math-dō
Talk about this in terms of 2 myths: the myth of 'math ability' and the myth that 'you have to learn it on your own'.
The way of math
Gambate kudazai! -- Work hard and never give up on yourself! In the
U.S. we have a strange concept called 'Math ability'--which some
people have and others don't. But in Japan noone believes in 'math
ability'. Anyone can do math if you work hard enough... and follow the way
of math-dō.
Eileen Pollack started out pretty rough at Yale... To do well at math you do not need to be white, male, socially awkward, or have aspired to be a mathematician since before you could read.
The way of math is a set of concrete strategies for doing well even if you don't feel like it. For each new topic (typically one section in the textbook), you should do several of the following.
- Read the textbook actively: Check and reinforce your understanding by
pitting yourself against the textbook examples: cover up the
author's solution and attempt the problem yourself and then uncover
what you did not understand by comparing the author's solution with
your own.
If parts of a problem still don't make sense, try to narrow in and write out a question, and / or highlight the part you don't understand. Then bring it up with peers or your instructor.
Early in the course, if we cover some topics that you have seen before,you may not need to do this as much. But there is a danger that you'll avoid the habit of taking on the examples until it's too late. So even with familiar material, you should at least occasionally exercise this discipline to keep yourself in shape. - Try some of the odd-numbered exercises. Answers are available for these online:
Just as with the examples, it's most useful to wait to look at the answer until after you've made an attempt to solve it yourself. - Complete homework assignments. After each lecture, you will
be expected to do problems, typically in WileyPlus based on the
material we just covered in class. These assignments will help to
solidify your ability to describe, use, and apply the concepts and
techniques.
One strategy for WileyPlus is to print off the assignment, work on it somewhere other than staring at a computer screen, and then log back in to input your answers.
Even if you work some of the problems as they come up on the computer, you will still want paper beside you to work out the steps of a problem. - Participate in class activities. Classroom activities will supplement the reading and the homework assignments.
- Don't hit your head against a wall alone! The most successful
students are not typically toughing it out on their own. Study
with a partner or a study group. Anything that gives you a chance
to talk through your reasoning with someone else will help you learn.
Bring someone less socially connected than you are into your group.
When you study with one another, try to do as much explaining or thinking out loud as your partners do. You will know that you have learned a concept when you are able to reproduce arguments developed during a conversation. - Seek assistance if you are having difficulties. Talk with your study group. Stop by my office!
- Review feedback on assignments. Make sure you understand anything marked incorrect. Complete a few similar exercises in the textbook to confirm your new understanding.
Regular study as well as regular attendance in class is very important to your success in the course. Unlike a literature survey course, what comes at the middle and end of the course depends directly on material covered at the beginning. So it is more important than in many other classes not to get behind, and to master all the material as it comes.