# I concede

OK world, I concede.

Math really is just a bunch of disconnected rules.

Keywords are a good instructional strategy because getting a right answer now is more important than learning so you can get right answers later on.

This thing has one formula, that thing has a slightly different one; and these have nothing whatsoever to do with each other.

If you’re in situation A, you should do this; unless condition B holds, in which case it’s this other thing.

Oh, and CAUTION! Be sure not to make this error.

If this is bigger than that, treat it this way. If it’s smaller, do the opposite. If they’re equal you don’t have to do anything. Unless they can’t be equal in which case, see the caution above.

These things are equal, while those are congruent. Don’t get these confused.

We can’t take the square root of these things, unless we’re in that class. Not even if you already took that class. But there is no class where we can divide by this. But we can multiply by anything. As long it’s this sort of thing.

Flash cards equal learning.

Memorization is the goal, and the standard by which all should be judged.

Thinking is for losers.

All of the useful ideas in mathematics have already been had by others. We should study those instead of reinventing the wheel.

I concede, world. I concede. You are right.

I give up.

### 15 responses to “I concede”

1. Christopher

Also teaching requires no preparation, and is in fact better when done completely spontaneously.

People learn better in pursuit of badges than when they are interested in things.

And “getting correct answers to 90% of the questions that I chose for you to work” is not an arbitrary standard; it is objective and meaningful.

Again, I concede. And I shall cease trying to put forth my own (previously held but now abandoned) contrary vision.

2. Eva

There, there, it will be alright soon.

3. Anne Bartel

A difficult teaching day? Would you support a rule requiring a “beliefs survey” exam to become a teacher (k-12) of mathematics?

4. See my second comment on your previous entry, particularly towards the end, when I talk about degrees of bad math teaching being the scope most people (teachers, students, parents, administrators) see as possible.

But on the bright side, there are enough of us with a more powerful conception of high-quality mathematics teaching and learning pushing to make a difference that I’m confident that things will improve. Giving up our efforts to improve our own practices and those of others simply isn’t an option, no matter how bleak the prospects may seem for a quick, overwhelming overhaul of the general state of things.

5. Christopher

Don’t worry, Anne. I’m OK.

I have been working with Calculus students who are hitting the limit (so to speak) of their ability to memorize their way through mathematics. It’s a painful process for them to give up their long-held view of the subject. And simultaneously, there is precious little support for it.

I have been working with one student, encouraging him/her to draw pictures to make sense of volume by integration. I cannot tell if I am meeting willful resistance or a lack of understanding of what I’m really asking (I suspect the latter). So I asked my student to send me a link to some resources he/she has found useful. A link to a video arrives (not this one, but might as well be) and there it is. Problem followed by formula. We are supposed to be finding volume by way of disks and washers, but there is no disk nor washer to be found.

And then my thoughts were drowned out by a basic algebra class this morning. That class sounded an awful lot to the students in attendance like my text above reads.

It was either bottle it up or let it out. I chose to let it out. Thanks for your concern. I’ll be just fine.

• Jim Doherty

Christopher
Last year in my Calculus Honors class I had a conversation in early October that you’ll relate to. One of my students was used to earning A’s in math and was at the C+ level. She stayed after more for advice than for help and she said “I thought my job as a math student was to know which formula to use and how to use it” This made me sad because this is more the responsibility of our teachers than it is of our learners. She only thought this because she had been receiving positive feedback for thinking that way.

6. Alex Otto

Rough day? I’ll be happy to listen to you vent if you need to. Usually I am the ventor, not the ventee!

7. Don

Hey there…If you were to give up then I’d have no hope. Jr. High students (at varying levels of abstract thinking) challenge me this way everyday. Student 1:”Why do I need to write down an equation if I can just subtract?”
Student 2: “It is impossible to flip a coin 100 and have it land on heads.” Student 3: “He’s explaining it to me easier.” [The other students uses the exact same language I do…she just thinks he’s cute so she listens to him.]
Student 4: “Thinking is hard.”
Student 5: “Opposites and reciprocals are the same. Whatever! It doesn’t matter.”
And so on…
On the other hand, I did teach calc for 4 years. I would start off class letting them know that some of them were in for a challenge if all they had ever done was memorize. Groans would spew forth and by the end of the year, half the class made progress and the other half still insisted that thinking was too hard.
Nonetheless, I believe I’m making a difference in this community. Kids are being exposed to more math than ever although I’m still in doubt about MEAP scores and Common Core evaluations…
Thanks again for sharing your thoughts!

• Christopher

Don’t worry, Don. I’m not actually going to give up the good fight. I’ll try to get back to being inspirational shortly.

8. Loved this post. I had been thinking recently about doing a post titled “A Lesson on Direct Variation.” The post was going to feature a graphical comparison with “teaching that supports constructivist learning” on one axis and “resistance from students and parents” on the other. As you might have guessed, I sometimes feel these two increase in unison.

In fact, I think most students actually love a classroom that is taught in this way. The problem is that it creates a great deal of cognitive dissonance because they have already “constructed,” if you will, a definition of mathematics that is in stark contrast to what we are trying to encourage. Thanks for your thoughts. Stay positive, it sounds like your work is amazing.

9. Kristin

I love this post….from an elementary perspective it goes something like this (just because it is kinda fun to just get it out…)

Math is just a bunch of rules.

If this “key word” is in the problem, do this operation, if it says another word, do that operation. No need to estimate, no need to reason, just follow the rules.

If you need to compute be sure to follow the algorithm, even if you are in 2nd grade and do not have a strong foundation of number sense. You just carry, borrow, and put that zero there as a place holder and it will all be just fine.

And flash cards for sums of 10 and multiplication/division facts are really the way to go to obtain fluency and tricks and mnemonics really speed up that process!

Yep, teaching the “way we learned it” is awesome.

You may win TODAY teachers, but I am on a “Mission from God” (couldn’t let an opportunity to use some Blues Brothers pass) and I will change the way you teach mathematics to our children!

Thanks for this opportunity….very fun!

10. Christopher

Feels good to get it out, doesn’t it, Kristin?

• Kristin

It does! It actually makes me laugh (after the fact) at the craziness that some teachers consider good teaching. I am finally going to dive into blogging for this reason…need to talk about the great, good, bad and ugly of it all. Not to mention the fact that my friends need a break from my “school talk”!!!

11. It’s so hard to break them out of this box, even as middle school students. I begin at the end and relate all of the math we do to the projects but so many of them just want a formula. They are begging for a “if I see this, can I always do that?” It drives me insane. And then, if it isn’t exactly like what they have seen before, they tell me they have no idea what to do. I don’t teach them the “rules” so their parents, older siblings, and tutors show them the shortcuts when they get confused. Why do they think confusion is such a bad thing? I saw the best saying once, “Confusion is ignorance leaving the brain just like pain is weakness leaving the body!” Sometimes I get the most ridiculous answers on their written work, even when I always have them estimate before answering in class. Where is the disconnect? How do we fix this? Mine are so young. You would think I could do a better job of changing things for them. 😦 It’s these things that keep me up at night. And sorry, but I HAVE had a rough day so I just jumped right on this instead of keeping quiet.

12. “Because math is so sequential, …”