Hello, reader! If you intend to post a link to this blog on Twitter, be aware that for utterly mysterious reasons, Twitter thinks this blog is spam, and will prevent you from linking to it. Here's a workaround: change the .com in the address to .ca. I call it the "Maple Leaf Loophole." And thanks for sharing!

Wednesday, March 24, 2010

Subversive Mathematics

There have been two students coming to eat lunch in my room. They're both in my homeroom. Juniors now. Lanky. Maddening combination of wise and clueless. Don't know what to do with themselves half the time.

R is in the just-enough-to-graduate math classes. He is convinced math is a stupid and pointless torture device of adults who are out to make his life miserable. 

I had G when he was a freshman in Algebra 1. If he doesn't see the point, he's out. He's not going to disrupt class; he'll just quietly work on something else. But, he came into homeroom super excited a few weeks ago. He likes to mix, in GarageBand, for fun, and he realized he didn't have to count beats for a whole minute if he set up and solved a proportion.

Me and G and R are very slowly working our way through finding the Ramsey number for three. They don't know that's what we are doing. They are having a great time. I'm having a great time.

G's Trig teacher saw him in there and told me it's great he's getting help with math. Uhhh. Is that what we are doing? A student teacher in my room this week got really confused. She wanted to categorize what she was seeing, real bad. Is this extra credit? Test prep? What?

I'm kind of used to other teachers thinking I'm nuts, but I could use a little validation right now. Somebody tell me I'm not wasting my time and theirs. I just need one comment from a sentient being that says "You are not crazy."


  1. Everyone else is crazy. The system is crazy.

  2. Sounds like a mini-math circle to me. Math for the fun of it. Math that goes deep. Yeay! (But you knew I'd think it was great.)

    It's what we do in class that gets me questioning myself, the system, and everything.

  3. Wow that was quick. Thanks.

    All I want is to make class more like that.

  4. Teaching is about the kids first. Passion about content is great, but preaching your content means nothing if the kids aren't with you.

    Keep it up. You've connected with a couple of kids and they will remember your transparency, your caring spirit, and your love of math 30 years from now. That is the heart of what we do!

  5. Seconded (thirded? fourthed?) that the system is crazy.

    We've been so indoctrinated into standards and grades and points that the actual knowledge seems to of secondary importance for a lot of people.

    Thank you for both reprioritizing things the right way around, and reminding us of the way things should be.

  6. I'm just going to say that sounds awesome and I have no idea why other people were so confused.

    Also, now I have to go read up on what a Ramsey number is. (ps. That is also awesome)

  7. It sounds wonderful. You're not crazy.

    What kind of crazy world is this where others don't understand doing math for fun? It's okay to read for fun, right?

  8. No one feels the need to categorize other kinds of fun kids (or adults) choose to have - are kids playing hacky sack or frisbee on the lawn getting extra credit for phys ed? How bout those who curl up with a book at noon? Remedial English? Shocking to a few adults, kids do talk about what's going on in the news, and they don't just do it for extra credit in social studies. A huge congratulations to you for finding a place that learning math can be fun for these boys (and you!) in an authentic way, that doesn't need to be labelled as anything besides "fun."

  9. add me to the chorus of agrees. any extra time students are engaged in worthwhile thinking, whether it's about current events or life or ramsey numbers (which, like josh g., i am now going to go look up), is time very well spent. especially if they are also building strong relationships and learning that math (and everything we teach them in school) isn't just about what happens between the Do Now and the Exit Ticket.

  10. I agree with the others. You're not crazy. In fact the students that you are working with will probably remember what you're doing longer than most of the math they learn in the classroom.

  11. Just tell 'em "I'm metal, baby", toss on your sunglasses, and ride into the sunset.

    (In seriousness, I'd probably give an answer kind of like that. You need a _reason_ to do math for the fun of it?)

  12. Well, you are kinda crazy, but not so much about this. Also, I see your colleagues' point, too.

    Everyone here is right in the ideal situation. The ultimate point of what we're doing is to inspire learning especially in math.

    On the other hand, if they're not working on state standards and this isn't helping them in their "school life" then we're not necessarily "doing what's best for the student." Ultimately, Einstein may have failed his algebra class and turned out a genius, but if a kid doesn't graduate because of his grades or gets turned off by his grades, then studying other things may be a "waste of their time."

    (Un)fortunately, I've been falling on this side with most of my students and going through the standards rather than finding interesting things to teach them about math for the most part. I REALLY want to be with you and do this sort of thing, but it's a tougher decision than just going with the ideal.

    So, not that you needed it because you seemed to have those issues in mind already, but that's the Devil's Advocate side for ya.

  13. Sounds like authentic "discovery math" at its best, when nothing was forced at all and they're working on a solution to a *real* problem. Granted, their particular problem may mean little or nothing to most of your other students, but it has significance to these two students and they're discovering how to come at the problem, not because the teacher lectured it to them, or because they read it in a math textbook, but because THEY perceive the need to come up with a solution.

    I wish that I could get that sort of thing going in my own classroom more often!

  14. I think it's fabulous. I don't know if it would work out if you were trying to do it as part of a class, or even with a whole class, but I can't think of a better way to spend your lunch hour!

  15. Another "you're not crazy"

    I have students who hang out in my room after school. Sometimes they do homework (various subjects). Sometimes they work on math problems. Sometimes they just hang out.

    Others have asked why I "let" this happen.

  16. The classroom across the hall from mine is filled before school and during lunch with students and guitars and their guitar playing 10th grade language arts teacher. It has nothing to do with English. It's just a safe place to be.

    You could categorize it as "relationship building," if you had to.

  17. Hi Kate,

    You're great, and I think you know you don't need anyone or anything from this world to validate you... you're following the voice from within that prompts you to do all these things.

    You remind me of a quote attributed to Plato, which was used on xkcd's school:

    "Do not train children to learning by force and harshness, but direct them to it by what amuses their minds, so that you may be better able to discover with accuracy the peculiar bent of the genius of each."

    Thanks for the inspiration!

  18. You, R, and G might try working out R(4,4) next. You could even attack R(5,5), but I wouldn't recommend R(6,6).

    Just curious: did you use the words "Ramsey number" with them, or just describe the problem?

  19. Not many kids have fun with math, enjoy them while they're there.

    I've been coaching a math team of middle schoolers lately---lots of fun.

  20. You are all great for my ego. Thanks for all the encouragement.

    Dave I understand what you're saying. In this case, I don't think they'd still come if I tried to make them work on math from math class. They'd just be off doing something else during that period. I do think it would be ideal if we could run classes more like this. We'd need to teach less content to less kids. It seems unrealistic to hope for. The greatest challenge of my day to day work is getting as close to that ideal as I can even though I have to plow through too much content with too many kids.

    John I haven't said "Ramsey number." It all started with G doing a little puzzle that was really graph theory. Then we started wondering about connected graphs and a relationship between nodes and edges. But they kept giving examples of real connected things, like people knowing or not knowing each other. So then I asked them how many people would you need to get to guarantee that 3 people either knew each other or didn't know each other. It took all this week but we finally settled on a way to draw different situations of people knowing/not knowing each other. They both noticed, very cool, that the an abstract drawing made it easier to discuss and compare the situations, and it was like "half the problem is just figuring out what the question is." I was like "YES." We need to take a little detour into the pigeonhole principle so if they come in tomorrow, I'll probably start talking about socks in drawers. Today I pointed out that they were doing math for fun. They were like "You dummy, this isn't math."

  21. Oh and as a little addendum, my 4th period is way into discussing incorporating "achievements" into our grading system. (If you don't know what I'm talking about, don't worry about it. Or ask a 14 year old.) And I can't help but see everything we're talking about through a lens of extrinsic/intrinsic motivation.

    Yesterday I thought a homework problem would be too hard, so I said "It's a 'challenge' problem - you don't have to do it" then I was (stupidly, I know) shocked that many of them came in and it was the only problem they even did, and they complained it was too easy. There has to be a good way to harness the positive energy toward things you don't have to do.

    I am seriously thinking of doing some wildly off the reservation grading experiments with that class during the final marking period.

  22. my 4th period is way into discussing incorporating "achievements" into our grading system.

    I'm working on a standards-based system website setup for a class with "unlockable achievements" where they can watch videos and so forth.

  23. Oooh, can I see that? When it's ready?

  24. I quit my day job as a schoolteacher in order to do stuff like this (hanging out with kids and/or schoolteachers and having fun exploring math) for a living. It's great that you have the opportunity to do this within your school. And I feel very lucky that I can earn a living basically doing this kind of stuff all the time.

    I'd think of it like running a math club -- the good kind, that's not too focused on contests -- and attracting some kids who would never join a math club by not calling it by that name. The math club (or math circle, as per Sue's comment) justification should work with any fellow teachers who question it.


  25. Kate- I have the exact same thing happen, although usually after school. And I get the same from other teachers, "Why do you let them do that? You know you could just go home?"

    And I can't. So what if we aren't talking straight math all the time? As teachers, are we really hired to squeeze as much math into students heads as possible and then send them out the door? I think we've got to help get them ready for life, both mathematical and in general. That happens in those outside of class conversations.

    (If you want something really insane, I just blogged about Facebooking with students about math. Now that's crazy!)

  26. Educationally subversive.

    Keep it up!


  27. When I used to go to math workshops we all would go around the table introducing ourselves and what we taught. I never said "Calculus, Algebra 2, and Algebra 1" I said "Students becoming better thinkers". Like you are doing. The subject is just the vehicle we use to teach "Life". I'm guessing you do a good job.

    If you came to my room at lunch you would see an unusual crowd. A student teacher wanted to drop them into a category, so I told her they were the students most likely to get a "Kick Me" sign taped to their back. Its your time, and its a gift to share as you please.

  28. Yeah I don't know why that crisis of confidence came over me. One of those mornings. I'm all better now. This blog is better than therapy.

  29. If you didn't question things about your day, and you didn't make yourself available, you'd be only there for the paycheck, and wouldn't have any impact on others.

    We strive to have true impact, or we live in quiet desperation, counting down days or hours. Keep your chin up.

  30. You, Kate, are definitely not intramural. (And that's why other people think you're crazy sometimes)

  31. Kate- Pretty sure you're not nuts. If the kids are interested, and you can go with them towards anything new, then that's all you can do. Nice work, don't ruin it with vocab until they're ready. They're interested and they see you as a resource, which is all we can ask for.

  32. Kate-

    Come and work with me at my school... No one would think that you are nuts here. It is definitely part of the expectation here. Screw retirement and live for today.


  33. This is fabulous. Math can be so difficult to make relevant to students sometimes (I think - I don't teach it that often with my English and social studies endorsements). And I think you have to really, really, really have a thorough and solid understanding of mathematics to really be able to make it relevant to students on a consistent basis. It seems that's what you're doing. Great work.

  34. I'm sure it's obvious by now, but you aren't crazy. I love that you are just doing math with your students.

  35. Crazy? C'mon. Isn't this why we got into teaching-I mean except for the huge paychecks and all the free time? Any time you have an opportunity to connect with a student, it's a good thing. They don't need more adults telling them to do things that they find worthless because it covers a standard.

  36. Definitely not nuts.

    I despise formulas and memorization. Most days I think my kids are better off for it.

    It's nice to see that so many others agree with teaching the distance formula through right triangles. I was chastised in a department meeting for taking this approach.

    Perhaps I need a new school.

  37. >I was chastised in a department meeting for taking this approach.

    Did they say why? I can't imagine anyone who 'gets' math objecting to making the distance formula make sense this way.

  38. My money is on "Not Rigorous".

  39. How would you teach the distance formula without right triangles...?

  40. @Sue VanHattum - They must know the formula and all correct mathematical notation. I asked if we were teaching how to write math textbooks or how to understand what's in a math textbook. This started a full fledged verbal battle royal until the department chair made us cool it.

    @Kate Nowak Rigor was mentioned numerous times.

    @ unapologetic 'Memorize it'. That was the approach of a few of my colleagues.

  41. It is so great that you are finding ways to teach them without them realizing what is being done. Keep up the creativity!

  42. "rigor" no longer bears much trace
    of its traditional usage (meaning
    something like "follow principles
    carefully"); the current usage
    appeals ("let's be realistic")
    to the uber-principle of
    "follow the rules as i
    (pretend to)
    feel the boss would
    want them interpreted".
    have fun storming the castle.

  43. I thought this thread about rigor was on the distance post, so I couldn't find it (shortly after Andy posted). I wanted to say something like what Owen just did.

    It's scary to think what crazy kind of definition of 'rigor' they must have in their heads. Right triangles is closer (than the distance 'formula') to rigor in my book. Perhaps they're confusing rigor with rigor mortis...

    To me, rigor in math is clarity about why something must be true.

  44. There's already a plethora of comments so I'm sure that this has been posted before, but it sounds to me like you're creating an authentic mathematics experience for them. There's nothing better for either learning or appreciation than doing a problem because you can. It re-fires that intrinsic motivation we seem to lose while jumping through all the hoops. Excellent job!


Hi! I will have to approve this before it shows up. Cuz yo those spammers are crafty like ice is cold.