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The students who learned the math abstractly did well with figuring out the rules of the game. Those who had learned through examples using measuring cups or tennis balls performed little better than might be expected if they were simply guessing. Students who were presented the abstract symbols after the concrete examples did better than those who learned only through cups or balls, but not as well as those who learned only the abstract symbols.
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<p>Although this makes perfect sense to me, I was just curious what other people thought about this. Especially since one of the biggest complaints I hear about math is that it's not applicable to the real world.</p>
<p>Real world examples should be for motivation. They have their places, but I don’t think they do a lot to teach the actual material.</p>
<p>The biggest problems that I see with the study are that different types of math might lend themselves to different teaching techniques and that college students might benefit from having more experience with mathematical symbols. It would be interesting to know what exactly they were taught.</p>
<p>There’s nothing wrong with using real-world exercises for practice. That’s what examples are for - practice. However, practice is worthless unless you know what you are doing. Otherwise you just end up burning the wrong method into your mind.</p>
<p>In order to actually teach mathematics, you need to explore the reasons why a concept works. I’ve found that it’s easy to memorize formulas and then apply them successfully after seeing the proofs because you understand what the formula actually does.</p>
<p>Funny story: I used to never use the quadratic formula. One time I decided to program the completing the square process into my calculator. I ended up with the quadratic formula.</p>
<p>I use the quadratic formula a lot more now (relatively I guess, I don’t remember the last time I had to find the roots of a quadratic).</p>
<p>Real world examples make it harder for me to learn than non-real, though I can definitely see why others might find it easier. Perhaps it is fine to show at least one real world example for some sort of math lesson just to show people why they’re learning it, how it’ll help them in life, and adding motivation to learn it. </p>
<p>My pre-calc teacher once said to our class during a lesson</p>
<p>“If you are a rocket scientist then you might use this in your life, if not, then you are only learning it to make a good grade in my class.”</p>
<p>Aww snap. I’m a Montessori kid. I’m married to examples. I learned numbers with beads, squares, with well, squares, and cubes with (you guessed it!) cubes. We learned addition and subtraction with the stamp game, and well, the other algebraic properties were just built off of those two. Outside of math, I was 100% certain that nouns were large black triangles and that prepositions were green bananas. I don’t think I learned anything without a concrete example or symbol until I was, maybe, 9, and even then, those were few and far between.</p>
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