I like this little writeup on Nine Dangerous Things You Were Taught In School from Forbes. It pithily gets into the consequences of having a system that’s so standardized that is responsible for educating–a fundamentally intimate and nonstandard task, if you do it right.

I find myself in a place of tension on this topic. I believe in public education, and I believe we’re better off with it than without it for sure. On the other hand, I’m aware of the follies of a creaking factory-age education system and its numerous failures, including it’s capacity for producing a kind of ignorance distinctive in those who have been systematically “educated.”

This comes down to some deep questions for me: is it possible to make space in the system of education for the real work of education? And if you do, how do you ensure that what needs to happen actually happens? And what actually is necessary?

Maybe this is a good time to mention that some people—like John Bennett, below—would go so far as to say that math, as it’s taught, isn’t particularly necessary. What do you think?

## Comments 5

I disagree with most of what he says. First, there is not a shred of evidence that math builds critical thinking skills – in fact, it has never been demonstrated that critical thinking skills in one area are transferable to another area (for example, being able to solve complicated algebra problems cannot be shown to improve the ability to apply critical thinking to a legal problem or to win a debate, both of which need critical thinking skills). What the average citizen does need, however, is math literacy. We are inundated by math and data every day in our personal and professional lives. We need to be able to estimate an answer, to extrapolate, etc. What has been shown with supporting data, is that students who take algebra have better quantitative literacy than those who don’t. I believe that this is what we need.

I just gave a lecture to my mathclub on this very topic of “why math.” I included Mr. Bennett’s reason, namely, that it is the best way to learn inductive/deductive reasoning, but I also added some reasons of my own. 1) inductive/deductive reasoning (as stated), but I would add that learning math gives you, as based on a Paul Graham essay, the ability to stay upwind. Do the hard studies, such as math, and everything else is easier, 2) the story – as human beings, we love a good story and that context is what makes subjects interesting. Just reading Shakespeare, without understanding the time period and the language is not interesting at all. Every form of math was created to solve a real problem that humans faced and still face. Give the kids the story (the context) and they will be more likely to connect with the material; 3) Literacy – there are all forms of literacy that go beyond literature including cultural as well as math/science literacy. Knowing the definition of mass and acceleration are just as important as knowing how to read. These facts are part of the world we live in and how it works. Math is a universal language and being literate in math is critical for our global economy.

Math should be something kids want to play around with and master, and I think an interesting story and showing the beauty of the topic will make math more relevant and compelling or, as you have so aptly stated “Math 4 Love”.

I agree with the story and the beauty being reasons — but of course those are almost entirely absent in most school curricula! I think this is the biggest point. When you teach math from a historical perspective, and tell the story of why it was invented, it’s a lot easier for students to appreciate.

And, I agree that we should scrap a lot of what we teach in favor of more data analysis and statistical reasoning. It shouldn’t be a march to calculus, and even to the extent that we do march to calculus, there’s no need for the calculus to be so symbol-manipulation-heavy.

To the extent that we want to teach reasoning, why not do it by means of logic puzzles and other fun things like that?

I’m not sure I agree with the optimism about teaching thinking skills that we saw in this TEDx talk or in Richard Rusczyk’s article at http://www.artofproblemsolving.com/Resources/Files/problemsolving.pdf … but I also don’t share the pessimism of Conrad Goldberg. I do believe people can be taught to be better problem-solvers.

_The Nature of Proof_ might be a good model to start heading towards. It was done in 1938, but the wheels of education reform turn slowly. You can get the full text at http://www.eric.ed.gov/PDFS/ED096174.pdf in a really ugly scan. It’s a book worth buying. I’ve written a bit about it: http://mathforum.org/kb/message.jspa?messageID=1360859 and http://www.amazon.com/review/REFYMPR8L8EH5 for example. It’s been about 10 years since I was telling every teacher I met about that book, so maybe it’s time to start again!

Unfortunately most teachers, parents and schools have that same type of mind set as Mr. Bennett. His presentation demonstrates a classic fixed mind set described in Carol Dweck’s studies at Stanford University and that is: either you get Math and you’re good at Math or you’re not.

Professor Dweck’s studies showed that this type of mind set is detrimental for the intellectual development of a child and a child that has been raised with the fixed mind set, will give up on trying anything they find challenging at school and in life, they don’t take risks, they do not persist until they get it right, they’re not analytical and never try to find out why s/he made a mistake. Mr. Bennett’s mind set is no doubt a fixed mind set. He thinks that you either you like Math and give it a try or you’re not. HE needs to change his mind set, and learn that anyone can get Math and be good a Math if they’re persistent. An interesting text to read is Lockhart’s “A Mathematician’s Lament” which negates the practicality of Math, he states that Math is an intellectual exercise, it’s Art, and it makes no sense trying to correlate to real life. I hope Mr. Bennett learns and start incorporating Carol Dweck’s findings and interventions on his own mind set and then passing it on to the children he’s teaching and their parents. Teacher has this much power to make the change.

I believe that it is a fixed mindset which still believes that mathematics above Algebra should continue to be taught as it is now – in California public schools, anyway. With a firm grounding in mathematical thinking and pre-algebra skills any student who wishes to go further in Math can do so at any time. I have been teaching middle school math for over 15 years and his talk is absolutely what we experience here. Students fail to learn year after year, and it’s a pretty remarkable young person who can keep a growth mindset after failing at the same tasks over and over. The new Common Core mathematical practices standards are a good place to focus when revising your math curriculum. If you have a math credential and want to help your community – teach Middle School!!! WE need folks who love and understand math to be willing to pass that along to our young teens.