Working in Groups
Though from time to time I make assignments which are meant specifically
to be done in a group, you are always encouraged to work with others
on out-of-class assignments
unless otherwise indicated. In fact, I urge you to find
one or two other students and agree to meet at a regularly-scheduled
time each week to study together. Here are some reasons for doing this
(some of these may apply to you more or less than others, depending upon
your innate mathematical ability):
- If you view math as a set of skills to learn, then you are
embarking on a very difficult venture indeed when you sit down
to learn in a detached way the myriad of skills that go with
a specific course. As it happens, these skills are generally
based upon a relatively small collection of ideas/concepts that,
if mastered, make the skills much easier to apprehend. You
will find it easier to master these fundamental ideas through
discussions with classmates (always striving to use the
terminology/vocabulary appropriate to the course).
You should talk about the concepts in each new section,
identifying carefully what they are and what they
are not. No section is likely to emphasize more than two
concepts, and often these are repeats (concepts that have
appeared in some form earlier).
- If you spend time demonstrating to others in your group
your solutions to various problems,
you will find frequently that another has solved
a problem in a substantially differently fashion than you.
Real learning begins when you grapple
together over the merits of different methods, and why
they do or do not lead to the same answer.
- You may find that another group member can solve a problem you've
tried unsuccessfully to solve.
- Even if you tend to get all of the problems, there is value in
explaining things to others. Every teacher you know will tell
you that they thought they knew a subject well before teaching
it, but gained new insights/understanding as they taught it.
- Studying together provides opportunity for Christian interaction.
We can encourage one another, bear one another's
burdens/frustrations, and share our gifts with others.
- One day you will seek employment. Companies are looking for people
who, while individually competent, have good teamwork experiences
and skills.
Having said all of this, remember that you are individually accountable
for your learning (exams, after all, are not group efforts). The end
result must be that you are able to discuss (usually in writing) the
concepts of the course. College subjects like mathematics and
statistics are not spectator
sports! Work on a problem by yourself before seeking help, identifying
specifically the place you get stuck. When you get help, ask for the
least amount of information necessary to get you going again. Once
you've made it to a solution, give that problem a rest and see if you
could do it again (without peeking at any notes) the next day.
A rule of thumb: Understanding what another has done does not
mean that you can generate the same solution on your own nor
critique it.
This page maintained by:
Thomas L. Scofield
Department of Mathematics and Statistics,
Calvin College
Last Modified:
Monday, 31-Aug-2009 11:09:11 EDT