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Topic: Mathematical Thinking
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Joan Reinthaler

Posts: 110
Registered: 12/6/04
Mathematical Thinking
Posted: Nov 20, 1995 4:15 PM
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In a previous posting I mentioned that I felt that math teachers in the
elementary grades should be "mathematical thinkers" and should "see the
world mathematically". There were quite a few replys to this and it seemed
to me that my concept of seeing the world mathematically and theirs was
not at all the same.
Here are some examples of the kind of thing I was thinking of when
I wrote about seeing the world mathematically in the fifth grade.
The first year I taught 5th grade was 1988-89 and during the
school year, the date 6/7/89 occurred (it also turned out that it was one
kid's birthday). How often does it occur that a date is made up of
consecutive integers? How far apart are they? How close can they be
(it being close to the turn of the millenium, this was a particularly
interesting question)
In one 5th grade class, the teacher pinned a very long sheet of
graph paper across the front of the room with the date on the
horizontal axis and every day, the first student in the door got to plot
the time of sun-rise and sun-set on the graph. From time to time the
subject of the graph would come up in class and kids conjectured about
its evolving shape - what would happen if they plotted it for years -
looked at its symmetries (or lack of symmetries), thought about what the
distance between the two graphs (rise and set) meant, etc.
I team-taught for a year with a 5th grade teacher who was a
wonderful teacher but a professed math-a-phobe. I knew she had begun to
see the world mathematically when she came running into my class, the
next year, excited because she and the kids had realized that this was a
prime year (1993) and were thinking about whether there had been other
prime years in the decade and how they could decide, easily, whether a
number was prime.
One way the "experts" estimated the attendance at the
"million-man-march" was by assuming that the density was one person per 5
sq. ft. How dense is that? what does 5 sq. ft. look like? What does it
feel like to stand at that density? How much room does a kid need to be
comfortable? what does it mean to even ask that question? what is
volume all about? What is the volume of a kid? How many kids could fit
into the classroom (if they were very good friends) - suppose they filled
up the room all the way to the ceiling?
Anyway - these are the kinds of things I meant when I wrote about
seeing the world mathematically (at a 5th grade level)

Joan Reinthaler
Sidwell Friends School

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