Scott A. Carr's website

Scott A. Carr

Computer Scientist

Learning, Memorization vs. Understanding

In my K-12 days I memorized plenty things: state capitals, multiplication tables up to 12 times 12, every cursive letter, etc. Even in my graduate level classes I usually have to memorize something, whether it be a formula, or worse, how many bits long something is.

Memorizing these things helped me score well on my exams, but did it help at all in real life? Some memorization is no doubt useful. Multiplying numbers up to 10 comes up frequently in daily life. However, I’ve never needed to recall the capital of Vermont. Knowing a DES key is 56 bits long doesn’t make me better at Information Security, but knowing that DES keys are shorter than AES keys (and that’s part of the reason DES is insecure) does. Every instance of memorization would better serve the student if memorization were replaced by contextualization. Knowning why this particular fact is important to remember, out of vast sea of facts, is as important as the contents of the fact itself.

An aside: a forward thinking teacher some day will let students answer in the form of Let Me Google That For You links. Everything I’ve mentioned so far is Google-able.

Some memorization in the beginning is unavoidable. Student and pupil need a common vocabulary, but people underestimate what kids can learn. There’s a part in a Richard Feynman book where he tries to explain the concept of infinity to a child. I was at Mother’s Day lunch with my family and for some strange reason a division pop quiz broke out. My nephew must be learning division in school. Taking inspiration from Feynman, I tried to give him some impression of the concept of infinity. As my relatives rattled of divison problems, I tried to get a feeling for what method he was using to compute the answer. Sometimes he would just immediately answer. For example, to the question “What’s 100 divded by 2” he replied “two” without any apparent mental math. On harder problems I noticed he was mentally counting. He would take the denominator add it to itself repeatedly until the sum equaled the denominator. (My family showed a rare instance of kindness and only gave questions with whole number answers.) Wanting to give a question whose answer is infinity, I said, “100 divided by 0.” There were grumblings around the table of it being “too hard a question,” but I knew his method would work just fine. At first, without much thinking, he gave zero as the answer, but I encouraged him to apply his method. I asked, “how many times do you have to add up 0 over and over to get to 100.” He said 500, presumably because that’s a really large number when you’re in second grade, but I said, “What if I add zero to zero 600 times?” He agreed that would still be less than 100. Taking inspiration from Feynman, we went back and forth saying increasingly large numbers of zeroes that still wouldn’t add up to 100. He understood what I was getting at, infinity just wasn’t in his vocabulary.

The process of learning to learn is more important than what is learned. Force a student to memorize some set of facts and he might do well on Jeopardy. Instead teach the student the process of gaining new knowledge and the sky’s the limit.

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