I gave a talk at Skepticon IV about the problems with math education and they already have it up online! (Nice work, HamboneProductions.)
Hope you like it.
I’ve read some things here and there about religious people attacking set theory for some reason. But never any specifics. Anyone what that is about?
I haven’t heard that one, but I remember reading on a theology blog that “God is not a member of any set.” Apparently not even of the set of gods, or the set of things that are not members of any set.
Just loved your presentation Hemant! Thanks for this!
So I attended this talk by a professor who had been teaching math for 50 years. His talk was titled “Why math?” He spent some time showing a kind of history of math books which demonstrated how absurd current math books are. His claim was that the math industry and parents and teachers have all become obsessed with trying to convince kids (and parents) that the math applies directly to life in one way or another.
I recall some of his examples included the math questions that instructors in Ancient Greece asked their students to solve – these were *not* easy questions and I would not expect to see them asked today. They were also just not applicable. He ended his talk with his answer: “Because!” His point was that math is exercise for the human brain. Exercise that it will not get any other way.
I taught math for 5 terms at college. I sometimes fell for the “when will I use this?” ruse. I usually brought up financial calculations as a defense. I like how you mentioned you sometimes don’t allow calculators. I *never* allowed calculators. Not a single test. This was Intermediate Algebra and Pre-calc (trig). No calculators at all. I highly recommend it. Too many students don’t even know their times-tables these days. Even if they have to break out pencil and paper and multiply some big numbers, they need the exercise!
Once again . .. . can’t teach creationism? I don’t know why you can’t have some classes teach “intelligent design” and some “evolution”. sigh . . . ok . . . . talk about atheist special priv. . I see it now . . . a large percentage of BOTH sides are fighting against each others very existence.
You can’t teach creationism because creationism is religion. It’s also stupid.
You can’t teach intelligent design because, aside from the fact that it’s still just religion, it’s pretty stupid in and of itself. The only way the design of this world is intelligent is if the designer was on drugs.
Schools are in the business of teaching what is known.
“Atheist special privilege.”
For the same reason science classes don’t teach planetary epicycles, alchemy or the battle between Marduk and Tiamat.
I DEMAND SOME ASTROLOGY CLASSES!!!111one
I’ve always wondered what there is to teach about “intelligent design” anyway. “Such-and-such is to complex to have evolved, therefore it didn’t. Thus endeth the lesson.”
That’s a pretty long video, and I have trouble focusing on, well, sounds for that long. Bit of an auditory processing thing. Is there a transcript anywhere?
I had hubby and son watch it as they are both math geeks. Hubby rolled his eyes and humored me when he saw how long it was but even HE (who NEVER watches youtube stuff or reads these blogs) was amazed at how fun a watch it was.
Yes, it’s long but it is humorous and very well presented. Hemant, you must be a fun teacher. My 11yo gifted son wants you to move to Oregon so he can have you as a teacher… NOW.
Just try it… I detest math and swore I’d watch only 5 minutes… 20 minutes later, I was shocked by how much time had passed. Give it a try.
Oh Hemant. You’re my hero. Thanks for the presentation. Now, about your problem with the clip from “The Office.” Have you ever seen Harold Jacobs’ book “Mathematics, the Human Equation”? It is, hands down, the best math curriculum I have seen for the ‘typical’ math student. (I love Art of Problem Solving for gifted math students.) The first chapter covers predictive reasoning, and uses a pool table concept for this sort of thing. So, the students use the multiple TV dimensions and multiple starting points to determine where and when the cube will reach a corner.
You are absolutely spot on about teacher ed programs. I’m an English teacher, and I only had one “methods” course, taught by a great professor who didn’t know the first thing about English. I find at my university there’s one professor who’s the “history” guy, who taught history and has good ideas about how to do it, and there’s a “math” person, who taught math and has good ideas about how to do it. But neither of them teach methods courses. They just teacher introductory “how to write lesson plans” courses.
That was an excellent presentation, Hemant – I really enjoyed watching it. I do agree that we are shortchanging future generations by the poor ways we generally teach math, and learning in general.
I’ve seen examples akin to that “lattice method” of multiplication you gave an example of, and it somewhat horrified me (I was asked by a parent friend of mine to teach her what her kids were asking questions about – because the math didn’t make sense to her. I looked at it for a bit – lots of circles, triangles, and squares; ultimately they were being used as stand-in symbols for algebraic notation – instead of x, y, z, etc!). Not only should we engage kids in the learning process, and in critical thinking, but we also need to instill in them the idea that if they want to go further in life, that having this kind of understanding is critical.
I recently (ok, a few weeks back) went through a section on probabilities and statistics for an online course at Stanford (AI class); it was by far the most difficult thing I have ever done, mainly because I hadn’t touched this kind of math ever (or if I did, it was well over 20 years ago). But, because I did have a background in critical thinking, and a good background in math, I was able to muddle my way through it, until it clicked; I won’t say I got a perfect score on that week’s exam – but I did much better than I thought I would by far.
Why was (I ended up having to drop the course due to reasons I won’t go into – suffice to say, it wasn’t my lack of understanding the material that precipitated the choice) I taking such a course? What possible purpose could knowledge of artificial intelligence apply in my life? Well, I am building a robot; an unmanned ground vehicle (UGV) to be exact. It’s my hobby. I intend to have this machine self-navigate intelligently. Without an understanding of these principles, I would likely only get so far with my system. Now, granted I’m not taking that course any longer (but I am continuing with another online course, the Machine Learning class, taught by Andrew Ng at Stanford) – but ultimately this knowledge will have an impact on my life; I can say later I have a knowledge of these problems, and how to solve them, and believe me, potential employers will look at this (because it will be on my resume), and perhaps ask me about it. I can tell them about my project – and how that extra-curricular learning and knowledge is something I can bring to the table, and apply to solve problems they may have. It may help me land a better paying job, or lead to other changes in life.
These are the kinds of opportunities for growth that we end up denying our kids, ourselves, and our society by not arming them with a knowledge of critical thinking, and a love of learning “for learning’s sake”. If this doesn’t change in this country, it will be a long downhill slide for us – and what is at the “bottom” won’t be pretty.
Thank you again for the wonderful video; I wish I could’ve been there in person. I hope it leads to change for students, teachers, and parents alike.
Oh, and any chance of a list of your favorite math blogs? I’d love to peruse them.
Wow, that was awesome. Very cool. When will Skepticon come to Toronto?
The only reason I liked math class was because memorizing formulas and plugging equations into a calculator was simple and gave me easy gratification. Every other subject was endless studying…
Fix the standardized tests, don’t abandon them. All the industries where there are no objective benchmarks are basically stagnant. Meaningful benchmarks are necessary for any kind of scientific approach to improving education. There is a tradeoff between cultural neutrality of the test and making interesting/relevant word problems. If you think you can write better tests, go work for the companies that make them. Also your example with the odd one out is basically testing G, not anything that can be taught.
The problem is that standardized tests are not meaningful in that they don’t really measure the things they need to measure. If it were only that the questions were stupid, it wouldn’t be as big a deal.
The problem I had with math growing up (aside from discalculia) is that I was taught rigid math. Numbers must be numbers and you must add 7 to 17! I literally couldn’t wrap my brain around 7+17, but I could wrap my brain around 5+15+4! If I tried to add 5+15+4, I would get MARKED WRONG because “no, it’s 7+17!” It’s like those formulas you mentioned in the start of the video. If I were doing those, I would do it the way you mentioned – subtract the volume of the small cone from that of the big cone, use the Pythagorean Theorem – and get them wrong because I didn’t use the proper formulas.
It’s incredibly important that students be taught that math is fluid. 7 isn’t just 7, it’s also 2+5, 3+4, and 1+6 among many other possibilities to make it easier. The only way I could pass math was by cheating the system and using my self-created methods to get past the numbers – and then making the formula look the way the teachers actually wanted them to look.
Hopefully some audience members learned something new… that truncated cone thingy is not a frustrum, it’s a frustum!
We had a great time watching the video, Hemant… as I said, my math gifted 11 yo son (who is doing 9th grade math this year) wants you to move here to be his math teacher in high school… and he LOVES his current math teacher! Several times, my hubby paused the video before you made a point about an example… he paused it right off the bat at the frustum one and asked our son how to find the volume and the Kid then explained it how you did when we started it back up… LOL! And the sample question with the colored squares and the “green” one and did the exact same process of elimination you did, ending with (A) being the odd one because it’s NOT odd and I just sighed. All math geeks are so alike. He even said the different colored one was green, like you, when I saw it as yellow. LOL!
It was an excellent video and one I will remember for a very long time. We have often had discussions about education in this house, with the Kid going to a charter school at a church no less, and each point you made were all the same points we’ve come up with, especially learning the math itself, not taking shortcuts, and we sometimes re-teach the Kid a math concept after he learned a rote or memorization way at school.
And… that Office clip is one of our most favorite clips from the entire show so great job!
Thanks for sharing that! It means a lot
Thanks for this. I’m a faithful (ha!) reader of your blog, and I’ve always wondered what was up with your alter ego, Mild Mannered Math Teacher.
I think all your suggestions were on the mark, but in addition, I’ve always felt that we’re leaving too many of our kids defenseless against the corporate powers that be. I know this is more content than method, but as with your opening about how the lottery is a tax on you know who, I think we need at least one mandatory semester at the high school level to teach everyone, especially those who won’t be pursuing any more math than they absolutely have to, all about mortgages, credit card debt, insurance, gambling, investing, compound interest, and all the other areas where the corporate interest count on consumers ignorance for profit. At least that will answer the question “when will I ever use this?”
I certainly agree that math is good for your brain “just because”, but I would argue that there is a lot in the math curriculum that we really could stand to let go of. But that’s an argument for another day.
Thanks again for the great blog, and for all you do in the classroom.
Hemant, my kids go to the other school district in town and I have always had an issue with how they teach math. I remember learning math and it being fairly simple and straightforward. I also had good teachers starting in junior high that would teach us alternative ways of solving problems, but only after we had grasped the basics.
Nowadays, it seems they teach what I call the shotgun method. They blast the kids with 2-3-4 or more ways of solving problems hoping that one of them will stick. In my opinion, this actually dilutes the lesson and makes it far more confusing for them. Both my kids have been in tears over homework in 4th & 5th grade because they need to solve things using a prescribed method and it may be one they just can’t wrap their brain around. Also, they way they are taught does not really lend itself to mental math all that well. Granted, I’m always second guessing myself when it comes to times tables, but I’ve been able to generate my own shortcuts and arrive at right answers because I was taught more than formulas and methods.
The other big issue is that they teach methods that we as adults never learned which makes helping them with homework damned near impossible. That lattice method you showed in the beginning? Makes my brain hurt trying to work it out. It also takes a lot longer than my way (in my opinion). There have been several times where I had to email their teachers to let them know that I was no help whatsoever with homework because I couldn’t figure out how they used these tools to arrive at the answers. Hell, they even teach a different way to do long division (which seems woefully inefficient to me).
They have also changed their math curriculum 2-3 times in the past 5 years or so. In the long run I fear that my kids aren’t getting the mathematical foundation that they need through the schools, even though the schools are very highly ranked.