Rigors of Stem

Mike Boyle, Dept. of Mathematics

1. How UMD Math (and STEM) is not high school.
(a) Pace
(b) Grading
(c) Level
(d) Freedom

(a) Pace
We move fast through a syllabus of material with an eye on a big picture of what you need. It's up to you to keep up.

Not just calculus courses and above are fast.
The following are VERY fast paced:
STAT 100 (prob/stat without calculus),
MATH 115 (precalculus).

(b) Grading
With few exceptions:
No "do-overs".
Very little credit for "effort".

(c) Level
Compared to most high school courses: the problems are harder and require more thought

(d) Freedom.
Fewer contact hours in courses.
Attendance much more optional.
Freedom to fail -- up to you.

2. How to succeed.
(a) Keep up/regular schedule.
(b) Friends/ groups.
(c) Think to understand.

(a) Keep up/regular schedule.
Make a regular schedule for your coursework. Follow it.

Don't fall behind! There are many specific things to learn in a math course, and often understanding tomorrow's material depends on understanding today's material.

Math is the worst subject to fall behind in, and the easiest subject in which to waste time. Get behind: the lectures can stop making sense.

Review your lecture notes same day -- before the vague points become gibberish, and you waste the partial understanding you got in the lecture.

(b) Friends/ groups.
Find people in your math course to talk with, maybe to work with. You can help each other. Articulating or explaining something is a good way to learn it.

(c) Think to understand.
This is the most important thing, and the hardest to describe.

In the short run -- it's harder to understand well, compared to getting answers for homework problems.

In the long run -- even over the course of a semester -- it is EASIER to understand than to try to memorize many examples. How? Most of the understanding happens INSIDE YOU and is done BY YOU. Office hours and tutors can't change that. Professor/student is kind of like coach/athlete.

If you don't understand some math quickly -- that's completely natural. (For mathematicians too.) But usually with work you can get there.

3. Get exercise (and sleep).
This is a STEM tip?
Well, yes. The mind works better when the body does.

4. Pitfalls: some examples.

(a) "I know this -- I took it in high school."
Common mistaken reason not to study hard.

(b) "I failed midterm 1 -- I give up."
There is usually space to recover.
Also, there can be a curve from course scores to course grade at semester's end.

(c) "I work backwards from the homework."

Rather than read the book, you begin with the homework problems. You look at a problem, can't do it, and look for a similar problem in the book. You see if you can do something similar to get the answer in the back of the book. If successful, you move on.

The danger with this method: it's easy to not understand in the end.

Try to read the section in the book (at least the main parts of it) before the homework.

(d) "But I understood it in my group."
Group work can be great, but it is easy to rely on others without really getting it. Be careful -- you don't take exams in a group, or (usually) get grades in a group.

One safeguard: work on homework together AFTER you have tried it individually.

(e) "Well, I missed that question, too late now."
(It will be on the final.)
(One of the best ways to learn math is to understand a mistake.)

(f) " My job is 20+ hours a week."
For most, this interferes with courselwork.
People are different, but rule of thumb:
10 hours a week on a job is fine.
15 hours: danger zone.
20 hours: trouble.

(g) "I stayed up all night studying for the test!"
Bad strategy for math. You need to think for the test, not just recognize multiple choice answers.

(h) "This professor is awful -- I go to the lectures, and I don't understand."
Read the book. Lecture is only one part.

5. Resources

6. On plans.

(a) Making plans.
I see at the Letters and Sciences STEM Exploration Site there are requirements that you make a "4-semester plan" or perhaps a "2-semester plan".

I think this is fantastic.

It's not a 5-year plan: But you are an active explorer checking out a direction.

(b) Course choices.
Which level of course should you take?
Be careful.

You don't want to sign up for failure-- respect the math placement test placements. Understand your preqreq courses! A lot of the troubles students have in calculus comes from poor understanding of precalculous (trig, logs, exponents, graphs, polynomials, factors ...) .

But ... it is also the case that the minimum requirement for a major program might not be optimal. Those requirements are your floor -- not your ceiling.

7. College and opportunity

Take initiative -- you can find great opportunities and resources at UMD.

Be passive -- and you can sink without a trace. So take advantage.

Finding a major that suits you, to a career for a life that suits you -- that's an important part of your growth and achievement in college. But don't stop there.

I wish you all a great intellectual adventure in your time at UMD.