Procedures for the MAT (Master of
Arts in
Teaching) Comprehensive Examination in the UN-L Department of
Mathematics
December, 2003
The MAT exam will consist of a
two-part "take-home" written section and an oral presentation to an MAT
faculty
committee.
Part I A. The committee will
select three questions from at
least two different courses the MAT candidate has taken. Two of the
questions
will be mathematically-based, and one question will ask the candidate
to
explain a mathematical concept and then show how studying this concept
will
help them enrich a course they teach at the secondary level. The
written
response to these three questions will amount to a total of 5 to 10
pages.
Part I B. The committee will
select a mathematical topic on
which the candidate will write an expository paper (including proofs or
examples as appropriate) of approximately 8 to 10 pages.
The candidate will be given 4 to
6 weeks to
complete Part I of the examination.
Part II. The candidate will
appear before an MAT committee
and give an oral presentation based on the work in Part I B. The
presentation
will be approximately 15 to 20 minutes in length. Following the
presentation, the committee will ask questions designed to probe the
candidate's depth of understanding of the topic. The committee may also
ask
questions related to Part I A if the committee feels this is
appropriate.
Examples. As an example of a
mathematically-based question from Part I A, the committee might select
a
problem from an analysis course that requires the candidate to
understand the
distinction between convergence and uniform convergence and provide
some
explanations at an "epsilon-delta level" of detail.
As an example of a question from
Part I A
that links mathematics and classroom pedagogy, the candidate might be
asked to
show how the alternating harmonic series can be rearranged to converge
to an
arbitrary term, and then relate this result to a discussion of series
in a high
school pre-calculus class.
As an example of a topic from
Part I B,
the candidate might be asked to show how the Steiner problem (find a
point such
that the sum of the distances from this point to three given points can
be
minimized) could be generalized to larger numbers of points, and
perhaps
provide an example of application to a scientific or engineering
problem.
Suggestions for the Part II
presentation. Click here
for suggestions on making the oral presentation.
(Added July 2006.)
The Initial MAT Committee. The
MAT
Committee will initially consist of Jim Lewis, Gordon Woodward and Dave
Fowler,
with the intention of bringing in new members to provide some long-term
continuity.