Math Wars: What if you're both right?

There is a lot of arguing these days about math and what it should look like in our classroom. I love that people have dubbed it the "math wars". It makes it sound so dramatic.  It is, I suppose, in a way. We are talking about the math education of the next generation. And how they feel about math will have a direct influence on the math education of the generation that follows after  them. Because let's be honest. How we as math educators feel about math has been directly influenced by our experiences as math students.

There are two sides to this debate, as I see them. Side one : Math should focus on the tried and true basic skills needed for addition, subtraction, multiplication and division. Students should practice these skills until they are second nature.  Multiplication tables should be memorized.  A solid foundation will provide the basis for any more complicated problem that wil arise. Side two: Math should be discovery based.  Students should be engaged in problem solving activities that allow them to discover math concepts on their own. They should be encouraged to try new methods, and to them share them with the class. It's the process that is important. 

Here is what I think: they are both right.  Or, really, they are both wrong. I don't think it should be one or the other. It should be both.  It should be MORE than both. It should be computation, problem solving, discovery, math journals, quizzes, tests, projects, investigations, gallery walks, bansho lessons, class notes, practice problems, three part lessons, guided math, independent practice, congress, workshops and mini-lessons. Too often we get caught up in one side or the other. What is important though, is that what we are doing engages our students and guides them to a deep, and authentic understanding of the concepts we are teaching them. They should be able to add and subtract, but also be able to tackle an unknown problem with confidence. They need to be able to explain what they did and why they did it. No textbook can teach that.  That is why we need so much more than just one approach in our classrooms. That is why we need to know our kids and teach them as they are.  

Math war generals, I say to you: We should all agree with one thing. Our students and their attitude and conceptual understanding of mathematics is what is important. How we get there looks different depending on the day, hour and minute.  Our discovery based activities need a solid foundation. Let's put down our weapons of math instruction and teach. And when I say teach, I mean learn together in community.

"No, we don't have fun here. This is school. It's not supposed to be fun."

If I had 25 cents for every time a kid asked me if we were "doing anything fun today", I'd be able to buy a lot of pumpkin scones for myself. Kids ask this all the time, and especially on Fridays, when we are all thinking about the weekend. And when they ask that question, I give them the same answer: "No. We don't have any fun here. What are you talking about?" I do, however, usually have a smile on my face as I say this. The truth is, we do have fun in my classroom. I like to think (perhaps wrongly) that we have a lot of fun in my classroom. There is certainly a great deal of laughter and enjoyment of learning together. But I will tell you point blank, having fun is not the learning target of any lesson I have ever planned. You will not see "Students are having fun" as one of the success criteria listed for an activity we are doing. Why? Because I don't think being a teacher is about being fun.

I cringe a great deal when I hear people talk about planning activities or choosing games (especially in math class) so that the lesson will be fun. We are educators. We are not entertainers. Our goal is not to entertain our students; it is to educate them. This is why we must learn to differentiate between engaging our students and entertaining  our students. I am currently reading "I'd like to apologize to every teacher I ever had: My year as a rookie teacher at Northeast High" by Tony Danza. In his book,  Danza writes about his experiences teaching high school English in Philadelphia. It's an interesting read, and thought-provoking, even for someone who has been teaching for a long time. One of the most insightful components of his book is the record of the conversations he has with other colleagues in the teacher's lounge. As Danza struggles to prepare for writing an exam for his students, he has a conversation about engagement with a colleague. This colleague wisely advises: "The mistake that many new teachers make is to confuse engagement with passive entertainment." (pg 94) I would say that this is not a mistake that is restricted to new teachers. I think it is something we must battle against every day. We teach in a time where kids are saturated with entertainment. They want to be entertained or they tune out. And consequently there is pressure on teachers to try to meet this demand. We feel that if we aren't fun, if our students aren't having fun, they won't like us, and therefore, they won't learn anything. It's a hard road to go down, and it's even harder trying to drive the other direction.

Now, I am not saying that our goal to should be to just ignore our students and just teach the curriculum. No, I am not saying this at all. What I am saying is that our primary goal needs to be to get to know our students, who they are as people, what they like, what they are interested in, what they are passionate about and to use those things as we seek to provide learning experiences that draw them in--almost to the point where they have forgotten that they are learning, and are truly engaged and are 'in the moment' with us. This is not always easy. I mean, let's be honest here, it can be a challenge to engage students in learning how to divide fractions. But simply finding a game about dividing fractions is not any better than us standing at the front droning on and on about how to divide fractions. Students need to be involved in the learning. It must be active.

I don't have a magic answer for how we do this. But I do know that engagement, rather than entertainment must be our mindset. It can't be the goal we set out with each day. Want to know why? Because we, and our students, will only be disappointed. Everything isn't about 'fun'.  And what we think of as fun, isn't going to be fun for everyone. What pressure to put on ourselves! We have enough to worry about without worrying about making it all fun.

Teaching and learning is a two-way street. The responsibility doesn't lie solely with us, the educators. Students have a responsibility as well. That is what learning is about. I can't learn for someone else. What I can do is to provide learning opportunities and invite my students to join me. Sometimes we have fun. Sometimes we don't. And that is just fine with me. 

So many notebooks

Okay, so I have this thing about notebooks. I like them. A lot. For some reason I am in love with the idea of a bunch of paper bound together in such a way that I can transport it with me wherever I go without fear of losing the pages. This appeals to me as a person, but also as an intermediate teacher. At the beginning of the year, kids are pretty organized. And by pretty organized I mean that they have mostly empty binders. We begin the process of filling them up on the first day. Outlines, expectations, get to know you activities, rubrics, etc. We punch holes and dutifully insist on the 'snapping' sound of opening and closing binders. We walk around and make sure they are putting things in. We give them Table of Contents sheets. "Yes!", we think to ourselves. "This year, we will have organized students." We proudly write "Organized Notes = Organized Minds!" across the top of our white/black boards. This year, we vow, will be different.

And then October hits. And by this time, at least one kid in each class has a 'binder of doom.' You know what I mean. That binder that has every single piece of paper from every class every teacher has ever given him/her and it's just all shoved in there. Hole punched, you say? No matter. This binder has mostly empty rings.  This. makes. me. crazy.

I am in the process of re-thinking how I have my students organize their work. For me, the binders and duo tangs just aren't cutting it. So this year, I have decided that my students will have a series of notebooks. Yay notebooks!  My literacy program is already built upon a solid notebook foundation. A few years ago I read "Notebook Know How" and "Notebook Connections" by Aimee Buckner and it revolutionized my literacy program. (Go. Buy them. Read them. Now.) And I began to wonder, if it works in my literacy program, why can't it work in my mathematics program as well?

I have dabbled in the Interactive Notebook previously, but this year...we are going there, all in. In addition to a carefully constructed interactive notebook, I have decided that my students will also have a free-form scrapbook notebook in which to write their mathematical thoughts, ideas and questions. Sort of the mathematical equivalent to a writer's notebook. I think my kids need a place to write down their thoughts, to work out different possible solutions, to brainstorm problem-solving approaches. This will be new to them. It will be new to them. There will be growing pains. Oh yes... and there will be piles of notebooks to organize and transport and store. But all those pages will be bound in, let me tell you.

So, we will have notebooks. I have 2 other notebooks that I'd like them to have, but it might be overkill. Or it might not. "So many notebooks, part 2?"

Mathematical Word Crimes

By now, Weird Al's "Word Crimes" video has travelled, well, probably mostly around the Facebook and Twitter world. The first time I saw it, I thought it was catchy, but mostly ridiculous. I must confess, though, that it has grown on me and I find myself singing it to myself at random times. "Just now, you said, you literally couldn't get out of bed....".  Anyway, I am so with him on this topic. I am that person that points out spelling mistakes on signs, in newspapers, in books and so on and so forth. I am that person. It drives other people crazy.

Recently, I have begun thinking about 'word crimes' in other areas. Well, okay, in mathematical areas. Because there certainly are word crimes in math. But for some reason, people seem to gloss over them. It doesn't seem to irk people the same way, as say, when people use the wrong version of to, or you're or who just throw apostrophes around.

For example, timesing. I mean, is that even really a word? And yet I hear kids use it all the time.

"Well, you have to times 4 and 5 to 20."

"Times?"

"Yah, you know...the X".

"Oh, you mean multiply."

"Yah, I guess. Multiply."

How about cross multiply? Okay, so this in itself is not a word crime. There is a mathematical operation that is often referred to as cross-multiplication. The issue for me is that kids just use it without even knowing what they are really doing, or without even knowing how to actually do it. "So, to get the x, I just cross multiplied". And even there: "To get the x..." How about, "to solve for x?"

This might seem nit-picky, or even bordering on insanity, but the truth of the matter is that we don't put the same emphasis on written communication in mathematics as we do in other curriculum areas. And the truth of the matter is, it is just as important. Our students need to be able to write about their mathematics coherently. Just as we learn to write, we write to learn. The writing in our mathematics classrooms is no different.