“So what you’re saying is that the statement at the top of this paper is for me to prove using these equations?”
I nod.
“OK, but I don’t get what f and g actually do. That’s making like no sense.”
[scribbles a bunch of notes on a board and, over the course of five minutes, gets to why mathematicians decided to write “f of g” with a dot but not explain how it actually works]“OK, that was really good.”
“Was it?”
After all these years of taking time after school to show my former students – now high schoolers – what their teacher meant, I turned to the work I need to do from 8am – 2:20pm: my current students. I’ve had hundreds of students come back either in person or through video chats to concretize the math they’re learning outside of my schools. Each session, I’m taking a few minutes of free time and then imploring them to talk privately with their current math teachers. Some come out with more confidence in advocating for themselves. Others say their teacher won’t slow down for them. Others still say their teacher is not me.
In all cases, I’m thanking them, but they really should run along and mend those relationships with the adults.
What people fail to understand is that math attitudes are often a reflection of the school culture. We’ve done a serious disservice to this thing we call math teaching. We’re confusing fake theatrics for actual intellectual sparks. For instance, we keep saying rigor, but we just like hearing that students must struggle and suffer while learning something difficult. It’s not to say that struggling and working through a problem doesn’t have its benefits. It is to say that difficulty isn’t the core of math; comprehension and comprehensiveness is.
The difference is that we’re stuck in making students catch up and zip by them, thereby pruning those who are “with it” and those who aren’t.
Secondly, it’s that we’re still stuck in arguments about results. Because math is numbers and results are numbers, then math is results and results are the only determinant for math proficiency. As Jesse Hagopian recently said, “High expectations for some means high test results and that’s not what we need.” There’s a huge difference between making math a core principle of the work you’re doing for schooling and quite another to use dehumanizing methods to assure that the testing numbers come out in the school’s favor.
This isn’t just a charter schools argument; this is an argument against any and all schools that dehumanize students to keep their doors open, their coffers filled, their names unsullied in the eyes of superintendents and newspapers alike.
Third, math shouldn’t be about the individual teacher who sparks their interest or makes them feel powerful in the math they’re learning. It’s unreasonable and inequitable. The easy thing to say is to force every teacher to visit [insert favorite math teacher here], but too much of what we consider “good” is steeped in personal privileges, biases, and agendas, implicit or otherwise. The teachers who get labeled a “favorite” by students, parents, and administrators feel like few and far between. Simultaneously, we’re so rife with results and myopia that we never investigate what makes the math teacher “good” or “bad” so we can either bring those practices to scale or discard the practices altogether.
Speaking of which, deficit thinking still reigns. We’re still caught up in saying “these students don’t know how to [insert all four operations and fractions].” That’s great, but two things. If students already knew everything when they walked in, we wouldn’t have jobs. Also, the conversation is never about what they do know. None of our kids come with nothing into the classroom. Aside from their full humanities, stories, families, and genetics, they come with knowledges we should try to tap into whenever we get the opportunity. How do math teachers – or any teacher – expect students to open themselves to new horizons when we’ve already shut down the curiosity they brought with them?
I fear that, in NYC, we assign the title of genius to people who’ve achieved heightened test scores regardless of how unimaginative and uninspiring their rendition of math is. We have opportunities to see and do math better. We refuse to reorient our understanding of math to meet the students’ needs. We prefer to keep teaching math in a way that keeps the winners winning.
Math is already everybody’s. When our city – and our country – starts to match that belief with that word, we’ll be on the path towards getting it.
Yo te gusto, as l-i-k-e is insuffiient, and spoiled by f-a-c-ebook
I’ve rarely read such a good description of the common problem we in the US have with math teaching. As a math teacher with more than 50 years experience, with many testimonials to “miracles” of success with math averse students, I wish to advise that the problem we teachers have isn’t with math or math attitudes, it is with teaching and teaching attitudes.
You are 100% correct that we need to value what the student comes into class with (and not focus on what he doesn’t have.) But it needs to be said what that something is that will become the foundation for “our” success with teaching math (or anything else) to that student. It is common sense and the student’s personal experience.
We need to appeal to the student’s common sense and experience when we present ideas. This is why, for the most part, abstract rigor of professional mathematicians has no place in early math teaching (like high school.) Rigor lacks connection with common sense and the limited experience of youth. To push it is to push a belief that math should be a game of some kind. Each act we perform as a teacher is a message within a message–there are our words, then there is the belief within us our of which our words are crafted. I call this duality “the message” and “the undermessage.” For example, if we say, “Oh, come on, what do you think you’re doing?” The message is pretty confusing (it’s not “what are you doing,” but “what to you THINK you’re doing.”) The “message” is a question. But the “undermessage” is a statement and a belittling one at that. As teachers, we should become aware that the undermessage is a much more powerful influence upon our students than our message.
Our “undermessage” needs to attest to how deeply we believe that math is built into everybody’s brain. Our “undermessage” needs to affirm that the student’s common sense and experience are all he needs to master whatever math challenge he (inclusive he/she) may be facing.
Lastly, when the student has his “aha” moment (the testimony we teachers look for to know when the student really “gets it”) we need to help him understand that what he has just “seen” is not something we told him. Rather it came from inside him, created out of his experience and common sense.
This last part is key to working miracles in teaching (math, especially.) We turn the student back upon himself. In so doing, we teach him how capable he really is. We quash that very common student belief that he is inadequate. In short, we prepare him for life’s many challenges to come. We take teacher pride knowing that we helped birth a mature adult. And yet we remain humble, knowing that the student did the real work and we were but a coach.
Thank you dear author, whoever you are, for your great summary of the problem and for the opportunity to elaborate out of my teaching experience. May we make a difference among serious teachers.
I think many subjects are dehumanized in schools due to tests, scores, and numbers. Schools often turn our students into statistics on a page and it is important that we teachers take the time to recognize their curiosities and humanities. As someone who struggled in school and often thought of myself as lesser than my classmates because I didn’t understand subjects as well as they did, I want to become a teacher who will avoid teaching in a way that only rewards the winners. Education should be rewarding for everyone.