If you really want to TEACH mathematics, you must
FORCE YOUR STUDENTS TO TALK!

Remember that humans have a strong need to communicate, especially in their early teenage years. Communicating helps all people to cope with the stresses of life, because it assures them that others have similar problems and experiences.

Teachers can USE this human need for communication to their benefit. Don't fight it. Design your learning environment to encourage talking, and then structure your lessons to FORCE communication about MATH. This will have a tremendous positive effect upon your students because you will be satiating their basic need for communication and at the same time you will be soothing their math anxiety through this communication.

When they are "forced" to talk, which is something they desperately need to do anyway, they will invariably share the stuff that they can't figure out with each other. Before you know it, you have kids, who can't sit and listen to YOU for more than 3 minutes, leading discussions and helping their peers.

Kids NEED to talk about their math because they speak the same language. They will be able to translate the teacher's formal math talk into the language of "kid" far more efficiently than the teacher. Sometimes they get so excited helping each other that you can't believe they are the same kids who ignore your ever so well planned lectures. You will see intelligence where you thought none existed if you can just get them talking about the math.

*As a note here we must emphasize, especially for any of you just starting out teaching, the teacher is SUPPOSED to talk mathematically correct. He or she may do some translating into the common vernacular as needed, but it is too dangerous to wander very far from correct definitions, theorems, and formal algorithms. Remember, in mathematics, words are never used as "fluff", if it's in the definition, then it's necessary. Like the definition of
prime number: a number is prime if it has exactly, two, distinct, whole number, factors, one and itself.

Now is the number ONE prime?
No, because it has only one, distinct, whole number factor, itself. So the word distinct is really needed here, it's not "fluff".

What about ZERO, is it prime?
No, because it has an infinite number of factors. Itself times any number is zero, so the word exactly is essential in this definition.

Okay, with all that said, your next question should be,"How do you get kids to talk about math?"

We have experimented with many scenarios and find that placing your room into groups of two to six people, with four being optimum, is the best way to start. When you want them to talk, they need to be facing each other. That way their attention is focused into the group and the noise level is much more easily contained. They wont need to yell across the room to get someone's attention if they are allowed to be talking in their groups.

Once your groups are established, more about that in "the gentle art of ice smashing", all you have to do is design some sort of GRADED activity that can be done in three to five minutes.

We do "homework quizzes". These are always done after the class has had an opportunity to ask questions on the previous night's assignment. They form their groups, and put their name and all the other names of the people in their group on a piece of paper. Then we place one problem at a time on the board. They will have three to five minutes per problem depending upon its difficulty.

The kids must all agree upon the answer and show all the work to back that answer up. This FORCES them to talk math because at the end of the quiz, we collect only ONE PAPER from each group, they do not know who's paper will be selected, and they ALL GET THE SAME GRADE.

Now this shouldn't be a big deal if indeed they truly all have shared in the ideas. Everyone has a chance to contribute, and they really do, because we walk around the class and listen to them talk. Any student who is not actively involved in the solving is quietly removed from the group and takes the quiz alone. No one wants to be removed from the group, so they all really try.

Then eventually, even the slower kids find that they can contribute something and that maybe they are not the only ones who don't understand everything. It is actually quite a math anxiety reliever and a tremendous TEACHING TOOL. This type of quiz is meant not so much to evaluate as to TEACH.

Getting mathematics into students in this way is a strong attitude enhancer too. They enjoy the talking, and arguing, and sometimes even laughing about math. And when people enjoy something, they do it. It's just human nature. Never underestimate the teaching power of a well motivated study group!