I've discussed some of these thoughts previously on my blog; however, they are the topic of this week's course blog discussion (not to mention a topic that is very interesting to me) so I decided to post about it again... memorization in math. Every educator has his or her opinion about memorization in mathematics. Is it ever necessary? Is it sometimes necessary? Is it the only way the students will pass the course? I happened upon a blog post titled "When Not Memorizing Gets in the Way of Learning." Link: When Not Memorizing Gets in the Way of Learning (Many readers held a discussion of the post at the bottom of the page, it is also very interesting!)
The author, a mathematics teacher named Ben Orlin, discusses how necessary it is for students to learn information that must be memorized. BUT, he also discusses how useless this information is if it is memorized out of context. For example, students in 5th grade math have no business memorizing facts for trigonometry. This is useless information that they have no prior knowledge of and will not continuing building on this knowledge until much further down the road. I share the same opinion as Orlin, in a nutshell. Like Orlin, I argue that the cell phone in your pocket does not take the place of the knowledge in your brain. Without those connections in your brain, without those basic understandings of the information you are learning, Wikipedia in your pocket is useless. You can't search for information if you don't know what you are searching for. This is critical thinking - using the tools you have to find relevant information in order to solve a (sometimes more complex) problem. So if you don't have the foundation to build on, the technology and the internet are going to be useless to you.
In this blog post, Orlin states that "the problem is when memorization spreads like a weed, and begins to substitute for reason. The problem is "ASTC," "FOIL," and other mnemonic shortcuts that circumvent actual mathematical reasoning. The problem is when all of algebra or calculus is reduced to chugging through formulas whose origins and purpose you don't understand. That's when math stops being math, and becomes Following Recipes 101, a far less meaningful and worthwhile class."
I really couldn't have said it better than Orlin. In so many math classes, memorization has become the substitute for reason. And when students get to high school math courses, they have no idea how to reason. They have only been exposed to fact memorization in their mathematics experiences; therefore, they think that fact memorization will continue to prove the best way to learn math. They don't understand that all of those basic concepts they have learned along the way are all coming together in a bigger picture, such as algebra or geometry. For example, algebra is all about letting letters represent unknown numbers. We convert real life situations into numeric equations and math is the tool that allows us to find the missing pieces. We treat these letters just like numbers (they are just holding the place for a number... but we use a letter so we know the number is missing. We could use hearts and smiley faces and it would serve the same purpose, but throughout history certain letters have come to stand for certain missing quantities. We can multiply, divide, add, and subtract these letters just as we can with numbers.) It's amazing really, but an alarming number of students have no idea what algebra is or what the purpose of algebra is... even after they pass algebra. I think that memorization has a place in mathematics, but never without proper context or without conceptual understanding to go along with it. We are doing our students a disservice in math by allowing them to memorize facts and never giving them the opportunity to learn real mathematics.
Amy,
ReplyDeleteI am intrigued by Orlin's blog because my students use memorization (for the first week or two when beginning a new script) and then we begin to add various other layers. I see huge growth with his (and my own) method and agree that it is a great jumping off point. Unfortunately, I think about our society's propensity towards testing and showing that students deeply know a variety of concepts that they have only learned in the past 8 months. I believe this is why rote memorization and mnemonic devices prevail, even when the evidence is overwhelmingly in favor of making learning active for students through experiences and individual interpretation.
Great, thought provoking post!
-Jamie Hipp
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ReplyDeleteInteresting blog link! I think Orlin is on point when he says "The problem is when memorization spreads like a weed, and begins to substitute for reason." There are many reasons why students memorize instead of reason. I went to a very competitive high school and I remember resorting to memorization all the time-not just in math, but in every subject. Not because I didn't have the capability to reason through and understand, but because grades were emphasized, not learning, and I didn't see the point in taking the extra time to attempt to understand it. It often was the easy route in the short term, but not in the long term...since everything builds on each other (at least in math). But when I took the time to reason through and understand material, then memorize the facts after I understood them, that was more helpful in the long run.
ReplyDeleteThanks for the link to this blog! Very interesting topics.
ReplyDeleteI always enjoyed math when I was in elementary and even through high school, but by the time I got to college I only took one math class because I had to for my major. There is a lot of math that I use on a daily basis, but probably more that I haven't used. I think the FOIL example is a perfect example of something many of us were taught to memorize, without knowing why.