In reality, I think students are really asking why they should study algebra and not how they will use it. Rarely do you ever hear art students question with dismay while learning to draw, "When will I use this stuff in real life?" Math is the language of how the universe is constructed in pure form. Not only does it explain many of the world's wonders, it also gives us a way to predict what might be before it is even discovered. It can explain things we can't even see. It connects all the disciplines and makes sense of our world. What student wouldn't want to be part of that sweet and satisfying connection? It is our job as teachers to not only make sure students can cook using fractions, but are also able to look at the beauty and connectedness of math to their world, and beyond.
I love this video where Samuel Khan takes a look at the beauty and connectedness of Algebra.
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