The struggle to understand why we teach K-12 mathematics in the order we do, and the content we do is real. I have wondered about this for a long time, and really have never found a good answer.

I threw out the idea of teaching y=mx+b as the only way to write lines (even though the district materials at the time said it was all we needed). I took a lot of heat for that decision from some people. I was told I was completely wrong; by teachers. I stuck to my guns because y=mx+b is a stupid way to teach lines. And in the end, I was told by other teachers that I influenced them to change too.

But really, K-12 mathematics education is nothing like this:

Think of Lockhart’s Lament. You read Paul’s words, and you are hit by the poetry he sees in math. It is also 25 pages long. I read somewhere that Lockhart’s Lament is the the most powerful and often cited mathematics education document that is never acted upon. What does that say about us, as educators, who cite it?

Lockhart is passionate about math education, and he feels that the current state (in 2002) of math education is in trouble. His words may be as apt today as it was then. On page 2 he writes,

In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

How much impact has Lockhart had on mathematics education? Often cited, rarely used or implemented. And yet, my Twitter feed and Facebook still have things like this pop up regularly.

What beautiful words representing fantastic ideals. Are you starting to see the cognitive dissonance I am feeling today? Too bad none of these ideals are found in our textbooks or our standards (and don’t get me wrong, I am not hating on the CCSS-M here). In fact, much of school mathematics is exactly how Seymour Papert described it here.

It *is* mindless, repetitive, and dissociated.

So as I was thinking of the question of “Why?”, I stumbled upon this article. Why We Learn Math Lessons That Date Back 500 Years? on NPR. To find out the answer is pretty much, “Because we always have,” is sad, disappointing and frustrating. We have taught it this way for the last 500 years, so we will continue to teach it this way for the foreseeable future.

I call B.S.

Seriously. We need to rethink how we teach math in a substantive manner.

We are part of a system that is not allowing learners to find the joy of mathematics, but the drudgery of mathematics and of learning. And this is not new. Not by any means. Edward Cubberly, Dean of the Stanford University School of Education around 1900) said,

Our schools are, in a sense, factories, in which the raw products (children) are to be shaped and fashioned into products to meet the various demands of life. The specifications for manufacturing come from the demands of twentieth-century civilization, and it is the business of the school to build its pupils according to the specifications laid down.

The fact that the specifications of education haven’t changed in hundreds of years is a problem (see the NPR article). It may even be THE problem. I am not so confident to claim that for sure, but it is definitely A problem.

At what point do we, as teacher leaders, rise up and demand this change. We see the damage. We see the issues. We must start demanding the curriculum be changed to meet the needs of our learners. I am not sure that the CCSS-M is that change. It seems like it is codifying the 500 year old problems that we are currently doing.

But it doesn’t not have to.

The Modeling Standard is gold. It is also 1 single page in the entire document.

I will just end this rant with that thought. Oh, and this thought. No more broccoli flavored ice cream.

I’m not sure I completely agree with this, or Lockhart for that matter. There are a lot of people who find joy and beauty in the curriculum, and there are lots of ways to encourage and celebrate that joyousness without throwing too much out. Will some people hate it? Sure. I didn’t like AP US History very much, though I liked my teacher. But I had friends who thrived there. And I’m okay with that.

Personally, I don’t think the ice cream metaphor is realistic. Math isn’t ice cream. Nothing is ice cream. No field or subject is as universally loved and delicious as ice cream, certainly nothing with any practical application. Math isn’t ice cream, it’s vegetables! So maybe “textbook math” is steamed broccoli and it’s up to us to add peas and roasted cauliflower and sweet potatoes (maybe even with some marshmallows on top) and even pickles, but the fact is some people don’t like ANY vegetables and some people like simple steamed broccoli the best and some people like ALL vegetables and, importantly, all of them are part of a well balanced diet. So our job is to be a math nutritionist.

I think I agree with a huge chunk of what you are saying here Glenn. Let’s assume that we two are in a majority that has been as yet disconnected and somehow out of power. What do we do with this passion? How do we, as public academics, affect the real and system-wide change to see our shared vision realized? I am not asking for any other reason than a very real desire to see that change occur.

Beautifully said, Glenn, and I couldn’t agree more. It was the one-two punch of Lockhart’s Lament and Dan Meyer’s Math Class Needs a Make-Over that started me down the MTBoS rabbit hole and the search for another way. If kids don’t walk out of math class with a positive, healthy feeling towards the subject then you might just as well throw all the content out the window, because very little to no learning will occur anyway. All we hear about is rigor, and coherence, and benchmarks. Where’s the fun? Where’s the joy? Where’s the excitement? I think you’re right that we see traces in the practice standards, but they’re heavily outweighed and often buried under the mass of content. Throw in the corrosive effects of high-stakes standardized testing and you have the situation you describe in your post.

Have you seen Justin Lanier’s Ignite talk The Space Around the Bar? My all-time favorite. When I get discouraged I watch it and it makes me feel better.

https://www.youtube.com/watch?v=6OHXJzfjZ9U

Christopher,

You pose an interesting challenge that I have been seeking answers to as well. How do we change the system from the inside? Not sure.

Thank you Joe. I appreciate Justin’s talk very much. Thank you for sharing it!