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unanimous on explicitness
Posted:
Aug 7, 1997 2:58 PM
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In my earlier note I suggested that learning problems might arise from
lack of explicitness in writing some expressions:
> 1 Dropping the sign for multiplication (*) between two numerical
> expressions or between a number and a variable name and depending on a
> space or juxtaposition or a fence (parens, brackets, braces, etc) as an
> implicit indicator of multiplication. We don't do this with +, -, or
/.
> Of course once we understand the math we can abbreviate, depend on
rules
> of precedence, etc to make our expressions as short as possible -- but
> should we do this for students while they're learning the maths?
>
Tad pointed to another example:
Actually, in a mixed number, we add the whole number part and the
fractional part to get the actual quantity. Technically this may not be
an operation case, but I have heard that some students were confused
about this.
And Terry confirmed the hypothesis:
You've heard right, Ted. Tho we think of a mixed number as a natural
sort of thing, many students in my experience DO get confused about the
juxtaposition of a whole number and a fraction, esp. after beginning a
study of algebra when juxtaposition DOES imply multiplication. And I
think a case could be made for a mixed number being "operational".
There's also the tendency to interpret the expression "3a" incorrectly
when evaluating it, for example, when "a = 5". Many of my students
simply write "35" and think of it as "thirty-five". They just take the
easy way out and don't think. Terry Trotter
***************************************************
Case closed; the problem exists, the solution is obvious, let's declare
victory and get on with it. I suspect that the group is ready to vote
unanimously in favor of a no-holds-barred campaign to get all school
textbook publishers to henceforth write all mixed fractions with a plus,
as in 3+1/7, and to always put in the multiplication sign, as in
16*timesec^2 and 3.5*b*c. But first a question, has this experiment
been tried before?
Ladnor Geissinger
Math Prof at UNC Chapel Hill & Math Chair at IAT
email: ladnor.iat@mhs.unc.edu
or ladnor_geissinger@unc.edu
phone: 919-405-1925
address: Institute for Academic Technology
2525 Meridian Parkway, Suite 400
Durham NC 27713 USA
IAT phone: 919-560-5031
IAT fax: 919-560-5047
IAT web home page: www.iat.unc.edu
LEARN NC home page: www.learnnc.org
Mathwright Library: ike.engr.washington.edu/mathwright/
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