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Topic: RE: manipulatives
Replies: 2   Last Post: Apr 17, 1995 2:15 PM

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Dean Matthew Crawford

Posts: 2
Registered: 12/6/04
RE: manipulatives
Posted: Apr 17, 1995 2:15 PM
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How can a student truly say that he understands linear equations
if you do not force him to look at the graphic representation. Read the
newspaper and see how most information is represented. There are graphs,
charts, tables and many other ways used to display statistical data.
I dare to say that most people would better understand the shape of the
earth's orbit for example, when they see the graphic representation of
an ellipse with the sun as a foci; or the path of a kicked soccer ball as
a negative parabolic function; or the cost of operating a car as a linear
function of the number of miles it is driven.
Personally, I believe that if a student cannot see the relation
in a graphical sense, then the student does not completely understand the
concept. I never truly understood trigonometry until I was able to see
the functions graphed and manipulate those graphs through their
equations. In my personal experience, I suppose that graphing has
brought with it much understanding of the topics I learned but never
mastered a long time ago!
Dean Crawford
South Garland HS

On Tue, 11 Apr 1995 wrote:

> I view manipulatives as a substitute for real life and real life experiences.
> The best way to learn math is through real life experiences. I was brought
> up in an abundance of experience to help me learn math which in turn gave me
> the background to learn the abstract representation of math that we call
> 'Algebra'.
> I think that kids today don't have the kind of experiences that gives them
> the background needed to learn Algebra. I believe that is why manipulatives
> are so popular-manipulatives are a way of trying to fill in for that missing
> real life experience.
> Labs are another way of filling in those holes in experience. In my opinion,
> a better way. (I know, they're not always feasible.)
> Parents providing experiences is the best way!
> Manipulatives are not new, as nothing in education is new. They are a
> passing fad as most things in education are. A smart teacher will keep the
> good parts that work for him/her and his/her students and use them whenever
> appropriate.
> Now to attempt to open a can of worms. I also think that the current
> emphasis on graphing is a fad. The availability of cheap and powerful
> graphing calculators is a driving force behind this fad. I don't use graphs
> as a major way of learning or visualizing. I very seldom draw a graph to help
> me see what is going on. I think there are a lot of learners out there who
> don't need graphs to help them learn. Graphs and graphing calculators are
> another tool for learning that a wise teacher will keep and use when
> appropriate.
> Dan Kiernan

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