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I’d like to start off with saying I am not a teacher so I don’t know how much of this is already trying to be addressed in math education throughout the world.

In talking to and tutoring fellow students, I have seen that most students think of math as solely applying formulas to given situations by rules given to you. Very few students see the beauty and creativity that goes into math. One consequence this seems to have is that students who find that they are bad at this rote application of formulas say that they are “bad at math”. Many of these people are creative and logical though, so they could possibly work with what in my opinion is the much more interesting math. Probably my favorite article on this is A Mathematician’s Lament by Paul Lockhart.

My question is what is being done about this in education and what can I do to help? I’m just a tutor, but I do try to show the students I work with the more interesting and fun parts of whatever subject they are doing. The more interesting proofs and properties and logic that goes with them.

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    $\begingroup$ While it is certainly a shame that a lot of people get this impressions of math, I think that very few people who are not able to become good at applying those formulas will be able to become good at math, simply because while those formulas do not properly represent what math is about, the sort of thinking that will make you able to do math will also make you able to apply the formulas. $\endgroup$ – Tobias Kildetoft Mar 27 '14 at 7:53
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    $\begingroup$ What I've actually heard more than I can't plug in values is the I can't remember the $20$ different equations on this test and I don't know which of them applies to this specific problem. The second part of that I could see as a problem for being good at math later on, but in my education so far memorization of a bunch of random formulas doesn't seem to help as much as actually learning where they come from and how you can find them yourself(I know this is how I passed grade school math). $\endgroup$ – ruler501 Mar 27 '14 at 15:35
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    $\begingroup$ @TobiasKildetoft, there are plenty of examples of prominent mathematicians who did poorly at school (particularly in the "drill <procedure>" department)... $\endgroup$ – vonbrand Mar 27 '14 at 21:54
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If you want to get a sense for what great math education looks like in 2014, you're blessed with an abundance of options.

Pick up the TERC Investigations curriculum, or the CME Project, or grab a copy of some of the NCTM journals. Or go check out some of the amazing work that educators are doing and sharing for free online. Shoot, go check out Christopher Danielson's blog, or Dan Meyer's blog, or Kate Nowak's blog, or Sam Shah's blog, or Nicora Placa's blog.

Now, you write that you try to show kids the "interesting" parts of math. I know what you mean -- things like knots or groups or puzzles and games, much in the spirit of Lockhart and those influenced by him. (I'm thinking of this article, in particular.)

What's remarkable about all the people that I linked to above is that they are innovating in education while teaching the same topics.

How you can help #1: Don't advocate for changing the curriculum.

This lets the entire system off the hook. The problem is not that school math is a different subject than real math, or at least it's not because the subjects that kids learn aren't genuinely mathematical.

School math is genuinely mathematical, or at least it should be. (The Common Core Standards say as much, by the way.) Every curriculum or person I linked to above excels at giving kids room to think mathematically about school topics. That means that rather than asking kids to memorize times tables, they ask kids to use strategies that make sense. Those educators use all their creativity and brain-power to figure out ways of presenting kids with opportunities to be mathematically creative with traditional topics.

How you can help #2 Use amazing resources for your students.

No educator is an island, and it's important that we don't all think through our teaching alone. I'm not saying that you are -- it sounds like you're a really thoughtful teacher! Still, it must be particularly difficult for you, as a tutor, to plan an activity or a lesson for your students. I would still recommend preparing yourself for your sessions as well as a teacher would prepare for class.

If your student is struggling with linear equations? Go do some reading about the struggles kids have with algebra. (May I recommend Fostering Algebraic Thinking?) If your student is struggling with rational functions? Go check out a high-quality textbook that's full of interesting problems and activities on the topic. (May I recommend CME Precalculus?)

How you can help #3 Show your students the multiplicity of mathematical talent.

It sounds like you're doing this already, but if school math often overemphasizes getting the right answer of remembering a procedure, then your students don't need you to do that. Instead, emphasize other mathematical talents. Value questions as much as answers. Value thinking as much as answers. Value ways of seeing, and not just ways of manipulating. Value explanations as much as answers. I'm sure others can add to this list.

Thanks for being such a thoughtful and supportive tutor! Your students are very lucky to have you.

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  • $\begingroup$ I'm really sorry if it seemed I was blaming the teachers. Most teachers do great. I've had a couple great math teachers that if they didn't do this in class they'd help me study on my own after class for the parts I was interested in. $\endgroup$ – ruler501 Mar 27 '14 at 15:31
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    $\begingroup$ Oh, no, I didn't think that you did! Sorry if it sounded like I thought that you thought that. That having been said, ultimately math teachers are the ones running math education, so any issues with math education are ultimately our responsibility. $\endgroup$ – Michael Pershan Mar 27 '14 at 16:09
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For new mathematics education research, I keep suggesting Jo Boaler's research, but only because I read What's Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject and took the free online course that she gave last year on "How to Learn Mathematics" (a MOOC through StanfordX - it's open again soon but it is not free this time around).

Boaler advocates the shift of mathematics education from the traditional, uninspired rote and memorization that many teachers and parents are used to seeing in the classroom (since they lived through those methods themselves), to the more active learning methods that challenges students to think of mathematics as a way to think about problems. Her book and course have more topics about this, ranging from shifting students' mindsets (neuroplasticity), creating collaborative classrooms, changing how we speak about achievement and assessments (making mistakes is actually learning), and organizing Number Talks to acknowledge how everyone has different methods in seeing and using mathematics. Boaler especially emphasized Carol Dweck's mindset research in first letting students know that they can have a growth mindset; consequently this awareness can encourage better learning habits.

Hence, I encourage you to take all these topics into account for when you teach mathematics because sometimes it takes the right kind of encouragement to really change how people see and feel about mathematics.

(As a side note, I get the "I am bad at math" comments from everyone, but once I let people in on this mindset idea they actually tell me that they start thinking about things differently!)

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