Tips for Teachers

Someone or other said that you never learn to write, only write the book you are writing. The same might be said for teaching: you never learn to teach, just (partially, and failingly) to teach the class and students you are teaching. Here are a few guidelines I have found helpful in my own teaching and in helping new teachers.
a) Start with somebody else’s stuff. The majority of your preparation should involve modifying the materials from the textbook or course materials found online, not creating new materials from scratch. Teaching is not about creativity, at least not in the way that we normally think of creativity–the students are much more likely to find your class “creative” and engaging if you aren’t wasting time making stuff up yourself.
b) Plan ahead, far ahead. Preparing a high-quality lecture or lessonis much better done in a series of passes than all at once the weekend or nightbefore. Make sure your syllabus (if you’re teaching college) or unit plan (if you’re teaching K-12) specifies the exact topic and readings for every week before the semester begins (this is for your sake more than the students’) and then plan ahead in a three week cycle: first week, make an outline. Second week, gather materials; third week, modify the materials into a polished presentation. The (unfortunate or fortunate) truth is that your level of pre-planning makes a much bigger difference to how much students think you know what you are doing than your actual depth of understanding of the material.
c) Think through what students are actually supposed to be doing. If they are taking notes, what would they ideally be writing down? If they are following along on printed slides or a guided notes handout, what questions are they answering, or what opportunities for discussion will there be? If there is a practice problem during the lesson, will they have a chance to work on it individually or in groups, or are they following along as you demonstrate?
d) Presentation, repetition, application, assessment. While there are students who can jump immediately to high-level thinking about a new concept, it is almost always more effective to approach a topic as a series of steps: a straightforward presentation, a fairly obvious check for understanding, a simple problem-set level problem, and only then a challenging test for deep understanding. Problem sets and tests can go through some of the same steps, which gives you a sense of the range of students’ understanding.
e) Unless you are in a very unusual setting, roughly zero of your students will be able to follow a mathematical proof.
f) Stay positive. Yes, American students have been coddled since birth, and maybe it is your destiny to crush their dreams and show them the limits of their abilities. But this has to be done with a smile on your face.

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