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Topic: FOIL, mnemonics, and all that
Replies: 12   Last Post: Sep 4, 1996 2:23 PM

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Kreg A. Sherbine

Posts: 26
Registered: 12/6/04
Re: FOIL, mnemonics, and all that
Posted: Aug 30, 1996 3:48 PM
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I'm planning to capitalize on the notions that Judy and others have made
explicit, i.e., that kids often have good intuitions about things but are
unable, or unwilling, to express those intuitions in terms of the
conventions that mathematicians and experienced doers of mathematics use.

Next week-ish I'll be starting a unit on statistics via a problem setting
that I hope will have meaning for my kids. Their task will be to develop
a presentation for a buyer for a local department store chain that will
give that buyer an accurate representation of what seventh graders would
buy and wear. In the course of the unit we'll cover data collection
(surveys, random samples, etc.); data representation (different types of
graphs, charts, tables, etc.); and data analysis (measures of central
tendency, interpreting pre-existing data, etc.).

I'm fully counting on my assumption that my kids, much like Judy's, will
have fairly strong and fairly reasonable ideas about what we're doing
even before we start. One of the biggest parts of my job, then, will be
not to present new concepts but to help my kids make their existing
understandings coherent to themselves and, in this case, to an outsider.
In the course of this work I fully expect that some of what we do will be
foreign to some kids initially. When such situations arise I'll do some
direct instruction if necessary or, more likely, will ask for those who
do understand to explain it in their terms. Again, my task will be to
help guide the kids toward speaking, writing, and (eventually) thinking
in ways that fit with conventional mathematical representations.

In all this I'm assuming some notions of fairness (for survey purposes)
and magnitudes of numbers (for representation and analysis purposes) on
the parts of my students. These are hard things even for adults to
express, so I expect that there will be many situations in which the
students will say that they "just know," without being able to articulate
their own understandings. Hence this is one of my explicit objectives:
to help my students develop the ability to know and to say what they're
thinking.

Kreg A. Sherbine | To doubt everything or to believe
Apollo Middle School | everything are two equally convenient
Nashville, Tennessee | solutions; both dispense with the
sherbine@math.vanderbilt.edu | necessity of reflection. -H. Poincare






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