The Way We Do Business

I’ve been thinking lately about math in high school.  This is not unusual, by any means, especially for someone in my position.  Nationally, we are struggling with math in high school; some schools, districts, and even states are getting it right, but most are struggling.

A word if caution: if you’re looking for solutions in this post, you will be disappointed.

One thing that frustrates me most about the work we (as a nation) have to do at the high school level is the lack of concern about instructional practices.  Most high school math teachers have a solid grounding in the mathematics that they teach.  This is often incorrectly equated to a solid understanding of how to teach that content.  Unfortunately, content knowledge does not imply pedagogical knowledge.  (I would pose the question: is the converse true?  My jury of one is still out on this, although I thought I knew the answer until about 30 seconds ago.)

So how do we change instruction?  I’m not even going to attempt to answer that today.  What I know for certain is that if we want the change to happen in the future, we have to start now.  That sounds pretty obvious, but here’s why:

  1. Current high school students who are thinking about becoming math teachers are learning how to teach even now.  They watch their teachers.  If all of that student’s teachers are teaching they way that they were taught, then that student is going to someday teach the same way.  The cycle continues because…
  2. Secondary teacher preparation programs at the university level do not do enough to promote a change in instructional practice.  Those that do are often ineffective in reforming students’ attitudes and beliefs about pedagogy that were learned in high school. The result is…
  3. More teachers, teaching the same way they were taught, and influencing the next generation of teachers.

You’re probably thinking that I’m the world’s biggest pessimist right now.  I really believe that we can change.  I also believe that we will not wholly change the way that high school math is taught in the future unless we start the change now.  In summary,

  • Systems matter – they need fixing sometimes.
  • Resources matter – they need to be of a high quality and aligned to appropriate benchmarks.
  • Instruction matters – it’s the critical third element that we too often overlook.

Changing the way we do business in high school means taking a close look at all three areas.  Until we do, we aren’t going to have the overall effect that our nation so desperately needs.

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Fluency for the Masses

I have a confession: I never really learned to type.  Granted, I can run off 50 or so words per minute, but I don’t “touch type.”  Sure, I know all about home keys and can type about half of my words without looking, but my errors go way up when I do this, and the whole process is slowed down.

This was very evident one morning last week.  I got up early to do some work at home, but I didn’t want to wake up the kids.  So…I tried typing without the lights on.  Two interesting things happened.  First, my work slowed down tremendously, because I kept having to go back and correct my errors.  And second, I found myself thinking less about what I was typing and more about how I was typing it.  I would not characterize my product that day as “high quality.”

This experience caused me to reflect on a discussion that I had had the previous day with a group of middle school teachers.  Our discussion turned toward what one teacher described as the “drill and kill” method of teaching math, and I couldn’t resist having them do an exercise.  In his book Elementary and Middle School Mathematics: Teaching Developmentally¹, the late John Van de Walle spends a few pages developing the ideas of drill and practice.  At the heart of the discussion is his belief that drill and practice are really two separate things with different outcomes – not one thing that we do to kids.

We had the teachers brainstorm about each (drill and practice) individually.  They drew some wonderful analogies to music, knitting, and other areas of interest.  They began to see and understand the benefits of both.  What this comes down to for me is fluency.  Drill is great for building fluency – when students already have an efficient strategy for doing the problems; otherwise it is frustrating.  Practice is necessary to help students develop efficient strategies for doing things.

You could argue that my strategy for typing (one that involves closely watching my hands most of the time) is not efficient.  However, after years of practice and drill, I would consider myself a fluent typist.  If I wanted to learn to touch type, sitting at a computer day after day would not fix the problem.  I need some targeted practice to help me become efficient with this strategy,  and then day after day of drill before I would be truly fluent.

Think about your students next time you want to give that 100 problem worksheet.  Is it building fluency, or building frustration?  Do we want them to focus on what they are doing, or on how they are doing it?

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¹Highly recommended reading.  The book discusses not only how to teach math, by why we should teach it that way.  IF the $100+ price tag is a bit much for you to swallow, check out the Teaching Student Centered Mathematics series by Van de Walle and LouAnn Lovin.  Mostly the same content as the $100 version, but broken into grade bands (K-3, 3-5, and 5-8; about $34 each) and without the pretty color pictures.

Communication in the Math Classroom

I’ve been thinking and talking about communication in math quite a bit lately.  For elementary teachers, it’s a common language that opens the door for further mathematical conversations.  For secondary teachers, it’s a critical component (a standard, in fact) that is too often given lip service.  As a result of all of this thinking and talking, I’ve come to a couple of conclusions.

  1. It’s about discourse.  I recently received my new issue of Mathematics Teacher from NCTM.  The focus of this issue is discourse: what it is, how to improve (or begin to use) discourse in the classroom, and some of the obstacles that discourage effective discourse.  Like inquiry, discourse ranges from being very teacher-directed to very open and student-centered.  It’s about student needs and scaffolding instruction to meet those needs.
  2. Model, model, model.  If we do not give students good models of talking and writing in math, then they’re not going to learn it.  They won’t get it at home, and they’re not likely to get it from other sources.  We can’t turn kids loose on a problem, ask them to talk or write about it, and expect effective communication if they don’t know what it looks like.  Pretty simple, but something that’s easy to forget.  Talking and writing about math is different than any other content; although the strategies are universal, the terms and the discussion are often different.  When you’ve done this, model some more.  It takes time for students to reach the formal level.
  3. Don’t expect perfection.  One of the biggest mistakes I made as a teacher was showing a group of students an example of a “good” paper that I had written.  They were so discouraged that none of them believed they could write about math the way I wanted them to.  In hindsight, they really needed to see the process of writing, not just the finished product.  The fact is, students are not going to write fluently about math until they’ve done it for a while.  In a recent post, Dan Meyer summarized this thinking:  “It got me writing regularly, an essential precursor to writing well.”  Don’t expect perfection to start with.  If we can get kids writing, the writing will improve.  It might take three or six months, or it might take two or three years.  Just get kids writing about math and keep them writing about math.

The bottom line is that it’s not enough to ask kids to write.  We have to support them as they begin to write; we have to model throughout the process; and we have to be patient as they develop the ability to write about math the way we want them to write about math.