How To Teach Math

From The MathLab.com :

1. Force Them To Talk

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!

2. The Gentle Art Of Ice-Smashing

Group work will not be successfull unless you GENTLY SMASH THE ICE.
People set up natural barriers bewteen themselves and the rest of the world. It’s a self defense mechanism, and we all do it to a certain extent. If you want teenagers to work together on math, you need to smash through those barriers and give them some common ground.
Most likely your groups will be mixed between sexes, abilities, and more, importantly social cliques. It is most productive to mix the groups in every imaginable way. It gives the kids more life coping skills and promotes an overall unity of classroom as the kids move from group to new group throughout the year.
So how do you get the homecoming queen girl with perfect nails, the fat smelly kid with zits, the loud mouthed football running back, and the multipierced black stained goth chick to pull together as a productive math unit? YOU PLAY A GAME!
There have been a few times where we thought all the kids knew each other and they didn’t really need the ice smashing activity, so we skipped it, only to have a whole nine week period pass with no fun and more than a few fights. ICE SMASHING IS ESSENTIAL for group bonding. Never overlook this step if you are serious about having your students learn together.
Here is a partial list of some of the games we have played over the years.
Micro-Pictionary
How big is my belly
Mystery sight
Speed acting
Rock Bands and Math Pods
Test of genius

3. Doing Is Everything

Get your students DOING math every lesson.
All people need varying degrees of “hands-on” experience to truly master a topic. Some need a lot, others a little, but we all need a portion, so be sure to supply it EVERY LESSON.
Introductory warm-ups are a great way to start a lesson. They can be different each day and act as a lead in to the lesson topic. They can be used to reinforce a skill that will be essential to the day’s lesson.
Things to remember are:
Let them be short, 3-7 minutes.
Have the students use their hands as well as their minds, to cut paper, or fold paper or arrange items, etc.
Keep it fresh so the class will look forward to what you are going to pull out of your hat each day.
You may be saying, “Oh sure, how am I supposed to come up with an enticing, fun, hands-on activity every day for every class and one that actually applies to the lesson at hand?”
This is a logical question. And the answer is, STEAL. Until you have taught long enough to have a wonderful repertoire of self made wonder gems, you will simply have to do what everyone else does, use other people’s ideas, and modify them to fit your own teaching style and students. themathlab.com is packed with some of our best wonder gems, but we also highly recommend the book MATH STARTERS.

Also remember, once the formal lesson begins they still need to be doing math. Be sure to throw out lots of questions like, “What would happen to this expression if…, Okay, now flip it over and what will it look like, draw this…, Will it work for negative one…, Will it work for zero…., Where does this fail to be true…, Draw me an example of one that wouldn’t work…,etc.
When you throw out these type of questions, GIVE THEM TIME TO THINK, walk around the classroom and look at what they are writing. You can also encourage them to come up with a group consensus, if they are sitting in groups. Communication between learners is essential. You’ll be surprised, when you open the math up to the kids, they will almost always come up with something that you haven’t thought of. Thus your own breadth of knowledge will be enhanced. It’s a very positive experience for everyone.
The next logistical consideration is, “How do you get them ALL working when you have a class with 20 or more students?” It’s seems impossible to get them all working and give feedback to each one quickly. If you could only see what they were all doing with just a glance it would be so much easier. Now if you have lots of chalk board space, you can send them all to the board, but in many instances this is not possible.
Here’s an idea that we use all the time. We use “think-boards”. These are mini chalk boards about one foot square. They fit on top of the student’s desks. They write their responses and then hold up the boards. We can see in just a few seconds who understands and who doesn’t. We keep chalk and clean washrags with these boards. Students pick these up as they enter the room on days that we are using the think-boards. Some students opt to dampen their washrags in the restroom before class starts. Everyone knows this is fine as long as it’s done before class starts.
You can make a classroom set of think boards. Simply buy a sheet of 4′ x 8′ masonite or 1/4 inch smooth plywood. Paint it on one side with a dark, FLAT, paint using a smooth roller, we recommend two coats. Let the paint dry, and then cut it into 12 inch square boards. If you don’t have the tools to cut the boards, ask your industrial arts teacher to cut them for you.

*NOTE OF EXTREME IMPORTANCE: If you want your students to do math willingly and with enthusiasm, never ridicule a student for giving a wrong answer. Find something good about their response, then rephrase the question or modify it in a different way and ask them again. This gives the individual a chance to publicly redeem themselves and not feel stupid. It also sets a tone of respect and safety in your classroom that will be appreciated. You will get a great deal more participation if everyone knows that they are not in danger of ridicule.

4. It’s Okay To Be Wrong

You must have one cardinal, unbreakable, totally accepted rule in your classroom. IT’S OKAY TO BE WRONG!!!. NEVER, under any circumstances, ridicule or be sarcastic to a learner who makes a mistake.
We all make mistakes, and nothing destroys a person’s desire to try, faster than public ridicule.
If you want your students to do math willingly and with enthusiasm, never ridicule a student for giving a wrong answer. Find something good about their response, then rephrase the question or modify it in a different way and ask them again. This gives the individual a chance to publicly redeem themselves and not feel stupid. It also sets a tone of respect and safety in your classroom that will be appreciated. You will get a great deal more participation if everyone knows that they are not in danger of ridicule.
A nice result of this rule will be that your students will extend the same respect to you. When you screw up, and you will, they will politely correct you and the atmosphere of trust will be protected.
If you, the teacher, violate this rule even one time, you will lose the trust of your students and the environment in your classroom will deteriorate immediately. You will see the students shut down. They will instantly believe that if you can embarrass one student you can do it to them too. So NEVER VIOLATE THIS RULE!!!
If for some reason, like lack of sleep or complete frustration, you let a rude or sarcastic comment pass from your lips, your only hope is to publicly acknowledge your mistake and apologize to the student you insulted in front of the others. Make sure you are sincere too or it will worsen the insult. Most people will give you one more chance if you are willing to publicly admit your mistake. But again, these infractions must be very rare or you will lose the trust of your whole class.

5. Keep Your Class Fresh

Would you want to eat the same stale tasteless meat day after day after day after day after day? No, of course not. So DON’T SERVE STALE MEAT TO YOUR STUDENTS.
Keep your classes FRESH!

People learn at different rates and in different ways. So if you do the same thing everyday, you will be doing a tremendous disservice to a large percentage of your students. Vary your methods of instruction frequently and you will keep more students learning.
Remember there are few people in the world who can learn just by hearing, these are auditory learners. Some can learn by just watching an example or two, but the majority of people need to involve more than just their ears and eyes. They need to touch it, sing it, dance to it, build it, draw it, write about it, act it out, argue about it, or in general just EXPERIENCE what they learn.
Okay so how do you get your students to EXPERIENCE their math? Give them something fresh and a bit fun every day. Here are some things that our teachers do to get you thinking of possibilities:

  1. Games
  2. mini-lectures (five minutes of talk, five minutes of try the idea)
  3. boardwork
  4. groupwork
  5. individual work
  6. projects
  7. videos
  8. writing assignments
  9. discovery lessons
  10. computer practice
  11. Internet research
  12. spreadsheet explorations
  13. humorous stories
  14. lively historical anecdotes and facts
  15. one on one peer tutoring
  16. experiments
  17. timed drills
  18. self checking worksheets with answer banks

7. Become Skillful THIEF

You must become a creative, skillful, THIEF.
No, we are not kidding.It is absolutely essential that you become an expert at sniffing out the best ideas and techniques of successful teachers. Once found, you must STEAL THEM and make them your own.
The key here is the “make them your own” part. The act of using someone else’s activity will become worlds richer when it is tailored to YOUR teaching style and personality and of course to your students.
To help you in your quest to steal the best and nothing but the best, check out these links.

TheMathLab.Com

 

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