Open Set

The amount of jargon that you hear every day in public school education now is matched only by the number of acronyms they throw around. The jargon I want to attack today is the phrase, “rigorous, grade-level content.” It comes up all over the place. 

The theory is, as far as I can tell, many teachers in the past did not teach rigorous math, instead they watered down the curriculum so that they could teach less, and kids would score higher. I don’t know, I wasn’t there. All I can say is that this is not what happened in my K-12 schooling. But one data point is hardly worth looking at. 

So teachers are being constantly asked to teach rigorous, grade-level content. The whole idea of “standards” is that they are explicit about what rigorous grade-level content consists of on a granular level. When you have standards clearly laid out, then teachers are required to teach exactly that. (At least, that’s how I hear it being used nowadays. Back in the late 90’s when I started teaching, “standards-based-math” seemed to be connected to NCTM’s Standards for Mathematical Practice, which are suspiciously close to CCSSM’s Math Practice Standards. It was considered “wishy-washy” by most people I knew. None of this really seems to be what people are thinking of today, at least, not that I can gather.)

The trouble, in my mind, is that “rigorous” and “grade-level” can be at odds with each other. 

Grade level content for Algebra I, for example, involves solving a one-variable equation using the distributive property and with variables on both sides, maybe with a fraction or decimal among the coefficients. The trouble is, if you have a student who does not yet know that x + x = 2x, but that 2x and x+2 have different meanings, then teaching that student how to solve that equation is going to be quite a feat. But that’s what the teacher is being asked to do. In that case, how could you possibly help students build their intuition and problem-solving skills? Teachers would have no choice other than to rely on rules, drill the patterns. And since they get up to solving such a complex equation, we say that they are teaching rigorous grade-level content. 

I see rigor differently. I think that rigorous math requires thinking. There is no standard for what the content needs to be, it’s whatever they are ready to figure out with the tools that they have. If I have a student who does not know how to combine like terms in the simplest of situations, then they could do some very rigorous work as they learn that. Doing rigorous math means solving a problem that leaves you smarter and more knowledgeable when you are done with it. 

I am very averse to dumbing down the curriculum. If you ask most of my students, they will tell you I’m the hardest math teacher they’ve had. And yet, I frequently find myself teaching below grade-level material. I keep the rigor high by pushing students to try the next-harder problem, to use what they know to figure out something new. I leave room for the thinking. But you can’t do that if the problem is completely out of their grasp. Once you are asking a student to solve a problem that they cannot possibly figure out, your only hope is to give them all the steps clearly. At that point, no matter how complex the problem is, I would say that you’ve taken away the rigor. 

So my teaching is rigorous. And unfortunately, I frequently have to go into the realm of “not on grade-level” in order to develop that rigor.