Re: [MATHEDCC] Graphing Calculators

Martha Haehl (haehl@KCMETRO.CC.MO.US)
Wed, 9 Jun 1999 21:43:34 -0400

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Before responding to the discussion, I thought I would put out a =
math joke. If you don't like jokes about mathematicians, fast forward =
to the serious stuff.
=20
Joke:
Three statisticians went deer hunting. They had not been in the =
woods long until they spotted a deer. Two of the statisticians took a =
shot. One shot went about one foot in front of the deer and the other =
about a foot behind the deer. The third statistician gleefully =
exclaimed "We got it!"
=20
From previous post:
"How do young people learn mathematics? How should such knowledge =
(?) relate to the activities, expectations, and understandings of =
teachers."
=20
Certainly, the question of how people learn mathematics needs to be =
at the heart of all of our debates as well as in light of a changing =
world, what mathematics should be taught (since in any curriculum we =
barely scratch the surface of mathematical thinking or skills). The =
first time I incorporated graphics calculators into college algebra, I =
was most shocked by students who had decent procedural skills but very =
little understanding of the connection of graphs to the skills. I was =
further amazed how difficult it was for them to make the connections. =
Some rote memory, whether that be memorizing algebraic procedures or =
memorizing key strokes, will no doubt always be a piece of mathematics =
instruction. =20
=20
The problem with either a traditional or technology approach comes =
when the content of the course itself is predominately rote procedures =
and students are not expected to interpret and apply their knowledge to =
situations other than ones that follow specific templates. Such =
teaching may build short-lived skills, not it is not likely to build =
mathematical thinking. Some students get the skills and mathematical =
thinking in spite of the system. We're the ones who teach math.
=20
Martha

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Before responding to the = discussion, I=20 thought I would put out a math joke.  If you don't like jokes = about=20 mathematicians, fast forward to the serious stuff.
 
Joke:
Three statisticians went deer hunting.  = They had not=20 been in the woods long until they spotted a deer.  Two of the=20 statisticians took a shot.  One shot went about one foot in = front of=20 the deer and the other about a foot behind the deer.  The third = statistician gleefully exclaimed "We got it!"
 
From previous post:
"How do young people learn mathematics?  How should = such=20 knowledge (?) relate to the activities, expectations, and = understandings of=20 teachers."
 
Certainly, the question of how = people learn=20 mathematics needs to be at the heart of all of our debates as well = as in=20 light of a changing world, what mathematics should be taught (since = in any=20 curriculum we barely scratch the surface of mathematical thinking or = skills).  The first time I incorporated graphics calculators = into=20 college algebra, I was most shocked by students who had decent = procedural=20 skills but very little understanding of the connection of graphs to = the=20 skills.  I was further amazed how difficult it was for them to = make the=20 connections.  Some rote memory, whether that be memorizing = algebraic=20 procedures or memorizing key strokes, will no doubt always be a = piece of=20 mathematics instruction. 
 
The problem with either a = traditional or=20 technology approach comes when the content of the course itself is=20 predominately rote procedures and students are not expected to = interpret and=20 apply their knowledge to situations other than ones that follow = specific=20 templates.  Such teaching may build short-lived skills, not it = is not=20 likely to build mathematical thinking.  Some students get the = skills=20 and mathematical thinking in spite of the system.  We're the = ones who=20 teach math.
 
Martha
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