With reference to "Polya's Ten Commandments for Teachers" (see Jerry Becker's post pasted below), it strikes me that several of the 'commandments' are in fact a strong endorsement of teaching via the 'discovery mode' rather than via the pure 'lecture mode'.
This does NOT mean that we have to do away with 'lectures' entirely - merely that there is much more to effective learning by students than simply 'lecturing' them in the belief that one is 'teaching'. Lectures should be recognized as constituting only a rather minor part of the 'teaching+learning' dyad - properly, we should in fact call that the 'learning+teaching' dyad.
GSC Jerry Becker posted Feb 6, 2013 4:20 AM: > *********************************** > From Mathematics for Teaching website. See > http://math4teaching.com/2012/07/28/g-polyas-ten-comma > ndments-for-teachers/ > *********************************** > George Polya's Ten Commandments for Teachers > > [Posted by Erlina Ronda] > > 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. > > ------------------- > > The Four Freedoms in the Classroom > [http://math4teaching.com/2012/02/01/the-four-freedoms > -in-the-classroom/] > > [Posted by Erlina Ronda] > > 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