feel free to use the methods presented here as suggestions for how to approach teaching the specific lessons I am presenting.

The first of these examples is a method by which to allow students to discover the Law of Conservation of Mass for themselves. Let’s say they want to prepare chemicals for a reaction. Now, the mass of the reactants should be the same as the mass of the products. Let them measure the mass of the reactants and the container used separately, then they should execute the reaction. Let the reaction go to completion. To ensure it has gone to completion, it is best to use a reaction that has easily visible evidence. However, be aware not to use a reaction that produces gas, because that gas has mass too, and some of it will escape, tricking students into believing that the Law of Conservation of Mass does not hold.

Once this is done for one reaction, the end mass should be roughly equivalent to the starting mass. Performing this experiment for one reaction alone is not sufficiently convincing–it shows that the Law of Conservation of Mass holds specifically for that reaction. Now is the time to replicate the experiment with different reactions involving different chemicals. They can be single-replacement reactions, double-replacement reactions, etc. It doesn’t really matter as long as none of the products are gaseous. After four or five such reactions students should be convinced that the Law of Conservation of Mass holds for all chemical reactions, even if one of the reactants is in excess.

To achieve the same intellectual benefit in a math classroom, however, a protocol more along the lines of a proof is more reasonable (it depends to some extent on the topic, of course). As long as the students can clearly understand each step of the proof, they will be convinced not only that the statement you are proving it is true, but why it is true. Furthermore, proofs often require the synthesis of previously taught concepts.

One of my favorite examples of this technique is the proof of trigonometric identities. I have written some proofs that demonstrate the step-by-step process and knowledge of other identities. See them here: http://www.opencurriculum.org/user/joshua/files/proofs-of-trigonometric-identities/. However, it is not sufficient to print these up, distribute them to your students, and have them read the proofs in solitude. At least initially, you should go over the proofs in detail with students. They should understand every step, as if they miss one tiny detail, their understanding of the entire problem falls apart. After doing some examples in class, let the students try their hand at writing proofs themselves (preferably in paragraph form over two-column form).

With these two examples in mind, the same conceptual framework can be applied to many different topics in STEM. When live demonstrations are not feasible due to safety or the amount of preparation required, Youtube is your best friend. Chances are the principle you want to demonstrate can be viewed online.

Varun Arora
Joshua SIktar is a the Lead Content & Community Lead at OpenCuriculum