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comment by lm
lm  ·  613 days ago  ·  link  ·    ·  parent  ·  post: An Axiomatic Approach to Algebra and Other Aspects of Life

I think it's a mixture of things:

- Teachers weren't taught the material this way, so they don't know to teach it like that.

- There aren't a lot of textbooks that rigorously follow this approach (or at least I haven't seen them), so you'd have to write your own curriculum.

- It definitely takes more work, and students won't like it if they're used to math being about the answer.

I had a physics professor who used the same philosophy, and I enjoyed that class--analyzing a physics problem was all about understanding how the different laws related to each other.




katakowsj  ·  613 days ago  ·  link  ·  

As a middle school math teacher, I can say that I try. From day one, our first and foremost class norm is "Our reasoning is more important than our answer." This unfortunately, for many, goes over like a lead balloon. This is my first year that I've made this norm as explicit as naming it every day. Some are buying in, which is good, while some are echoing Mom and Dad at home and complaining about this "new" math.

It's a slow go, but we're moving forward. With testing culture as prevalent as it is, the focus on using tricks to find the answers is at a premium.

In my classes, I do have a great number of students conditioned to proving their claims with evidence and reasoning. They're beginning to recognize the value of sound reasoning and problem solving.

Now, if I can find a way to remove the cultural acceptance of math illiteracy that occurs around me. Why is it that parents will meet with me at conferences and condemn their kids to math ignorance? For example,"I know little Billy is struggling with math, but I was never a math person myself anyway...can you just give him some extra credit?"

No. No I cannot give him extra credit. You are not supposed to undermine his education by asking that, or get all ticked off when I try and explain that this is a bad idea.

Can you instead give him a stronger work ethic and convince him that he will understand math better when he actually listens and follows through with his math? Oh, he'll have the grades and test scores you want too.

Yes. It's a slow go.

kantos  ·  611 days ago  ·  link  ·  

    From day one, our first and foremost class norm is "Our reasoning is more important than our answer." This unfortunately, for many, goes over like a lead balloon. This is my first year that I've made this norm as explicit as naming it every day.

I can count on one hand how many of my math teachers explicitly enforced this idea through encouraging such work ethic via their rubric/grading. That alone was enough for a later instructor's motto, heard at least twice a week for the 3 years I had him, to resonate: "a problem well-defined is a problem half solved." For those it sticks with, I can assure you it will be worth it. It was for me, at least.

b_b  ·  611 days ago  ·  link  ·  

Of course on the other hand reasoning being more important than the answer is the reason that Aristotle's ideas about physics were stuck to religiously (literally) for 2000 years.

ThatFanficGuy  ·  612 days ago  ·  link  ·  

    while some are echoing Mom and Dad at home and complaining about this "new" math.

It isn't new, though, is it? Solid, traceable reasoning has always been the basis of mathematics. The fact that a man once spent more than two hundred pages just to prove, with fundamental footwork that even religious fanatics shall envy, that 1 + 1 = 2 seems to prove it. It's the lack of mental rigor that undermines the solid structure that mathematics is based upon, which is what your kid's Mom and Dad have aplenty of.

Tell them "Your lack of mental capacity to understand the necessity of hard mental work when it comes to hard science shouldn't undermine your child's future capabilities" next time someone complains about "not being a maths person". I'd love to see their faces when they hear that.

You're doing divine work. Bless you, and best of luck with your work. Don't give up because of a few bad apples: dust accumulates all by itself, but people who make effort to shine are what's worth looking at exactly because they don't stand to stay filthy.

katakowsj  ·  612 days ago  ·  link  ·  

Thanks. I appreciate the support. It's a nice reminder that so many folks like you are out and around as well.

I have tried, on various levels, to give the math and reasoning ignorant a piece of my mind, but that never goes over well. Venting my feelings here on Hubski helps a bunch.

In the meantime, I know that I must win their hearts before their minds. I'll be killing them with kindness as they slowly recognize that reasoning increases the happiness in their lives as it does mine and yours.

Thanks. Let's keep that dust from settling where we can.

ThatFanficGuy  ·  612 days ago  ·  link  ·  

    I'll be killing them with kindness

That's a reasonable way to deal with it. Mine was cheeky, merely to create spite; not a wise one, and certainly not the one to act on when dealing with antipathy. You can't subdue fire with fire.

    In the meantime, I know that I must win their hearts before their minds.

Do you have any particular methods or lines of thought that you attend to in order to do that? Sounds like a good thing to learn from someone who's dealt with the issue of pupils' parents before, since I aim to be a teacher myself.

katakowsj  ·  611 days ago  ·  link  ·  

Glad to hear that you plan on teaching. It can be a bumpy, yet rewarding journey. There is no formula, or maybe actually, too many formulas to actually generalize what works. That's the art of teaching I guess. Knowing your audience is definitely primary to figuring out your strategy. I don't know you too well, so I knocked out as general a plan that I've found to works for me right now. Best of luck to you.

Firstly, in order to win over the parents and students, you'll want to fully recognize that change will come slowly. It's like watching a tree grow in your yard that you planted as a kid. It seems like nothing is happening until one day, you gain a new perspective and find the little tree has a trunk you can barely wrap your hands around.

Secondly, you'll need to up expectations by educating them on the importance of their endeavors. For example, you might set up a study into fractions, "Have you guys ever realized what portion of the hours of your week you spend, sleeping, in school, etc... Let's check that out." Relate the subject to what they know.

Thirdly, generate interest and enthusiasm through open dialogue with the subject matter as the center. This is generally more difficult in math than say science which is likely to be immediately relatable. I find that for math, continually relating, "Math is just patterns and puzzles about the world that people have discovered. Today we're checking out how _________ pattern works. What do you guys know about it so far?"

From there, I'd say, always have a clear and fair instructional system and give them lots of feedback. Students, especially my middle schoolers, as they are working to take full responsibility for their learning, when frustrated, will look for excuses out of their responsibilities in learning.

By having a system that is clear and fair, they will less likely to take the easy way out, and then learn to adapt to the expectations you have of them.

Thanks for asking the question. It's nice to rethink my reasoning for my teaching.

ThatFanficGuy  ·  611 days ago  ·  link  ·  

Glad my question helped, and thanks for giving me some guideline. I find it difficult to work without even a faint idea of what I'm supposed to do, and to have some ground makes it seem far more tangible.

    Firstly, in order to win over the parents and students, you'll want to fully recognize that change will come slowly.

Man... Patience. Always had problems with it. Though I'm growing into a better model of thinking, I'm sure it'll still be difficult for me to grasp the consequential nature of learning and teacher-student interactions until a few years later, when I do see the trunk grow. Any advice you have on keeping my mind on target through the daily drag?

    Secondly, you'll need to up expectations by educating them on the importance of their endeavors.

I can relate to that. It's much easier to grasp something you can relate to, and for me, it's like telling a story. I've been doing this for a long time, so it shouldn't come as a problem. I am, after all, going to teach languages: they are what makes stories, so as you learn the language, you learn how to tell a story, and the importance of that... Well, I'm sure I'll be able to relate the kids to that. :)

    Thirdly, generate interest and enthusiasm through open dialogue with the subject matter as the center.

That's where things get blurry. Where do you draw the line between having a dialogue and having to teach the curriculum? From what I hear, it's a big deal, to finish the curriculum before the end of the year; and of course, I don't want not to teach them something if the subject is concerned with it. And yet, dialogue is extremely important. So, how do you make it work, and how you do reign in a discussion gone rogue?

    From there, I'd say, always have a clear and fair instructional system

Are there any examples you can give, good or bad? Again, it's about tangibility for me; to learn where to go and what to refrain from. I have a vague idea about it - I did have some good teachers at school - but I'd like some concrete examples.

    By having a system that is clear and fair, they will less likely to take the easy way out

It probably depends on the person as much as most everything about teaching is, but - how do you reign in the pupils who fall angry at being tired of failing to learn or understand something? Simply explaining it won't do, because that's not the point, important as it may be afterwards. How well does talking straight ("I know you feel frustrated because you can't understand it...") work, in your experience? What else might work well?

Again, thank you for answering that. The more I learn before diving into the world of teaching, the better.

ThatFanficGuy  ·  612 days ago  ·  link  ·  

I wonder if this could be applied to linguistics. Mathematics and natural sciences have structure in them that you can easily follow, given similar rigidness to what the blog post describes. Linguistics is about a subject that's in constant change, miserable in size as it may be to an observer; the only "solid" parts about it are grammar and phonetics, and even then...

lm  ·  612 days ago  ·  link  ·  

I'm sure it can--phonics is a good example: once you know it, you can almost always pronounce words that you haven't seen before. Same thing with algebra and equations/derivations/proofs you haven't seen: if the axioms are part of how your mind works, the math comes naturally to you.

Interestingly, I think computer science has some things to learn from linguistics about how to teach programming. I'd like to take the time to properly develop a curriculum for teaching a programming language as a written language one of these days.

ThatFanficGuy  ·  612 days ago  ·  link  ·  

    Interestingly, I think computer science has some things to learn from linguistics about how to teach programming.

That's something I came to think as well. There's a reason they're called "programming languages", even if people relate them closer to mathematics. The grammar might not be particularly human-friendly relative to English, but then - it isn't often with languages you're only starting to learn.

If you'd ever like to discuss the matter - feel free to message me: I'd be excited to merge my two passions for a purpose. If you already have some observation on the matter that you could share - please do, here or in IRC: I'd be delighted to hear it.

lm  ·  612 days ago  ·  link  ·  

I'd love to! Probably over the summer, since this semester I'm TAing a different class.

ThatFanficGuy  ·  611 days ago  ·  link  ·  

Feel free to leave me a message anytime.