Math teacher Denis Sheeran talks about what math should (and shouldn’t) be. Make math meaningful and real with these tips and ideas.
How We Should be Teaching Math in Classrooms Today
Link to show: www.coolcatteacher.com/e303
Date: May 2, 2018
Vicki: Today we’re talking with Denis Sheeran @MathDenisNJ. He is the Director of Student Achievement at Weehawken Township in New Jersey. He has two books — one book is Instant Relevance, Using Today’s Experiences to Teach Tomorrow’s Lessons and a book that came out in March called Hacking Mathematics: 10 Problems That Need Solving.
Denis, today we’re going to think about how we should be teaching math in our classrooms.
How should we be teaching math?
Denis: That’s a BIG question that I love talking about.
How should we be teaching math? Look first at how we shouldn’t.
A lot of it comes from how we shouldn’t be teaching math again.
That’s the interesting part. Our students right now have the opportunity to learn virtually every aspect of mathematics — on their own, sitting behind the computer screen, going to YouTube, going to Khan Academy, going to other resources, going to online courses from Ivy League schools. They can learn from great people.
So teaching math can’t be content delivery anymore. It can’t be, “I’m the math teacher. I know everything. You don’t know anything. You have no way to find it without me, so I’m going to tell you. You’re going to remember it. Maybe one of you will become the math teacher who tells somebody else.”
That’s where the change really needs to happen.
Vicki: So Denis, you talked about what we shouldn’t do because we can get all this content.
What should we do?
Denis: Well, there are a lot of different approaches, and what great teachers are doing out there right now is thinking about what their students really need, where they are, and how they can progress them farther along in their mathematical learning.
And that’s a really big question because for some teachers they start to think, “How am I supposed to do that for a hundred high school kids if they are all in different places? Or for twenty second graders if they are coming at me with such different skill sets?
But the real future that we need to see in teaching math is starting to create a deep appreciation for the mathematics around us and that we can actually learn by investigating that math, and not do what is the opposite of that that we have seen for so long, which is teachers trying to teach abstract mathematical concepts followed by the hope that they might be able to use them one day.
Create a deep appreciation for the math around us. Investigate that math.
I remember teaching the Pythagorean Theorem and telling kids, “You know, well maybe one day you will be building something and you need to be able to find out how to make a right triangle, so you are going to grab some pieces of wood that are three and four and five feet long and you will have your right angle.”
And what kind of ridiculousness is that? So the reality is we need to be able to teach team – and show them – that the math truly exists all around them, and then give them the skills for investigating it, learning it, conceptualizing it, and practicing it.
Vicki: Denis, give us a creative example of what this looks like in the classroom.
What does this look like in the classroom?
Denis: So one of the things we might do in the class is think in geometry, our students are learning about volume and learning about surface area. And that is one of those standard things that eventually you end up having a formula sheet for, some reference guides to.
What has happened in the past is you show someone a shape, talk about its attributes, talk about the formula for finding all the components of it from area and volume and then we would test them on if they recognize that shape, and if they could remember the formula and do the math.
But the reality of it is we were just asking our kids to do arithmetic. They were not learning about volume or surface area, they were just considering how to do multiplication. Or maybe division. And so, that is the difficult thing to come to grips with is most of the math we thought we were teaching really comes straight down to teaching our kids arithmetic.
So we can approach it differently. We can give our students a situation where they are looking at an object that is nontraditional in shape. One of the things that I discuss — being very close to New York City here in New Jersey — is you can look at the New World Trade Center building and I dare you to try to define it.
It looks like a cone — a pyramid — that was chopped off at the top but halfway up you see it is being sliced off in a different direction and it is not definable. But it is modelable. And it is an opportunity for our students to look at it, and think about it, and then consider what would we need to do to model this if I was to make a scale version?
What would I need to measure? How would those measurements be important? How is the area, how is the volume important? How much of a substance would I need in order to be able to make this?
And as they investigate that, sure, there is arithmetic happening, but the concept of volume and how it relates to the shape and the features of that object are starting to become more conceptually concrete.
They are actually being able to turn the concept of volume into something that matters and something that is applicable. And whether those students ever go on to become engineers or not, when they see something, they recognize that there’s mathematics involved in it. And that is huge.
Because somewhere between three and four percent of our students go on to high-level math and engineering careers, which means ninety-six percent of the kids we teach truly need to appreciate, understand, and recognize the math more than they need to be able to do it at a high level.
Teaching math is about thought, investigation, conversation and discourse
Vicki: So Denis, you are about hands-on.
Denis: Absolutely. Even if that hands-on doesn’t involve a manipulative or a piece but it involves thought and investigation and conversation and discourse.
Vicki: Fascinating. Now is this a shift for most math teachers? Is this how they were taught to teach math in college, or how do we move this direction?
Denis: That’s going to depend on which college you went to. Some progressive universities and colleges are definitely engaging K-12 educators in college pre-service teaching programs — which I think is where the shift truly needs to happen.
If I think about my later years in education, I think I would like to be in a program like that at a university where I am working with teachers. Pre-service teachers.
But there are teachers who have been in the classroom for forty years. There are teachers who have said “I am fed up with doing it the same way” and they are going deep into understanding conceptually how to teach children in a new way. And there are brand-new teachers who come out like hardened, seasoned, forty-year teachers who are saying to me “I do not want to do it differently, I learned it it this way and it is fine enough for me.”
So there is no stereotype to it — other than that teacher who is willing and aware and interested in true mathematical growth of their students, and who understands they live in a very different world than the one in which they grew up will make the shift.
You need to harness their power as a school administrator and leader and not necessarily put them up on a pedestal for what they’re doing, but help others become motivated the same way they did. Tap into what helped them make the change, and learn what helps people change who are in similar situations.
Vicki: We all have to be willing to learn – we’re asking our students to learn! If we get stuck and fixed and not willing to grow, then we’re just sending the wrong message… and we want kids to really understand math, don’t we?
We all have to be willing to learn a better way to do this
Denis: Absolutely. We want them to understand it, we want to see that they can understand it and the idea of productive struggle in a math classroom is that idea that our students are really grappling with an idea and might be getting stuck with it: not to the point of frustration, but to the point of “I need something — I need to learn something more — I need a new tool to solve this.” And we can provide them with that new learning or that new tool.
We can help change what it is they don’t know into something that they can know. And that’s a shift away from giving students steps to follow and procedures to follow which we used to teach in something they couldn’t do and turn it into something they can now do.
Right now I am trying to teach them, what is it you don’t know, and how can you find what it is you do know so you can apply this to any situation.
Vicki: And this term “productive struggle” is an important one, because sometimes we teachers jump in a little too fast and don’t let kids struggle, do we?
Productive struggle is an important
Denis: We feel like it’s a MASH unit where you have to go triage kids one kid at a time. This kid has a mathematical cut? Give them a band-aid. This kid’s got a wound to the neck? We’d better pull this kid over here to help him a lot. He needs a lot of help!
The struggle is less that than it is identifying what I call a “riverbed moment” which is that opportunity where the current is slowing down a little bit for the kid, but really we just need to help them direct around the corner and pick back up. It is not a time for us to jump in and cut off the conceptual pathway.
Vicki: We could explore so much of this, but the book is Hacking Mathematics: 10 Problems That Need Solving. And Dennis, you’ve really challenged us in math!
We have to make every subject real and authentic and relatable to our students’ real world that they live in. If kids feel like it is not relevant, they just kind of wonder, “What’s the point?”
As a teacher, I would wonder “What’s the point?” if I don’t feel like it’s relevant as well. So we need to hack mathematics and pretty much every subject don’t we? (laughs)
We have to make every subject real, authentic and relatable
Denis: I agree, and that’s why I approached this book not as a tips and tricks for teaching specific content. You are not going to come in here and find a better way to factor quadratics. You are not going to come in here and find a better way to add fractions. Although I have one of those.
The idea is much broader than that. It’s to approach teaching and how we approach teaching and how we approach homework and practicing and how we approach joining other math teachers in a global community.
It’s about when it comes to finding those golden opportunities so that teachers everywhere can think about this from a pedagogical viewpoint, not looking for tips and tricks and hacks that are going to be a simple fix to a specific problem, but definitely thinking more about how they are approaching their students and their career.
Are they going in day by day and doing what they always did because it works? Or are they looking at those students trying to find the best opportunity for them, to be their coach, their guide, their instructor, to be mentor and to be what a math teacher needs to be to students who are probably very eager to learn but also very likely to be turned off by many of the ways that we currently teach.
Vicki: And with that, we really have a challenge to level up our math. Thank you, Denis.
Denis: Thanks for having me, Vicki. I really appreciate it.
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Transcribed by Kymberli Mulford [email protected]
Bio as submitted
Denis Sheeran is the author of Instant Relevance, Using Today’s Experiences to Teach Tomorrow’s Lessons and Hacking Mathematics: 10 Problems That Need Solving
He is an engaging, fun, highly requested nationwide speaker, and as Senior Consultant at the Rutgers Center for Effective School Practices, Denis delivers workshops and professional development for school districts across the nation.
Denis has a Masters Degree in Educational Leadership and a Bachelor’s Degree in Mathematics Education with a minor in Music. Before becoming the Director of Student Achievement for the Weehawken Township School District in Weehawken, NJ, Denis taught high school math, from Algebra to Advanced Placement, for thirteen years at Lake Forest High School in Lake Forest, Illinois and supervised the mathematics programs in Sparta, Edison, and Chatham NJ.
Denis lives in NJ with his wife, four children, and his litter box trained dog, Scout.
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