TUTORIAL STRUCTURE MATH 3968
Tutorial sheets have required and recommended problems. You should do
all the required problems. The recommended problems are additional study
material so that you have worked problems to help you study for the exam
(in lieu of past exam papers).
The required problems are divided into
(1) problems to write up
(2) problems for presentations/group discussion
(3) other required problems.
These will be treated as follows.
Problems to write up. What happens: Everyone needs to bring neatly
written solutions to these problems to the tutorial. In small groups, you
will briefly discuss these problems and mark one another’s work out of 3
according to the scheme below. If you solved the problem and the other
person didn’t, try to give them hints as to how you thought of the answer.
Please provide CONSTRUCTIVE feedback to the person whose write-up
you are reading on how they have structured their argument, letting them
know both what you like and don’t like.
0 if essentially no attempt was made on the problem,
1 if a minimal attempt was made on the problem,
2 if a good attempt was made on the problem but a full solution was
not reached,
3 if a full solution to the problem is given.
Not all written solutions will be looked at in each tutorial, this will be
randomly selected on a week by week basis. If you are absent from the
tutorial and you have not provided a good reason (e.g. you are sick) then
this counts as no attempt. Your best 11 (out of 13) marks count.
Why
• Structuring your argument clearly is an important skill; this will help
you get feedback on how you have done this and see how someone
else went about it.
• You can learn from others how they thought about the problem and
hence improve your problem-solving skills.
• Some extra incentive to do the problems before the tutorial,
Problems for presentations/group discussion. What happens: A
group will be assigned to present a solution (everyone needs to take part
in the presentation). As well as discussing the solution, please reflect upon
how you were able to see what to do. There will be two sets of marks out
of 5, namely
1
2
TUTORIAL STRUCTURE MATH 3968
Mathematics mark: any correct solution receives full marks in this category, partial marks much as if marking an assignment/exam answer.
Presentation mark: this is based on how well the solution was explained:
Could we easily follow the explanation? Were the steps motivated? Was
there an explanation as to how one could reasonably come up with this solution? Was the right amount of detail given? (It may not be helpful to give
all the details of a long calculation, but the important arguments need to
be carefully explained.) Was what was written on the board enough so that
if you only have that, the solution would still make sense? Was a solution
neatly written on the board in lettering large enough for those at the back
to read, first erasing what was there before and then starting from the top
left?
Why:
• It helps everyone learn better when the person of the board gives a
good presentation
• Presentation skills are important pretty much regardless of what
career you pursue. You need to be explain yourself clearly in order
that people understand what it is that you can do.
Discussing problems within your group. What happens:You can
choose to work together on any problems you couldn’t solve or the new
problem given within the tutorial. The tutor will come around and help.
Why: Learning from one another is highly effective, especially when there
is a tutor available to give everyone some hints.
Rationale. The primary purpose of upper-level mathematics tutorials is for
you to engage deeply with the mathematical content by solving problems
and to improve both your understanding of the subject material and your
problem-solving skills. Solving challenging problems is the best way to understand the subject and improve your skills. These problem-solving skills
are highly valued by employers of mathematics majors. To develop these
skills simply being shown the solution to a problem is not effective, it is
necessary to struggle with the problem for yourself. Hence it is extremely
important that you do the group discussion problems before the tutorial, regardless of whether it is your turn to present. If you have
struggled with the problem and not been able to solve it, this is exactly the
time when someone’s observation of how one can think of a solution is most
helpful, not only to showing you how to solve that problem but to helping
you learn techniques for getting yourself “unstuck” in the future.
You will get the most out of tutorials if you work hard on the problems
beforehand and then ask questions and participate regardless of whether
you managed to solve everything. It is supposed to be a supportive learning
environment, the marking system is there only to encourage you to do the
work and so that you can receive helpful feedback.