I like this quote from the Otten article a lot: A different type of preemptive approach is one built around a learning environment in which the question “When am I ever going to use this?” is not raised because … the students are happily engaged in learning mathematics and unlikely to challenge its purpose (e.g., students are finding intrinsic value in mathematical discovery and sense making).

It is so easy to forget that the symbols of math carry no inherent meaning, and therefore it is also easy to unintentionally be asking the students to “Think!” about something they can’t really think about. When students work with a visual pattern, or a bar model, or a set of balance pans, there is enough information there for them to see the relationships and reason with them. Math symbols are meant to represent mathematical thinking, and they can’t replace it.

Every once in a while, I open an open algebra or calc class with something like this:

https://www.youtube.com/watch?v=74IsySs3RGU

The question is now preempted with a new one:

What can’t you do with skill in mathematical or scientific reasoning?

“What you learn today, for no reason at all, will help you discover all the wonderful secrets of tomorrow.”

Here is an essay written on the “When will I ever use this?” question that I have used with my students. It really helps some of them have a different attitude about learning, not just math.

Tama

http://www.maa.org/sites/default/files/pdf/Mathhorizons/supplement/MH-CoreyWeb.pdf

I then asked him, when was the last time his side ever did a drill on the field in a game. Never, of course.

And so it is with Maths. We practice so we have skills. That practice is simplified so that we can work on only one thing at a time. If we don’t practice skills, we won’t play well even though we never use those actual practice drills in the game.

It seemed to work.

My answer to the student demand: “Probably never. But the more willing you are to take on challenging tasks you learn from, the more opportunities you’ll have in life, both professional and personal. Call me crazy, but I see this as a good thing.”

From my math class to a brutal Dolores Umbridge is a slippery slope, I guess, but I’m good with that.

I think what math teachers often envision doing is converting the kids who would otherwise never use it into kids who would. That’s highly unlikely, though.

Admittedly, this requires some rapport and trust. I’m honest with them (most of the specific tasks are useless, the mode of thinking is not). I relate things from my life (learning to fix a garage door, replace a radiator and build a fence) … things they wouldn’t expect a math teacher to do outside of class.

My aim: if I can branch out and do something I’ve never done before, maybe they can, too.

Math (especially those hard-to-support-with-“real-world applications”-techniques…I’m looking at YOU factoring cubics!!!…) can be viewed as mind-training, for some future competition of the mind. A workout that will both make the mind stronger, and open it up for further training in the future, even if today’s workout may be boring, or appear meaningless in the short-term.

Regardless of what we think such student questions mean, the insincere and dismissive response uniformly employed by John Mason is only going to make students feel smaller and stupider.

Okay. I get that you aren’t into the intro quip at all. But “what are you struggling with?” is kind of the opposite of insincere and dismissive.

Chett and John have similar responses. Here’s Chett:

It takes a strong mind to pass Algebra 2. It takes a strong mind to make it in the world. My classroom is a gym for your mind.

Here’s John:

The ability to persevere through something difficult and the ability to make sense of the world around us. Math can do that for your brain in a way not much else out there can.

But I wonder if this response ever finds a ceiling. That is to say, a horrible teacher could ask her students to write the same equations 100 times, in the dark, using dull pencils, and if the students complained, both responses would still apply. “This is hard, but so is the world.” Mason’s response seems to put more of the burden on himself.

Kudos to Matt E for the Otten citation (never not appropriate) and Mr. C for a superior response to Mason’s.