The Difference Between Calculation and Mathematics

This piece originally ran on Bluffcityed.com on July 29, 2014;

In mid-July last year, I was ready to try something completely different. I had previously taught Algebra I, but I was moving to a new content; geometry. I’d taught it before under the old Tennessee state standards but had left the course feeling like the kids never truly connected to the content. They were great at calculating and finding the right answer, but weren’t connecting to the math. Surely there was a better way to make the course meaningful! In that spirit I decided to do something radical; rewrite my entire curriculum to align to the Common Core state standards.

Lets be clear; the shift to Common core is hard. In some courses like geometry, it turns the entire structure of the way we’ve taught it on its head and requires both kids and teachers to make new connections. Common Core was also a struggle at first because these standards are much more rigorous than what we’ve been demanding from our children for years. They require, in the words of Jordan Ellenberg, prioritizing actual mathematics over calculation. Let me explain what I mean by this. For years we’ve been requiring math students to primarily calculate, that is, find a numerical solution, and do a small level of thinking. Common core flips this on its head and puts the emphasis on mathematical thinking by requiring students to explain their strategy, their work and their answer.

After a year of wresting with the Common Core state standards I have three takeaways that I think might be useful to teachers embarking on their own journey with common core for the first time:

Don’t Panic – there’s a learning curve because Common Core requires us to teach predominantly in ways and strategies that we aren’t use to utilizing on a daily basis; exploration and manipulation. For example, the first few times I tried using exploration based learning, I fell flat on my face simply because I hadn’t taught using that strategy before. It took a few tries before I figured out how to do it well, but once it’s become one of the more rewarding teaching techniques I employ!

Enjoy the freedom – the new geometry standards have given me freedom in what and how to teach. It eliminates some standards and expounds on others. Consider trigonometry. Under the common core state standards I’m to teach trigonometry in any contextual situation that I want, as long as students understand that they are ratios. Contrast this with the old standards, which required me to do so using only surface area and volume.

Dive deeply – the common core state standards reduced what I needed to teach, freeing me up to dive deeply into certain contents that I would have had to skim previously. For example,previously compasses and protractors were fun tools, but not all that essential to the way geometry was taught. Now they’ve become essential tools that allow us to explore concepts in a much more direct way, through our own tactile senses.

Like I said, last year was a huge learning experience, as it will be for most math teachers adjusting to the common core. Now that I’ve had a chance to grapple with the standards, I have a much better understanding that I can use to shift my focus for this year to three key things – concepts, application and proofs.

Concepts – I’ve figured out even more so where the deadwood is and can focus much more deeply on the most important Common Core concepts. I’ve cut out a few units

Applications – with fewer concepts I can start thinking through applications for each unit. For example, my first unit with lines and angles will be using the theme of mini-golf, with the culminating project being to create a mini-golf course where a hole in one is possible using segments and angles.

Proofs – I’ve completely retooled the way I have students display rational thinking through proofs. Old geometry required 2 column proofs. Common core doesn’t require this, so my goal this year is to have my kids focus on the paragraph proof as the method of displaying their thinking because this mirrors more what they will be required to do in real life.

Common core is new and it has a learning curve. But it’s the law of the land and if we can get past the initial struggle, I feel that we’ll find as a profession that the standards are much more liberating than we at first might have believed. It will be tough, but it doesn’t have to be a negative experience. Learn from my struggles and my mistakes and shorten your own learning curve and before you know it you’ll be doing Common Core in your classroom like a pro!