Study tips for Math 184 Section 106
November 10, 2015
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How did you study for the midterm?
Make a list of what you did to study for the midterm:
Compare this to the following list:
• Worked through the suggested textbook problems, workshops and
webworks,
• Worked through all practice and actual quizzes,
• Memorized all definitions, theorems, and rules/laws e.g. continuity,
rules or differentiation, intermediate value theorem, etc.,
• Used the “learning goals” to structure my studying and make sure
there were no gaps in my knowledge.
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How to structure your learning:
Through the rest of the semester you should do the following on a weekly
basis:
1. Every Friday review the learning objectives along with your notes.
Identify where in the notes different goals are addressed. This is crucial to digesting the new information – you should have been doing
this all along but now it’s really really important since many of you
also need to allocate some time to learning older material.
This is a good time to:
• Make flashcards for definitions and formulas.
• Address anything you were confused by during lecture by coming to office hours or using piazza.
• Work the suggested problems (at least several of them).
2. Keep up with Webwork, workshop, studying for quizzes, etc. Note
that the midterm problems were nearly identical to problems from
webwork.
3. Allocate some time, (3 hours at least if you failed the midterm) to
understanding older material, use the general guidelines above. As
a starting point, go back to your quizzes, webworks, workshops, and
the midterm and make sure you can solve all of the problems you’ve
seen before. You must start doing this now since it will be WAY too
much to deal with the week before the final exam.
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General guidelines
• Study actively not passively – don’t just read a passage from the
textbook or your notes, make sure you re-enforce the ideas you’re
consuming them by working through a practice problem or checking
that you understand each step in a worked example.
• Self-test your skills using old webworks, workshop problems, and
quizzes from our course. Do you remember how to do the problems
from webwork number 2? Make sure by re-doing each and every
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problem trying not to use your text, notes, etc. Since you’ve done
them before they won’t take as long this time but you’ll reinforce
your understanding and be able to answer similar problems much
more easily on an exam. You’ll also identify your weaknesses so you
can address them.
Related to this, do not assume that after following someone through
an example you can duplicate the solution unless you actually test
yourself. So, a review session where someone works problems for 5
hours while you watch is of deceptively little value – your 5 hours
would be better spent trying to work the problems yourself and then
using office hours or piazza if you get stuck.
• Review the learning goals – these are the topics we’ve covered each
week in the course and what we expect students to know at the end
of the course. As you glance over them, ask if you’ve met these goals.
For instance in week 3 we had the goal: “ state the definition of the
derivative and use it to compute the derivative of a given function in
simple cases.” To satisfy this goal, you should have memorized the
definition of the derivative and worked problems where we use the
definition to find limits explicitly. If you can correctly work all of the
suggested problems I guarantee you will get a spectacular mark on
the final exam.
Key words are important. If a learning goal states ”define...”, ”know
the...”, ”be able to explain...”, or ”be able to state the...” then you
should memorize something, e.g. the definition of continuity or the
intermediate value theorem. Vaguer words like ”compare and contrast..” might mean you should be aware of examples or counterexamples. For instance, “explain using sketches of appropriate functions the relationship between continuity and differentiability.” means
you should know that diff. implies cont. but not the other way
around. You should have in mind a counterexample such as |x| to
illustrate that a function can be cont. but not diff.
• Treat studying like training for a sport. Can you run a marathon
tomorrow? Probably not. If you train for the next three days will
you be able to run one in five days? Probably not. It’s the same with
learning. You should be thinking today about the final exam. Also,
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in sports, taking a week off means losing fitness. In math, taking a
week off means you have twice as much to learn the following week.
So be diligent and study regularly. Review the learning goals on a
weekly basis.
• Don’t squander learning opportunities. Every problem you work
has value. If you copy a friend’s approach to a webwork problem
without struggling with it yourself you will not understand it. So,
what was the point of doing it at all? Focus on the long term objective
of acing the final exam and treat each exercise as if it will improve
your mark (because it likely will).
• Practice, practice, practice!
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