I like math, writing, and teaching. I can’t draw. That much you could probably guess.

This blog is about the things I like. It’s also about the things I can’t do. I hope that the juxtaposition here – polished, thoughtful writing alongside art that my wife (charitably) likens to “the average 6th grader” – captures the contradictory state of the teacher, of the mathematician – and, what the hell, of the human. We are all simultaneously experts and beginners, flaunting our talents while trying to cover our shortcomings the way an animal hides a wound. You could call this a “math blog,” or a “teaching blog,” but I would call it a blog about owning up to weakness and drawing strength from successes, however transient or trivial they may seem.

Other facts: I’m a ~~math~~ maths teacher in Birmingham, England. Before that, I taught in Oakland, California. I’ve taught (or am currently teaching!) every level of mathematics from Grade 6 through AP Calculus or the IB, and I’ve also taught Psychology, Biology, English, and even (in a dubious feat of strange scheduling) Earth Science.

To email me, just use my name (Ben Orlin, by the way) at gmail. Or follow me on Twitter (#mathwithbadhashtags). I love to hear from readers, whether you stumbled here accidentally or are my college roommate Michael Wayne. (Hey, Michael Wayne!)

Love,

Ben

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I appreciate so much your insight and honesty on this topic. I have spent many hours pondering mathematics/learning and teaching. I flunked high school algebra 3 times (3x!) although somehow managed to earn straight A’s attending community college in California just two years later. I have several theories about this which include all of the following: my disbelief and discomfort in my ability to do math was inhibiting, teacher talent is critical and different learning styles require different teaching approaches. As a child I was always told I, “was missing the math gene”. I no longer give credence to this assertion; anyone can learn math with proper time and instruction. Second, in high school, my teachers were always the basketball coaches or the tennis coaches, and I’m sorry to say as a 15 year old female, I doubt I was on their radar at all. Finally, I have realized that there are unique learning styles and some students require more explanation than other students. My husband and my brother for example needed little instruction, being able to almost intuit their teachers’ explanations. I myself respond to a six step approach which I found worked when I helped teach math to 6th graders (ironic!)helping in my children’s classrooms. 1. Teacher explain and example. 2. Walk through an example with student(class) 3. Repeat step 2 4. Student does example independently 5. Repeat step 4 6. Students explains. Students who are stuck seldom say help or I don’t understand, they just say to themselves, “I can’t”. Thanks for the forum. : )

Thanks for your story, Carla! It’s almost a perfect microcosm for issues in math education today: the destructive, false view that mathematical ability is somehow innate or even genetic; the need to teach the full range of diverse learners, not just those who pick stuff up quickly from lectures; gender dynamics (my fiancee has had some interesting – and sometimes very sad – experiences as a woman in math); and the importance of quick cycles of feedback when learning (so that there’s not a long gap between seeing a demonstration and practicing a skill yourself).

I’m glad those 6th graders got the benefit of your thoughtfulness and reflection!

I’d love to hear some of your fiancee’s stories.

This sounds like our local high school but I don’t want to get anyone in trouble by naming names. Let’s just say we’re in southern Cal in an otherwise very good school district.

hi, the problem with math is easy to fix.

All day you speak and write English, plus you hear and read English all day as well. Think of the count less hours your doing English out of a classroom.

Now think about how much the average person spend on math in a typical day. Not much.

So that is the answer, to get much better at math it has to get the same attention as English. So when you take a bus the driver will give you a math problem, When your watching TV for 3 hours a day it’s all math TV. You get my point. We need 6 hours a day of math to be good at math. If we had 6 hours a day of math from K thru 12 by the time you get to college math would be easy. For an example look at the kids who win the spelling bees, many are immigrants whose parents spend all day doing repetitive spelling test. Math is no different.

Thanks

MH

Hey Michael, thanks for reading. Not sure I would’ve wanted 6-hour math classes, but I’ve got to say, the bus would be way more fun if the drivers asked trivia questions (mathematical or otherwise).

This is a joke..right? I can’t disagree more with this. This is the mentality we need to eliminate from our schools -skill and drill, stacks of worksheets with math problems, quantity over quality -especially in K-4. To get inherently better at math you have to make someone curious about how things work, why they work.

(I can’t tell if it was sarcasm or not… but quizmaster bus drivers is an awesome proposal either way.)

I’m afraid I have to disagree here. Elementary students learn their math topics better than any students after them. That is, they internalize the math skills from grades 1-4 far better than they will in grades 5-12. While the topics are not directly comparable, I feel a large part of what is missing from math in grades 5-12 is repetition and rigor, which would encourage much deeper understanding. Quality is important, no doubt, but you cannot be good at math without a fair bit of quantity, too.

thanks for this site… discovered through a link on slate.com.

i teach math (as does my brother) and i am sharing this site and the article from slate with all of my colleagues!

Thanks, Jon! Nice to hear from another teaching family – my sister and father teach math, too.

Everybody.

(N).

With two any integers (a) and (b)::

[a(a+1)/2]^2 – [b(b+1)/2]^2=(b+1)^3+(b+2)^3+……..+a^3.

Therefore:::

z(z+1)/2]^2 =[6(6+1)/2]^2+(6+1)^3+(6+2)^3+……..+z^3

[x(x+1)/2]^2=[5(5+1)/2]^2+(5+1)^3+(5+2)^3+……..+x^3.

[y(y+1)/2]^2=[2(2+1)/2]^2+(2+1)^3+(2+2)^3+……..+y^3.

And:

[z(z-1)/2]^2=[6(6+1)/2]^2+(6+1)^3+(6+2)^3+……..+(z-1)^3

[x(x-1)/2]^2=[5(5+1)/2]^2+(5+1)^3+(5+2)^3+……..+(x-1)^3

[y(y-1)/2]^2=[2(2+1)/2]^2+(2+1)^3+(2+2)^3+……..+(y-1)^3.

Therefore,first equation:

[z(z+1)/2]^2 – [x(x+1)/2]^2 – [y(y+1)/2]^2=[6(6+1)/2]^2+(6+1)^3+(6+2)^3+……..+z^3 – [5(5+1)/2]^2-(5+1)^3-(5+2)^3-……..-x^3 – [2(2+1)/2]^2-(2+1)^3-(2+2)^3-……..-y^3.

And second equation:

[z(z-1)/2]^2 – [x(x-1)/2]^2 – [y(y-1)/2]^2.=[6(6+1)/2]^2+(6+1)^3+(6+2)^3+……..+(z-1)^3 – [5(5+1)/2]^2-(5+1)^3-(5+2)^3-……..-(x-1)^3 – [2(2+1)/2]^2-(2+1)^3-(2+2)^3-……..-(y-1)^3

Because have the extra equation :

[6(6+1)/2]^2 – [5(5+1)/2]^2 – [2(2+1)/2]^2.=[5(5+1)/2]^2 – 2[2(2+1)/2]^2

Therefore, first equation become:

[z(z+1)/2]^2 – [x(x+1)/2]^2 – [y(y+1)/2]^2=[5(5+1)/2]^2 – 2[2(2+1)/2]^2+(6+1)^3+(6+2)^3+……..+z^3 -(5+1)^3-(5+2)^3-……..-x^3 – (2+1)^3-(2+2)^3-……..-y^3.

And second equation become:

[z(z-1)/2]^2 – [x(x-1)/2]^2 – [y(y-1)/2]^2=[5(5+1)/2]^2 – 2[2(2+1)/2]^2+(6+1)^3+(6+2)^3+……..+(z-1)^3 – (5+1)^3-(5+2)^3-……..-(x-1)^3 -(2+1)^3-(2+2)^3-……..-(y-1)^3

Because::

[5(5+1)/2]^2 – 2[2(2+1)/2]^2=(-1)^3+(-2)^3+(2+1)^3+(2+2)^3+……..+5^3.

Therefore:

[z(z+1)/2]^2 – [x(x+1)/2]^2 – [y(y+1)/2]^2=(-1)^3+(-2)^3+(2+1)^3+(2+2)^3+……..+5^3+(6+1)^3+(6+2)^3+……..+z^3 -(5+1)^3-(5+2)^3-……..-x^3 – (2+1)^3-(2+2)^3-……..-y^3.

And

[z(z-1)/2]^2 – [x(x-1)/2]^2 – [y(y-1)/2]^2=(-1)^3+(-2)^3+(2+1)^3+(2+2)^3+……..+5^3+(6+1)^3+(6+2)^3+……..+(z-1)^3 – (5+1)^3-(5+2)^3-……..-(x-1)^3 -(2+1)^3-(2+2)^3-……..-(y-1)^3

Define:

f(z,x,y)=[z(z+1)/2]^2 – [x(x+1)/2]^2 – [y(y+1)/2]^2

So

f(z-1,x-1,y-1)=[z(z-1)/2]^2 – [x(x-1)/2]^2 – [y(y-1)/2]^2

And define:

g(z,x,y)=(-1)^3+(-2)^3+(2+1)^3+(2+2)^3+……..+5^3+(6+1)^3+(6+2)^3+……..+z^3 -(5+1)^3-(5+2)^3-……..-x^3 – (2+1)^3-(2+2)^3-……..-y^3.

So:

g(z-1,x-1,y-1)=(-1)^3+(-2)^3+(2+1)^3+(2+2)^3+……..+5^3+(6+1)^3+(6+2)^3+……..+(z-1)^3 – (5+1)^3-(5+2)^3-……..-(x-1)^3 -(2+1)^3-(2+2)^3-……..-(y-1)^3

Suppose:

z^n=x^n+y^n.

Special case:

z^3=x^3+y^3.

With any integer (z):

z^3=[z(z+1)/2]^2 – [z(z-1)/2]^2

So:

[z(z+1)/2]^2 – [x(x+1)/2]^2 – [y(y+1)/2]^2=[z(z-1)/2]^2 – [x(x-1)/2]^2 – [y(y-1)/2]^2.

So:

f(z,x,y)=f(z-1,x-1,y-1)

Because:

f(z,x,y)=g(z,x,y)

Therefore:

f(z,x,y)=f(z-1,x-1,y-1)=g(z,x,y)=g(z-1,x-1,y-1)

Can not survive the three integers (z, x and y) satisfies both:

f (z, x, y) = f (z -1, x -1, y -1)

and

g (z, x, y) = g (z -1, x -1, y -1)

and:

Six equations.

ADIEU.

Hi, Ben!

You charming son of a gun.

I do what I can

Hi Ben!

I am a Mathematics undergraduate of NUS (National University of Singapore). I’m supposed to be revising for my mathematical analysis :O final exam tomorrow but I’m glad I stumbled into your blog! :)

Your experiences make me excited about teaching in future :D

-Rachel!

Hey Rachel, thanks for reading. I hope that final exam went well!

Nice blog. Really enjoyed the topology post.

Thanks!

Hi Ben!

I stumbled on your blog after I read your article on edutopia (I think).

Just wanted you to know I think you are sooo cool!

xo

Jennifer

Aka…Mrs. Cataldo

Thanks, Mrs. Cataldo! I hope everything’s going well with you guys.

Ben, this is fantastic – I aspire to make neuroscience this clear someday! Can’t wait to read more!

Thanks, Erin! I’ll look forward to reading “Neuroscience With Actually Pretty Decent Drawings” soon.

Hi

I guess you have read Bret Victor’s series on Kill Math. I sense there is a same problem statement in your introduction. I’m curious to know what you think about his proposals.

Haven’t actually come across Bret Victor yet – but I’ll add him to my list of things to check out.

Keep blogging! I plan to share some of your posts with my students, especially the posts that illustrate mundane concepts in fun ways. In fact, I’ll probably make “What it feels like to be bad at math” assigned reading for the first day of class, just so they know they’re not alone and I sympathize.

I’m glad you’re finding it useful! If they read “What It Feels Like to Be Bad at Math,” they should check out the comments, too (here or on Slate). It really drives home how common that experience is.

BEST MATH BLOG EVER!

Good blog for maths lovers!!!

Hi! I liked the blog, I’ve just scrolled around and read a few entries; they were interesting. I first came across this website when a friend directed me to the page about the tic-tac-toe variant; that was cool. Also (you might already know this) – tic tac toe can be extended to 3 or 4 or really any number of dimensions. It’s fun to play on a 4X4X4X4 board (not that I can really “see” a hypercube, but still). There’s also a weird but cool variant called quantum tic tac toe, you can look it up on google if you want.

Anyway, this is the summer before my 12th grade year of high school, and I’m starting to think of what major I want to study in college (as well as narrow down my list of universities, and attempt to get in my top choices). I definitely want to study something in science/math side, but I’m conflicted between pure science science and engineering. I think a degree in mathematics would be very interesting, as would a degree in physics or chemistry etc. I also think a degree in electrical or mechanical or chemical engineering or computer science etc. would be interesting. My parents however, are strongly pushing me away from pure sciences, as they want me to study something “practical” like engineering; they say a degree in math or physics would greatly limit my employment opportunities after college, that I’d find it harder to make a living or pay bills than if I studied engineering. Though I I think engineering would be interesting, I don’t want to be so quick to throw out the possibility of a pure math/science degree. You graduated from Yale with a degree in math, so I’m curious – what do most people with math degrees do after college? What are their employment opportunities, in addition to teaching?

Hey Ryan, thanks for reading the blog.

The simple answer: People with math degrees from Yale tend to filter into consulting, finance, and academia. (When I graduated in ’09, Wall Street wasn’t really hiring, so finance was out. But I hear it’s back in.)

On careers: I encourage my students to learn how to program. Across the board, my friends who are happiest with their jobs right now tend to work as programmers. (Teaching, consulting, grad school, med school, engineering, and law school all get more mixed reviews.) Partly that’s because I live near Silicon Valley, but mostly it’s a reflection of the economy right now.

So my advice would be: Major in something you love, and take lots of computer science to learn how to program well. Outside of grad school, there aren’t many jobs that use pure math or pure physics. If you really enjoy your classes, you’ll do well, and develop your problem-solving abilities, which employers will appreciate (especially in a perceived “tough” field like the ones you mentioned). And if you also become a great coder, then you can have it both ways – a rewarding edcuation and good job prospects.

I think you’re absolutely right about learning how to program, Ben. Not only is it a highly marketable and cross-disciplinary skill (atmospheric science graduate student, heyo!) but you find yourself approaching problems in new ways. I never knew how many different methods there were to differentiate equations until I had to start dealing with boundary conditions and discrete time steps in arrays!

I’m a maths student from Germany. This blog is great.

But I couldn’t find an RSS-Feed to follow your blog. Could you give me a link? This Mailsolution…Well, I would like to have your articels where I expect interesting blogposts, not where I search for mail from my girlfriend.

Hi, Ben Orlin!

I accidentally stumbled upon your blog because, well, I was fishing for advice on how to improve (or rather, completely comprehend, universally understand, and finally, please, excel in math) but I found out a month later that I had dyscalculia, sooooooo…yeah, I am inherently stupid in math. *sigh* it doesn’t reaaaaaaaaaallly help at all when the numbers and signs are all dancing tango. :/

Hey, I’m sorry to hear about your diagnosis – although I hope it proves useful to you in getting some support. I can imagine it’d be hard to tackle a problem when the symbols are busy cha-cha-ing.

I don’t know much about dyscalculia, but it strikes me that “inherently stupid in math” is a little harsh. There are a lot of different skills that go into math. Even if you have a deficit on several (say, arithmetic, working with symbols, and estimating measurements), there might be others that lie within your grasp (like deductive reasoning). You seem like somebody with good independent initiative (which is a good deal rarer than calculating ability!) so I’m sure you’ll do well one way or the other.

Dear Ben, I greatly enjoyed reading your beautifully written Euclid-infinity-of-primes poem (http://mathwithbaddrawings.com/2013/07/04/a-fight-with-euclid/) and would like very much to quote it in a free online math magazine I edit, ‘At Right Angles’, aimed at high school and middle school math teachers and students. (Here’s a link to the latest issue: http://teachersofindia.org/en/atria.) Would I have your permission to quote it there? I will of course give it along with the link to your blog. Thanks. Shailesh

Hey Shailesh, thanks for reaching out! You’re welcome to quote as much of the poem as you like. The magazine looks very cool – I’m downloading your latest issue right now. (I notice you’ve got it as a pdf – have you looked into using issuu?)

Thanks, Ben! I’ll send you a link when the issue does come out. And thanks also for the suggestion about Issuu. That’s a new one for me – I did not know about it. Cheers.

Dear Ben,

The latest issue of At Right Angles has just come out, and it has your piece “A Fight With Euclid”. See http://www.teachersofindia.org/en/periodicals/right-angles-november-2013. Thanks a lot for allowing us to reproduce the piece!

Best regards,

Shailesh

Thanks, Shailesh! The whole magazine looks great.

Dear Ben,

Happy Birthday! I hope I have the correct Ben Orlin. Then again, how many could there really be? And if I do have the right Ben, then it pleases me immensely that you have become a teacher. And that you use drawings. I hope we cross paths someday. All the best. -Brigid/Ms. Nulty

Hi Ms. Nulty! (I still don’t use first names with former teachers… even though I now have graduated students who want to call me “Ben.”) It’s great to hear from you. Are you still in Wisconsin? I’m in the Bay Area for another year – let me know if you’re ever in the neighborhood!

Hi Ben. A friend shared your blog post about ‘splitting checks’ which I really enjoyed. Check a few more posts and found them interesting as well. Happy to follow your post :)

P.S. Your drawing is wayyyyyyyyyy better than mine. I can’t even draw a straight line (without a ruler)!

Thanks for reading!

This is part of the reason I use the whiteboard – when my should-be-straight lines come out crooked, I can just erase and redraw!

This is better than xkcd, and I mean that as a huge compliment! I look forward to many more thought-provoking and entertaining math posts!

Hey, I take it as an (undeservedly) huge compliment! Thanks for reading!

Ben,

I was reading something somewhere and found a link to your blog (I think it was clicking on links randomly and ran across a link to your blog). I don’t remember how I got here, but I know I stayed for several hours and read every single one of your posts, mostly with tears in my eyes from laughter. I can’t wait to see more of your writing (and drawing)! It reminds me of my favorite teacher I had in high school for AP Chemistry and AP Physics, Mr. Gregory. He used to have bad jokes posed as questions that you would only get if you fully understood the current topic. I really think he used the laughter (groan?) of the class to gauge where we were at in the learning curve.

I submit the following:

Q: What did I eat on my cereal this morning?

A: Barium Sodiumide

Relevance: Barium Sodiumide = BaNa2 = BaNaNa (a fictitious substance that forced you to think of the periodic table, elemental symbols, and show understanding of empirical formulas and how to combine atoms)

Thanks for making me smile!

-Lucas

Hey Lucas, thanks for the kind words! It’s really gratifying to hear that you’re enjoying the blog so much.

Also: I’ve gotta say, I dig the banana joke. Partly because it’s very clever, and partly because the capitalization in “BaNaNa” just tickles me.

I’m flattered by the comparison to your teacher–and I’m glad I’m not the only one who interprets student groans as a good sign!

Notify me of new posts via email.

There’s a form on the right-hand side of the homepage!

FYI, I nominated you for a Liebster Award. I really enjoy reading your posts!

http://theadventuresofbeka.wordpress.com/2013/11/29/this-is-awkward/

This site is great! Someone forwarded me the link (assuming I’d appreciate maths humour) and I’m loving it. Your Hollywood Movie thing make me laugh a lot. I fully intend to print it out and put it up on my classroom wall… so through the wonder that is the internet you’re getting wall time in Bulgaria! (I’m an international school maths teacher)

Thanks! I’m honored that my silly jokes have reached such distant Bulgarian lands.

Did I imagine that somewhere on this site I came across a cool discussion of why 0.9999999 = 1?

A couple of my students came up to me arguing about it today and I wanted to send them the link but now I’m wondering if I just imagined seeing it on here. If it’s here can you please point me to where. Thanks!

You didn’t imagine it! My post is here:

http://mathwithbaddrawings.com/2013/08/07/0-999-and-the-debate-that-repeats-forever/

And I highly recommend the article by James Tanton I linked to at the bottom, which is:

http://www.jamestanton.com/wp-content/uploads/2012/03/Curriculum-Newsletter_September-2012.pdf

Perfect! Thanks so much. I’ve emailed them the link. The James Tanton article is interesting but I think your less wordy article (with drawings!) will be more to the liking of my students.

Cool. Glad to help!

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Mr. Ben Orlin,

I was pleased to see how well you use stick figures in your website. I am a sucker for stick figures, and have incorporated them into my own blog. As a tribute to the versatility of regular ol’ stick-man and regular ol’ stick-girl, I have created a blogroll rightly titled “Other Websites that Use Stick Figures.” I am happy to inform you that a link to your fine site has made it into the current ranks.

On a related note, you may (or may not) find the following article interesting: http://thechildlikeauthor.wordpress.com/2014/02/27/stick-figures-and-their-derivatives/

Cheers!

The Childlike Author

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Stumbled into your blog today ! And it is simply brilliant. I love the way you put your idea across ! Thanks a lot for sharing ! :D

Hello! I just wanted to let you know that I think you’re blog is fantastic…so much so that I’ve given you the Spectacular Blog Award! You’re awesome. :D

http://nerdinthebrain.com/2014/06/05/the-spectacular-blog-award-math-with-bad-drawings/

*your (ugh)

Ben, I really enjoy your blog. I would like to recommend you as a potential speaker for the NCTM conference in Minneapolis, November 2015. Let me know what you think?!

Hi Lesley, thanks for the message! That’s very kind to offer the recommendation. However, I’m actually moving to England for the next few years, and probably won’t be able to travel to the states while school is in session.

Thank you for responding to my email. Maybe another time. Good luck with your new adventure. That is wonderful!

Wicked !

I found you via dkane47

Have fun in Birmingham, or Brum.

The challenge is “Learn how to speak like the locals”, that’s when you’ve figured out what they are actually saying.

Hi Ben I just stumbled upon your blog and I don’t like Math at all but I think I’ll follow your blog. Hope I’ll learn math…:D Nice to meet you.

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Hey Ben,

I found your blog through a Google search, and I love your original approach to explaining math concepts. Bookmarked!

Thanks,

Josh

Adam Spencer: Why I fell in love with monster prime numbers

Hi Ben

Thought of you when I saw this :)

and this one too..

Hi, your blog is refreshingly unique and i couldn’t stop laughing for the most part of it! I wish somebody taught me maths like that! Actually i love maths but never looked at it the way you presented… kudos!!

Its midnight here and i have to stop now and go to sleep. but i don’t want to yet… That’s how engaging this blog is :)

Your drawings are great! There is so much soul in the simplicity…and there is humor, and a deep understanding of how challenging understanding can be! I look forward to following your blog and reading your posts.

Hey Ben! I absolutely love your post about headlines from a mathematically literate world. I am super impressed by your experience with teaching, too. I am considering work in the field of math education; I currently tutor a couple dozen students in their high school math (from algebra thru BC Calc) and would love to hear some of your opinions on how math is taught, especially since I live very near Oakland! I feel there is a lot of unnecessary repetition in the American curriculum, and far too much emphasis on memorization rather than deep understanding of core concepts.