Thursday, March 26, 2015

A Silver Bullet for Math Teaching?

This school year, I had the opportunity to step away from the classroom and move into a district level teacher leadership position. I teach one class in the morning, and then I visit K-12 math teachers around the district for the rest of the day. Or I attend meetings and provide input about the needs and desires of the math department. Or I plan professional development sessions for the middle school and high school math teachers. And I'm supposed to do some teacher coaching too.

It sounds kind of great, doesn't it?

I do not like it. There are a lot of reasons why but I'm not writing about that right now. Maybe another time. What I do want to reflect on now is the challenges of how to respond when teachers ask me questions about teaching. 

A few days ago, I was at a school and stopped in to see a teacher I had visited before. We have a pretty good rapport and she said hello when I walked in. Mind, I hadn't been to the school since November. I saw that all of her students were on computers working on various math tutorials. I've been in the room for about 30 seconds and then this conversation takes place:

Teacher: So, do you have any advice?

Me: About what?

Teacher: About what we can do to teach math better?

Me: Um...

At this point, I think I mumbled something about not knowing what they were doing or how the year was going or that I couldn't possibly give any feedback since I had only just stepped foot in the classroom. The weird thing is, she asked me the same question during lunch, "Do you have any suggestions for what we can do to teach better?" Again, I had to mumble something and try to avoid the conversation. What could I possibly say?

It's taken a few days of unpacking and reflecting, but I think I know why the question has stuck with me. I should also put out there that I think the question was an earnest attempt to engage me in a conversation about pedagogy but nonetheless, two things about it has bothered me a bit. First, I think the question betrayed her belief about her own teaching. She believes that her mathematics pedagogy is not good and is in need of repair. Perhaps she was being self-deprecating; perhaps she was telling me what she thought I wanted to hear; perhaps she was trying to learn something. It is entirely possible that she was really asking for help to improve her practice but didn't really know how to ask. I'd be happy to do some coaching with her, if that's what she really wanted but I suspect that is not what she wanted.

The second thing about the question is more important to me. It felt to me like the teacher expected some kind of silver bullet. She was hoping for a quick fix. She expected me to have some new technique that she had never heard before that would turn her instruction on its head, be easy to implement, and raise standardized test scores in weeks. I have no such tricks. I doubt those tricks exist. My suggestions for how to improve your math teaching isn't popular or easy. Here goes:

1) Make sure you know the math - Seems obvious, right? It's not. Read the textbook. The student edition AND the teacher edition. Work the problems. Work all of the problems. Don't skim the notes to the teacher. Most modern textbooks for elementary teachers (and middle and high school too) have pretty substantial notes to the teacher that alert the teacher to student misconceptions and tips for teaching. The best books also explain why a particular topic is important and how that topic fits into the overall curriculum plan. It's also worthwhile to plan with your colleagues and collaborate on the problems and explore the mathematics. Learn different approaches and algorithms and models. Be sure that you can attack a problem from multiple angles. Be able to respond to students' questions about "why" with something more than, "that's the rule". Make sure you know the math.*

2) Make connections with kids - Seems obvious, right? It isn't. I suspect that we all knew or had a teacher that seemed to hate kids. You know the ones: the teacher who snaps at kids when they have a question, the teacher who talks down to children who are just trying to learn, the teacher who blames a child for his inability to keep up with the rest of the class, the teacher who thinks that some kids just aren't capable of learning math. The list could go on and on. I have a lot of colleagues who spend their day talking at kids, a.k.a. lecturing, and them complain that kids don't pay attention and they haven't learned any math. I say, of course kids haven't learned. You need to engage kids where they are and nudge them towards understanding mathematical concepts. If you leave work bothered because your students have not complied with your requests, you need to ask yourself why the students didn't comply. Maybe they didn't understand the instructions. On the other hand, if you leave work every day wondering what you could do differently to help them learn more and better math, that's a sign that you're trying to improve. Keep at it. Talk to colleagues about it. But not the people who hate kids.  

3) Only scratch when you have an itch - Every single mathematical concept or algorithm was developed as the answer to a question. A lot of times, we teach a concept or procedure before kids consider why anyone would want to know that. Think about these different ways to start a unit on fractions: "Today we're going to start talking about fractions. This can get tricky so make sure you pay attention." versus "I was wondering, are there numbers between numbers?" Which one creates an itch? One of these openers will almost certainly deviate from the district sanctioned pacing guide but might result in deep and meaningful understanding of fractions. When we don't ask any questions, we essentially tell kids what to think. I sometimes like to call this, "opening everyone's presents for them". Even worse, we give students the false impression that mathematics has no human aspect, that the rules of mathematics are irrefutable because they have been gifted to us from the Creator, that mathematics is done by memorizing and acting with certainty and not by understanding and exploring. I'm not saying that we need to give kids a practical, real-world example of how mathematics is useful. Sometimes there are physical situations that lend themselves to mathematics. Sometimes we try too hard to manufacture a scenario where impose mathematics that no one would actually do. A question about an interesting phenomenon can trump a physical situation. Think about which one will create a better itch to scratch.

4) Be patient - This one seems especially obvious but it is probably the least apparent suggestion. You have to understand learning theories. You have to remember that kids learn at different paces and in different ways. Kids will learn math. But, it might not be on the timetable that the textbook or the school district give you. It will be stressful for you and for them. But you have to embrace the stress and not let it consume you. Most of all, you have to rid yourself of the noxious belief that some kids can do math and other kids cannot. I firmly believe that all kids can learn math. (Excepting children with severe developmental disabilities.) If a strategy you find appealing isn't working then you need to try another one. Use a different kind of representation. Get a concrete model. Draw a picture. Use base-10 blocks. Don't resort to giving the child an algorithm before he or she is ready for it. You're not helping when you prematurely move him to the finish. She needs to get there on her own with your support and guidance. He will never get there if you don't give him adequate time to play, experiment, and figure things out.

These are not glamorous suggestions, but I think they are true. More than my own belief about teaching, I think we can find pretty solid research for each of these suggestions. It's not an easy path to take, but it can work. There is no silver bullet for teaching math. Teaching math well entails knowing the subject and how to represent it in a variety of ways, connecting with students and their individual learning progressions, and asking questions instead of giving all the answers. It's hard work... and I love working at it. 

*By the way, it's still pretty much an open question about how much math you need to know to teach it well. There is a very robust area of research devoted to this very topic. Many scholars have worked for many years investigating a construct called "Mathematical Knowledge for Teaching". Still, we don't know exactly what comprises MKT. 


  1. We have had a number of teachers serve in a similar capacity during my tenure in the district. Each one has faced the same crossroads you describe. The difficulty in these positions seems to come from the interpretations of the position by other teachers, administrators, and your own expectations. I wonder if your four suggestions could be tailored to fit your situation? They are sound recommendations, and you might enjoy the position more.

  2. Number three reminds me of a great quote from Frank L. Lambert, Professor Emeritus at Occidental College, Los Angeles. Many years ago he said, "Why would I fill the board with answers to questions that have not been asked yet?". so, your teacher has asked "the question". One that will be answered in small doses for the rest of her career as long as she remains a student of mathematics and students. Your perspective is great, if you can help her break down her question into manageable sub-questions perhaps she can see the sign posts that you are giving her.