Math and Communication
By Kay Toliver

Before I taught mathematics in grades 7 and 8 at East Harlem Tech, I taught all of the other elementary grades, starting with the first and gradually moving up through each grade, one at a time. It may have been this background which led me to want to use mathematics instruction to develop my students’ communication skills, because I saw that, for all students in all grades, communication skills were among the most important abilities that I could help them to develop.

Over the years I have learned that there are two sides to this coin. Not only can I use math class to develop children’s abilities to speak, read, write and listen, but by stressing these communication activities I am able to be a better mathematics teacher.

By encouraging students to speak up in class, to explain their reasoning, and to define the words that we are using, I learn a great deal about how well they understand the lesson. And from the math journals that they keep daily I learn how effective I am being as a teacher.

There are a few tips that I have picked up over the years from various sources which may also help others:

· Make it easy for students to speak up. I do not interrupt or criticize the statements a student makes, and I don’t allow other students to do so. I generally let them take as long as necessary to say what they want to say. If their answer is wrong, I will often ask the rest of the class if they agree or disagree, and will call upon a student who says she disagrees. If the answer is partly right, I will ask if anyone has anything to add.

I tell my students that I don’t mind them giving me a wrong answer, but I do mind when they don’t speak up with any answer at all.

· Use discussion to determine what knowledge your students bring to the subject of your lesson. As any teacher knows, students get restless if you try to teach them things they already know, and they get confused if you assume they know something that they don’t. The best thing to do is find out, and I’ve found that an excellent way to do that is by asking questions in the context of class discussion.

· Get them to explain their answers. A wrong answer is a valuable commodity, a clue that can lead to the discovery of what the student doesn’t understand. I try to always follow up on these clues. A right answer, on the other hand, doesn’t always mean that the student has got it down-you won’t know unless you find out how that answer was reached.

· If they understand it, they can write it down. I can’t necessarily get to every student in the course of a class discussion, but I can-and do-ask every student to write down his or her own explanation of a lesson point, or definition for a term. This can be done as part of the math journal, or independently. It’s true that it takes time for them to write it down, and for me to read what they’ve written, but the payoff is that I can spend my teaching minutes with each student in the way that will be most beneficial to that student, because I know exactly what that student needs.

· Notice what’s right, not just what’s wrong. In guiding a class discussion or responding to a writing assignment, I try to find the part of the answer that is right, and that’s the part I draw attention to. For example, if I ask, “what is a fraction,” and the response is “it’s a number with two parts to it,” I might say “That’s right-it does have two parts. What else can you tell me about a fraction?” Of course I’ve recognized that the student’s understanding is probably incomplete, and I will use that knowledge as I work with the student, but I see no point in beating him or her over the head with it.

When your students feel it is safe to talk, when they know that what they say will be listened to, when they see that what they have to communicate is considered to be valuable by the teacher, you will have opened windows into their minds.

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