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Mathematical Thinking
Posted:
Nov 20, 1995 4:15 PM


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 198889 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 sunrise and sunset 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 teamtaught for a year with a 5th grade teacher who was a wonderful teacher but a professed mathaphobe. 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 "millionmanmarch" 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



