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Student Reactions to the Course and Typical Problems
These courses come as a shock to most students.
This is not the way calculus (or precalculus) is "supposed to be." Most
University of Michigan students were admitted because they performed well in traditional
courses; our approach may be unsettling and painful. You can sometimes head off student
uneasiness by being very specific about exactly how the course may be different from what
they were accustomed to and why.
This isn't calculus! I've had calculus and this isn't it!
This complaint usually comes from exposure to the traditional high school calculus course
where they spent a lot of time with symbolic manipulation. They may be a little
disgruntled because they hoped that taking calculus in high school would give them a head
start and possibly lead to an "easy A". Assure them that it is calculus but that
we are purposefully using a different approach -- that they will understand how calculus
is used and gain some valuable skills that will help them throughout college. Tell them
that it's hard, that it's supposed to be hard, and that they have what it takes to do it.
My instructor isn't teaching; we have to teach ourselves.
Students are used to template learning. They think that a "good" instructor
should simply lead them through each problem step by step. Real understanding, the kind
that lasts, comes from struggling with the ideas. In this course we are trying to develop
problem-solvers.
This course is taking too much time.
The University's rule of thumb is that a student should allocate at least two hours of
study time for each credit hour, so they can expect to spend 8-10 hours a week minimum on
calculus. We are requiring new types of work; they may be inefficient in performing it. We
have to help students learn to read, write, work, think, and cooperate without spending
endless hours of wasted effort. Talk with students in or out of class; listen carefully to
what they say about study habits and related matters. Remind them of the Math Lab, both as
an environment conducive to getting work done and as a source of help with whatever may be
slowing them down.
Why are we having to do all this writing? Writing has nothing to do with
mathematics!
Certainly traditional calculus courses do not emphasize writing. Many students adopt the
strategy of writing as little as possible; their expectation (not necessarily a conscious
one) is that the instructor will supply the right words to make sense of the mathematical
symbols. "If I write something out, then I stand a better chance of being found
wrong." You should make the case that writing is a crucial part of the thinking
process, and that it will help them understand the material.
Our homework problems are completely right and you're taking all these points
off!
This stems from the common student view of grades as reward or punishment rather than
feedback. Tell them that they are not competing against other teams. Explain what you mean
by good work. They may think of a homework score such as 15/20 (which they convert to
75%--a high school C) as well below average, whereas you probably consider it to be a
score indicating good progress.
I've never gotten grades like these.
From the point of view of many of our first-year students, a great deal hinges on getting
the very high grades they are accustomed to getting in high school. The mean high school
grade point average (recalculated using only their strictly academic classes) of the
entering freshmen is 3.6, so most of our students think of themselves as "A"
students. There is bound to be some resentment as students acclimate themselves to college
grading standards. Just try to be both realistic and encouraging.
I can't read the textbook--it is too confusing and ambiguous.
Often this type of complaint comes from the fact that when they read the book they cannot
find a "formula" for answering the problems at the end of the chapter as they
are accustomed to doing with math books. Help them understand why the book is written the
way it is and that the problems are meant to be hard and to require sustained thinking.
Once they get used to thinking hard and develop some problem solving skills, they will
find that everything they need to work out the answers is provided in the text. Let them
know that one of the reasons for having homework teams is to help them learn the skills
they need to succeed.
Make sure they understand that reading mathematics is not like reading the newspaper.
It is unlikely they are going to get everything they need the first time through. Help
them learn how to read the text. Make sure they are trying the embedded exercises;
encourage them to mark up the text, and ask to see their copy when you hear this
complaint. Encourage them to discuss their reading with other students in the class
(teammates or not), to ask questions in class, and to use the Math Lab.
We never know if our answers are correct.
There is a fundamental problem here. Students are conditioned to believe that the only way
to know that an answer is correct is to see if it agrees with the back of the book or if
the teacher says it is right. They need to be encouraged to look at problems in
alternative ways, to see if the answer is consistent with intuition. Spend some class time
on checking procedures. For example, it is not enough to tell students that derivative
calculations can be checked by doing one or more difference quotients on their
calculators-make them actually do it and share the results with each other.
It isn't fair for my grade to depend on the work of others.
Group work is a new idea; cooperation is a new idea. Tell students that there is research
evidence that even the best students' grades can improve if their group is working
together properly. Many students' normal mode of operation is cutthroat competition.
Remind them that there is not a preordained number of A's, B's, etc. Point out that when
they go to work in the real world, their performance will be judged on how their group
works. Also, if you adopt some form of evaluation of individual efforts, this may help
students accept the grading scheme as "fair."
Someone in my group isn't doing enough work.
One of the skills students need to learn is how to work together. Part of their
responsibility is to ensure, as much as possible, that everyone is contributing. In most
jobs they will work in later, they will be told to get together with certain people and do
something. Their boss is not going to be impressed if they are not able to work together.
This said, it still may be the case that one or more members of the group is (are) not
doing enough work. Remind the students that teams will change. If a member of the team
does no work on the homework or a project then his or her name need not appear on it.
Students may find it difficult (especially at the start) to leave off the name of a
non-contributing teammate, but this is one aspect of making the students responsible for
what the group produces.
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