Monday, October 8, 2012

Making Math Class Easier

One of the things that I've been thinking about lately is this idea of "making math class easier." @ddmeyer asked about people's opinions on foldables earlier today and linked to a blog post that stated, "I really wish I had math notes like these growing up…math would have been so much easier!" Now, I'm obviously not ripping on this woman. I'm sure that she's an awesome and caring teacher. It just really made me think about this idea of "easier" and whether this is what we should be aiming for in math education. I have seen lots of teachers teach "tricks" or "mnemonic devices" that are supposed to help students remember concepts and procedures. A colleague of mine tells her students about colored socks - she pulls two socks out of her drawer and if they are the same color, that's good, but if they are different colors, that's bad. This is supposed to help students remember that when signs are the same, the product is positive, but when signs are different, the product is negative. Most of us have probably seen the little mnemonic device for absolute value inequalities: greatOR and less thAND to "help" kids convert absolute value inequalities to and/or compound inequalities. There are a lot of these hanging around.

To me, foldables are in the same category of "cute" device that will help you remember something. Yes, kids love them. They are easy. All these devices are colorful or cute or make a little rhyme or whatever. But like it or not, I feel that there's a tension between this aspect of math and the side where kids are grappling with rich problems, constructing meaning, and having ownership of ideas. I understand that many teachers use these "shortcuts" as ways to summarize a concept or wrap up a discovery lesson. And hardly anyone gets away from teaching any shortcuts whatsoever. Maybe that's not the point. But I do think that we need to think critically about what we're doing when we emphasize these shortcuts. Even if it comes at the end of a deep, rich lesson, there's going to be a bunch of kids that are going to remember the "trick" superficially, and it's going to be what the lesson was all about in their mind. It's going to train them, to some extent, to expect tricks like that in the future and avoid the harder work of understanding and internalizing the concepts underlying the shortcut.

Yes, a hook can be powerful for motivating student engagement. But I think it can also be junk food that distracts us from the substantive meal, which is not as shiny or easy to digest at first glance. Let's look instead for ways to make the mathematics more profound, more apparent, and more rich for kids. It really doesn't need to be dressed up and tricked out because it's pretty darn awesome on its own.


  1. I don't think a foldable necessarily falls into the category of a shortcut. It can be used as a summarizing or notetaking tool for students as they work through rich problems. In this case I don't think foldables are aimed at making the math easier but making what they've learned/discovered easier to remember.

  2. I agree with misscalcul8. It is another medium for learning. Like notebooks, posters, white boards, smart boards, powerpoints, transparencies (gasp), graphing calculators, or anything else.

    Bottom line is that if a teacher is skilled with a particular medium, students will generally be more successful. I am not skilled with foldables so I don't use them.

    That said, I'd question a teacher who uses foldables ALL THE TIME because at the end of the day it's just fancy notetaking.

  3. We probably only need a mnemonic for order of operations. Can't think of anything else in math that truly needs to be memorized.

  4. To piggyback on misscalcul8's comment:

    I have seen all grade students and all level students who really are able to improve their vocabulary development and/or their skills development by using foldables. I have had English Language Learners as well as AP Calculus students who benefit from using them. It's as much about learning style as it is about the math. For many students, the artistic/creative nature of this organizer brings the "math pieces" all together for them.

  5. Thanks for your feedback and comments, all. I guess that my main hang-up is that foldables are being sold as interactive and engaging, whereas in my mind, they are just glorified note-taking so the "engagement" is happening on a very surface level. It's not like I'm against all note-taking ever by anyone. It's just that I think we need to be honest that hey, I'm going to tell you some stuff now, and you're going to write it down. It might require students to think in terms of organization and remembering, but it's not going to be about doing heavy mathematical lifting. I think foldables can make everyone feel that engaging, exciting things are going on in a classroom when it's actually the traditional mode of instruction. Basically, I don't love them because they make direct teaching more palatable to students. I group them with tricks and games as distractors that take the focus off the underlying math.

    P.S. I had kids make two foldables in class last week. I use games sometimes to practice. I'm not saying they are evil incarnate.... just to be thoughtful about what it is we are doing when we use them.