0.2 A summary of principles

More aspects

Tell the truth . Many teachers believe that if they don't have all the answers, they're worthless. No one has all the answers. If you answera student with "I don't know," perhaps you can also extend it to "Let's find out." Guide your students to become collaborators in their own learning.Invite them to be subject matter experts. Students need authenticity, not awe.

Make it human. In designing curriculum, find out what makes people relate to it. Mathematics was invented for a reason, so describe aproblem it can solve - a real one. All great teaching makes complex ideas clear by tying the abstract to a human enterprise.

Emphasize what you want students to remember. Go for depth, rather than breadth. Play with the important points by introducingdifferent ways of going about understanding the key issues. (More on this later, in "Learning Styles.") For now, focus on what, at the end of the day,students can identify as the core of the lesson - what they will remember. When all the hacking away at the clay has been completed, what is the elegantsculpted piece that results?

Questions are as good as answers. Good questions require thinking. Nobel Peace Prize winner Elie Wiesel is reported to have come homefrom school one day and to have sat near his mother at the kitchen table. Instead of asking him "How did you do?" or "What grade did you get?," hismother asked him, "Did you ask any good questions today?" Questions probe. Answers come from study and should themselves be the stimulus for evengreater and more extensive questions.

Less is more. We are not suggesting that you teach less, but teach more by talking less. When you ask a question, don't dive in and answerit if you don't get something back immediately. Cherish the thinking time. Listen. Pay attention to how students are feeling, grappling with thematerial, treating each other.

Give students an opportunity to teach. We all know this to be true: teaching is not separate from learning. Since that is the case, let usnot reserve teaching for teachers alone. Allow opportunities for students to become experts in an area and to share their expertise. Provide chancesfor older or more competent students to tutor younger or less competent ones.

Think about how athletic coaches and artists work. The coach demonstrates what s/he knows, explains the rules, gives the student anopportunity to practice, provides feedback, and puts the student into real-life situations. So should a teacher. The artist assembles materials, conceives of the piece, works at it in stages, and collects thework for critique. So should the teacher. The athletic coach and the artist are non-traditional teachers, and they have a great deal to offer all of us.Their techniques are the key to many students who would otherwise not "get" the material from lectures, memorizations, or handouts.

Assignment 1: your assessment of aspects of good teaching

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