Every year, there are a number of students who have poor mathematical skills. I find it helpful to identify them as early as possible; if we wait until they have already struggled or failed a test, the damage will be much harder to undo. Better to start working on those skills immediately. And that means there has to be an assessment of how proficient they are at those skills. The trick is to find out who needs help without scaring them at this delicate moment at the start of the year.
“To be successful in this class”, I begin, “there are certain mathematical tools that you will need. We use the English language to talk about how things work, but we also use the language of algebra, which turns out to be a powerful tool for describing the world very succinctly. We also use graphs and something called vectors and lots of diagrams. (By the way, one of the benefits of taking this class is that I’m going to teach you how to draw diagrams and sketches to express yourself.)
“Then there are all kinds of things you need to know, like the metric system and scientific notation for describing really big and really small things. My guess is that, if you haven’t used scientific notation or the metric system in a while, you’ve probably gotten rusty. So we’re going to spend the rest of today and all day tomorrow working on a station lab that I’ve set up in the back of the room. You’ll be able to practice some of these skills and see if they come back to you.”
Like most science teachers in this school, I have a large room; the front half of the room has a chalkboard and teacher’s desk along with collection of individual student desks arranged around the rug. The back half of the room features a dozen lab tables large enough to seat four or five students. Around these tables are wildly colorful old wooden chairs, painted and repainted by students. The chairs and tables all show a good deal of wear, carved up by generations of students. To my eye, they are a great antidote to the orderly look of the rest of the school.
I ask the students to come to the back of the room, where I have set up ten stations in order to allow them to review material they have seen many times in prior science classes. If they have already learned those skills, a quick review will probably be sufficient for them to retrieve what they know. If they haven’t learned them yet, they won’t learn them in this quick exercise. One by one, I show them each station and what they are going to do there. The tasks include measuring things with metric rulers, solving equations for an unknown, using scientific notation, and so on.
“Some of you are really good at these skills, like manipulating equations in Algebra for instance, and probably some of you won’t remember all of them. Rather than waiting until you are struggling in this class, let’s find out right away who needs to practice the necessary skills and do something about it -- get everyone up to speed as quickly as possible.
“A couple of days ago, I told you about the merit badge approach to taking tests. Well, I want all of you to have an algebra merit badge, and one for graphing and one for the metric system. After you’ve spent some time warming up and seeing how much you remember of these basic skills, you’re going to take a test on them. This won’t be for a grade; it will simply make sure that you and I know which merit badges you already have. And if you don’t have one of them, we’ll know right away what you need to start practicing.
“Here’s an important point about this class: once we know who needs to practice, only they will practice; if someone is good at a certain skill, practicing it would be busywork. I don’t want you to do busywork. You may be curious as to how we’re going to have a class where some people are doing a certain piece of homework and others aren’t. Believe me, we’re going to be talking about it a lot over the next few days and weeks.
“I need to say one more thing to you before you get to work: learning takes courage. Today, for instance, you may be working with people you don’t know yet. As you go from station to station, you will probably find you remember some of these skills, but not others. If you do know how, make sure you show the people you are working with how you did it.
“If you’re not sure how to do it, I want you to find the courage to ask questions about it. That’s the hard part; it’s scary to admit you don’t understand something, but it’s also the most powerful tool you have if you want to learn. So be brave. Ask questions.”