This is George Polya's 10 commandments for teachers:
1. Be interested in your subject.
2. Know your subject.B 3. Know about the ways of learning: The best way to learn anything is to discover it by yourself.
4. Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place.
5. Give them not only information, but "know-how", attitudes of mind, the habit of methodical work.
6. Let them learn guessing.
7. Let them learn proving.
8. Look out for such features of the problem at hand as may be useful in solving the problems to come - try to disclose the general pattern that lies behind the present concrete situation.
9. Do not give away your whole secret at once-let the students guess before you tell it-let them find out by themselves as much as feasible.
10. Suggest it, do not force it down your throats.
I got this from the plenary talk of Bernard Hodgson titled Whither the mathematics/didactics interconnection? at ICME 12, Korea, where he highlighted the important contribution of George Polya in making stronger the interconnection between mathematics and didactics and between mathematicians and mathematics educators.
If it's too hard to commit the 10 commandments to memory then just remember the two rules below which is also from Polya. Combine it with Four Freedoms in the Classroom and you are all set.
The first rule of teaching is to know what you are supposed to teach.
The second rule of teaching is to know a little more than you are supposed to teach.
You will find that by providing the following freedoms in your classroom an improved learning environment will be created.
The Freedom to Make Mistakes
Help your students to approach the acquisition of knowledge with confidence. We all learn through our mistakes. Listen to and observe your students and encourage them to explain or demonstrate why they THINK what they do. Support them whenever they genuinely participate in the learning process. If your class is afraid to make mistakes they will never reach their potential.
The Freedom to Ask Questions
Remember that the questions students ask not only help us to assess where they are, but assist us to evaluate our own ability to foster learning. A student, having made an honest effort, must be encouraged to seek help. (There is no value in each of us re-inventing the wheel!). The strategy we adopt then should depend upon the student and the question but should never make the child feel that the question should never have been asked.
The Freedom to Think for Oneself
Encourage your class to reach their own solutions. Do not stifle thought by providing polished algorithms before allowing each student the opportunity of experiencing the rewarding satisfaction of achieving a solution, unaided. Once, we know that we can achieve, we may also appreciate seeing how others reached the same goal. SET THE CHILDREN FREE TO THINK.
The Freedom to Choose their Own Method of Solution
Allow each student to select his own path and you will be helping her to realize the importance of thinking about the subject rather than trying to remember.
******************************************* -- Jerry P. Becker Dept. of Curriculum & Instruction Southern Illinois University 625 Wham Drive Mail Code 4610 Carbondale, IL 62901-4610 Phone: (618) 453-4241 [O] (618) 457-8903 [H] Fax: (618) 453-4244 E-mail: firstname.lastname@example.org