I’ve realized more and more how truly powerful the internet is for learning, if you want it to be. This is why I am so pleased to see that Google+ is available to the public today. Aside from its innovative privacy settings and excellent video chat, Google+ is social media right there with your gmail, google docs, and reader. (If you don’t have some of this stuff, you may be missing out, especially if you seriously want to get into something.) Google+ and Twitter are now central to the way I grow as a mathematician and a teacher. I once heard, “Facebook is for the people you went to high school with. Google+ is for the people you wish you went to high school with. G+ is for people you want to talk with over coffee, and Facebook is for people you wouldn’t meet for coffee if they were in the same town.

Two great places for exchanging ideas are the #edchat and #mathchat on Twitter. Tonight’s question was, **“If you could clear one misconception about mathematics and/or teaching it, what would it be?” **(Share your own in the comments?) I found this more enticing than my Field Theory class, so I fired a few off. Thought I’d share this mini-manifesto. (140 characters at a time)

* * *

*must change misconception: geniuses do real math. Otherwise math is math class.*

*you have to get As and 800s to do math or like math.*

*you’ve gotta climb the ladder to get to the good stuff in math.*

*you need the high school math to do ______ And you definitely can’t study topology until ______!*

*you’re either an applied person or a pure math person. Bleh.*

*math is math class and homework should look like homework.*

*you really need to know algebra for the real world.*

*fractions are wrong if their not reduced.*

*practice is the best way to get better. (personal experience actually is)*

*you have to play the role of “teacher” to get class to work.*

*must change misconception: “there are problems I need to solve, and I need someone to show me how to do that.” – Salman Khan! No joke!*

*“they” write the problems. I just answer them. Can we tell what “they’re” asking?*

*must realize: math is made by humans like the ones in the classroom. So let’s make math.*

*must change misconception: it’s ok to say “I’m so dumb at math. I’m not just not a math person.” especially for kids*

*stick to the book or you’re in trouble (aka I don’t trust you)*

*go with your first instinct. Your second is wrong (aka don’t trust yourself)*

*you need the teacher to learn math. You need school to learn math.*

*texting in class is bad. (I’m in field theory class enjoying this much more)*

*-@ColinTGraham: “OK I AM SHOUTING NOW… YOU GET TO CHOOSE ONE MISCONCEPTION PEOPLE… Phew… CAPS lock off…”*

* oh ok. Boo! Too many to choose. How about this one: you can tweet forever without battery death. (I have to go)*

** * **

Lots of old thoughts there, and I could include links to old posts, but this is already too self-indulgent.

The preponderance of general misconceptions about math seems so overwhelming and frustrating at times. A large part of my teaching is an attempt to give math a good name with my students by showing them mathematical traits and habits already within them. This is my little force against the mathematical boogeyman. I’m glad I got some of that off my chest.

This is all nice, but don’t you say that math is a dying art form? I can’t help but wonder, if one could make an argument of this type about anything. All of the subjects that you learn in most schools are based on an out dated way of thinking (including Saint Ann’s curriculum, sorry.)

Are you trying to say that we should have passion and love for math just because? I can understand that certain misconceptions about math can have an initial deterrence for lots of people, however, without those misconceptions maybe it’s just that people aren’t necessarily interested in math. It’s difficult to make people feel a certain way about something, even though you’re so inspired by it yourself, it certainly is noble though. I can’t help but think that this is how people have done great things in the past. However, shouting your inspiration from every social platform is slightly exhausting and maybe not as effective?

An argument can be made for music, art, english, etc etc. I understand you’re a math teacher and so of course you’re going to argue that math is so compelling and anyone can be a mathematician.

Anyways, I’m rambling now.

I don’t like to allow anonymous responses, because I think people should stand by their internet presence and their thoughts. You make some very good points, so I am happy to have them read. Allow to me respond:

I have said before that I think math is dying, because of the sorts of misconceptions I listed here, and I would agree that you could make a similar argument for most things. School definitely puts these immense, broad subjects in boxes based on standards and testing, and in the process limits them, even when “extra credit” and extension work is available. And yes, indeed, even at Saint Ann’s, a lot of what goes on is almost ancient in form – behold ye olde chalk and talk. (We have little in the way of curriculum, however)

I don’t mean to say everyone should be passionate about math, (be serious about something for sure!) but I think some of our “school math” practices turn people off to something that they may enjoy, if taken differently – threads that may already exist in their thinking. There are ways to experience mathematics outside of learning this, showing that and answering “their” questions. This is totally working for my fifth graders. (a small sample set, I know)

I am indeed a math teacher, and so I must continue to share what I find compelling about math, with whoever will listen. I don’t mean to shout on social media, and certainly anyone may tune me out, but I feel compelled to show people, especially young people, that math is broad and accessible – that a part of them is naturally mathematical, and exploring it may be pleasant and fulfilling.

Thanks for your thoughts. I hope you’ll comment again, with your name, perhaps.

What’s the difference if I post my name or not? If you don’t know me?

So if school math turns people off, then why are you teaching “school math”, wouldn’t you rather spend your time teaching something that is meaningful? Instead of things that allow people to pass the test, get into college, etc. Despite not having grades at Saint Ann’s, I don’t think it is fair to say that kids don’t think about tests, they still have to face the music at some point, whether it be the SAT’s or some form of grading in university. You say you teach your 5th graders in a non traditional school math way, why not with all of your students?

I’m not trying to argue, I just see a lot of comments on this blog, without any question of what you’re saying.

Perhaps it’s a small point, but I want my readers to stand behind their views. If you weren’t being so darn thoughtful, I probably would have removed the comment.

You bring up a really good point: I’m advocating for something far more radical than what I, myself, am doing. Saint Ann’s curriculum, though minimum is still based on building arithmetic skill and mathematical thinking in middle school, and following a fairly traditional program in high school (Alg1, Geom, Alg2). I have worked to change this to some extent, as I wrote in my last post, but you’re exactly right. The bubble eventually pops. Students

wantto go to college, and I mostly cannot blame them. There is a system outside of the one I control, and when they leave, they will be a part of it.I teach my students standard material, because I owe it to them to give them every opportunity they want after Saint Ann’s. Along the way, of course, I try to help them see the wider, more human, view of mathematics as something people actually

do. There is a foolish culture (rampant at Saint Ann’s and wealthy NYC culture in particular) that if you can reach Ivy League, you better do it, and I try to alter this perception, but there’s only so much I can do. All of that is not to mention the fact, that I get the sense people outside my department want us to just get the school-math stuff in their heads. (parents, administrators, scientists, etc.)Lastly, I do in fact try these other things in fifth grade, but it is all part of the same developmental process that involves numerical and logical thinking as well as arithmetic. I suppose my view is a little nuanced and personal, but I think every teacher is entitled to that.

Thanks again for your comments! I really appreciate your reading.

This conversation is really interesting and if I may, I have a couple of comments. Basic math skills are neccesary in order to be able to learn more complex math, you won’t be able to do advanced math if you learned to add with a calculator. It’s in the way that Math is taught were the differentiation beggins. For example in most colleges (at least in Mexico) the math education is based on Newton’s Calculus which is excellent but this isn’t the only way you can learn math. In regional contests alumni are taught math based on the other two pilars of math which are Algebra and Geometry and this gives students a different logic frame in order to solve problems. This structure, based on logic and intuition other than formulas and a close frame of assumptions which not necesarilly are “natural” generate a different kind of mathematitians. I believe it’s important to restructure the way we teach math because I agree a lot of people can be excellent mathematitians if they find a teacher (or the teacher finds them) that can break through the stereotype that math is difficult. Some students just need a different approach to the problem or the solution.

Thanks for your comment! I agree about learning foundations. Every student needs really successful and personal experiences as. Young mathematician in order to keep feeling good about math, and certainly our experiences build and call upon prior experiences. I also agree, the trouble is the way arithmetic and “basic math” is being taught.

I’m also glad to hear about places that open up the world of math beyond sheer myopia, and yet there is yet much more than algebra, geometry, and arithmetic. I hope we find ways to share this with the interested.

Are you reading from Mexico? If so, I’m wowed. Thank you!

The biggest hurdle I face when trying to use social media for teaching and learning is parent and school (staff + administration) concerns about student privacy and safety. What is ok to make public and what is not?

You have this problem, as do I and everyone else. I’ve been pushing for permission to use google+ with my classes because of it’s selective sharing features. You constantly have to answer the question, “who do I want to see this?” Of course Facebook followed suit with a similar feature.

My sense is this: Using the Internet and maintaining an appropriate internet presence is HUGELY important! So let me help them with that.

Thanks for sharing.

Thank you and yes I’m from Mexico City. I actually got to your blog because I’m also interested in Juggling.

Just to complement an arithmetic concept. I’ve heard and seen the basic arithmetic operations being done as set theory. It’s an amazing way to do this since you don’t have to explain the concept of number or memorize the multiplication tables in order to understand what you’re doing. I’ll try to figure out a way of explaining this ideas, in the meanwhile, have a good one!

Yeah, you’re very right about the foundations of numbers being built out of set theory. I’m actually teaching this in my Algebra 2 class right now. It’s a “functions and abstract algebra” version that students may choose. Really fascinates me, but it’s getting mixed reviews with them – all part of the continuing struggle of customer service.

Cool to know you’re into juggling! Hope to hear from you again, sometime. Thanks for your thoughts.