math-dō
The *way* of math
Gambate kudazai! -- work hard and never give up on yourself!
There are cultural barriers to learning math/science:
- The Myth of 'I'm Bad at Math'. This is the idea that some people are good at math, and others just can't do it. This can be a self-fulfilling prophecy.
- Eileen Pollock has written eloquently about the implicit and explicit biases faced by women.
- The Dunning-Kruger effect occurs when people with the least competence at a skill are also the least able to recognize their own incompetence, and consequently tend to overestimate their abilities.
- The flip side is that folks who have reached higher levels of skill are more aware of what all they still don't know, or can't yet do. So paradoxicaly, more accomplished people are more likely to fall prey to imposter syndrome.
In Japan there is much less belief in 'math ability'. Instead, it is thought: Anyone can do it if you work hard.
"Dō" means "the art of" or "the way of". E.g. Tae Kwon dō is the the way of kicking and punching! So I'm only partly tongue-in-cheek in coining the term...
"Math-dō"--the way of math--approaching
math as a martial art that you practice to get good at.
Jeff Berger
Instead of worrying about your ability, here are some concrete strategies of things you can *do* to develop in the way of math:
- Read 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 the problem still don't make sense, highlight and/or write out a question to bring 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.
- Answer the reading questions. For some reading assignment, I will give you a list of reading questions. These questions will help focus your understanding of the textbook/class presentations. Your answers will be checked for completion at the beginning of the day and will serve as a basis for class discussion.
- Practice! Work through daily homework assignments. After each morning, you will
have Edfinity problems assigned, based on the material we just covered in
class.
These assignments will help to solidify your skills by having you
describe, use, and apply the concepts and techniques.
Have paper & pen(cil), or a whiteboard handy to write out parts of the problem, carry out algebra, keep track of intermediate results, etc.
The assignments might also include completing handouts started during class.
- Participate in class activities. Classroom activities will supplement the reading and the homework assignments.
- Study with a partner or a study group. Anything
that gives you a chance to talk through your reasoning will help you
learn. Bonus: 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. Come and talk to Paul. Drew Smoker will be running a near-daily drop in problem solving session.
- Review feedback on assignments. Make sure you understand anything marked incorrect. Complete a few similar exercises in the textbook (the odd-numbered exercises have answers supplied).
- Make the most of your notes, ideally soon after each class: Highlight things that are not yet clear. Reflect to identify connections with previous content.
Here are more research-based study strategies, .pdf, from ACUE.
Regular study as well as regular attendance in class is very important to your success in the course. Because of the highly concentrated format of May term, we will be covering material at a very rapid pace. It is essential that you make every effort to keep up. Procrastination is penalized 3$\times$-4$\times$ as quickly in a May term compared to a regular term.