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MTE 482
Methods
of Teaching Mathematics in Secondary School
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Fall 2007
Basic Math Interview
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Instructions
for the Basic Math Interview
Your assignment is to explore with someone (e.g..
a
roommate, friend, even a parent) his/her understandings of some
mathematical
concept usually labeled “basic,” specifically multiplication of
decimal numbers. The reasoning behind this assignment is that in order
to teach
mathematics and assess students’ understandings well, one must first
have
a good sense of what it means to know and/or understand
mathematics. This
activity will ask you to reflect on that issue.
This assignment counts as two writing assignments toward your final
grade.
See if you can engage the person with the following discussion of
“basic” math. During the interview, you should avoid
proposing specific models to the interviewee. Instead, try
following the
person in how they are thinking about it. Remember, the goal is to
figure
how they are thinking, not to teach!
Interview Problem:
When
carrying out “decimal multiplication” typically you ignore the
decimals, carry out the multiplication, count the number of numbers
“behind” the decimals and then count over than many decimal places
in the answer. Why/How does this work?
For example, consider
1.96
x2.15
Would it matter how many places you moved
the decimal
place? Do you have to move the decimals to get the answer?
What to Write Up:
The assignment is to carry out
the interview and write up what happened with
enough detail that someone in the class could follow your description.
Discuss
what happened, how you kept the process going, how the person thought
about the
task, and what you found interesting. Make sure to take significant
notes so
that can go back and think hard about what went on in this interview.
Audio
recording the interview and keeping the written work of the interviewee
is
highly recommended. Your paper should be about 3 pages typed.
The evaluation will be
based on:
- How
successful you are in giving an accurate account of the interviewee's
thinking. Another person should be able to read the account and be able
to explain the interviewee's approach.
- How
successful you are in identifying what the learner DOES know.
- How
successful you are having the interviewee build on or extend what they
do know in a way related to the interview task. Avoid telling the
person how you think they should approach the question, even through
your body language. This is about
getting them to BUILD on what THEY understand.
- Your Reflection. This can either mean your
reflections/observations about the interview (e.g. something that
surprised you or the person's shifts in emotion).
Additional suggestions:
- You
should include the diagrams the interviewee used, etc. in your
submissions. They can be attached at the end.
- Set
up a definite time with your subject and move to a place that doesn't
have an audience. Don't try to talk to someone over dinner or in the TV
lounge in the dorm. If you don't respect the situation enough to set it
aside and give it importance, you can bet that the person you are
interviewing won't either.
- Allow
your subject time to REALLY think through the problem you select for
them, you should tell them that you need at least 30 minutes of their
time. If they commit to that time limit going into it they will be more
willing to engage their mind, if you don't set a time limit they will
try to end the conversation as soon as possible.
- Remember,
a substantial portion of your evaluation will be your reflection on the
interview and your ability to describe your subjects
strategies. In-other-words, a transcript of the interview with no
additional thoughts or explanations will receive no credit, although
excerpts of such as transcript can provide valuable reference points
for inclusion in your paper.
- Be
sure that YOU have thought hard about the question so that you are
ready to recognize and pursue interesting aspects of the discussion.
- For
your own information and to help the reader form a picture of your
subject, find out some of their background with math (e.g. Do you like
math? Were you good in math in high school/college? If you were good do
you think you really understood or were just good at following
instructions? What is your current major/job? Do you perform
mathematical operations on a regular basis?)