Q&A #1659

Teachers' Lounge Discussion: Graphing calculators

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From: Paul

To: Teacher2Teacher Public Discussion
Date: 2003041015:14:22
Subject: Re: Graphing Calculators

The one surefire way to keep calculators under control is to disallow
them on tests while making the calculations all integers.  A student
should be able to find the integral of 3x^2 in their heads, and if
they show their work, they should have no trouble at all.  The art of
getting integer answers mainly lies in trying a problem, and modifying
the constants until the answer and all intervening steps contain only
integers.  If the students have trouble with integer arithmetic, then
consider some way of setting aside time to drill and quiz them until
they know how to add and subtract multi-digit numbers and multiply and
divide single digit numbers by multi-digit numbers.

Knowing every function that most graphing calculators have can help,
and here's an idea of what a state of the art calculator can do.

Graph: 2d, 3d, polar, parametric, and plot points

Statistics: Most elementary regressions, basic combinatorics, and

Calculus: Maclaurin and Taylor series, differentiate any function,
symbolically integrate any function that can be integrated with
elementary methods (Nothing beyond real analysis), and will
numerically integrate even more functions.  Also does sum and product
series, finds local maxima and minima, and arc lengths.

Algebra: Matrices, Vectors, Gauss-Jordan, Norms, Determinants, but
probably not Eigenvalues and Eigenvectors.  For single equations of
one independent variable, can solve for zero, simplify, expand, factor

Complex numbers: Fully supports all basic options, not certian about
prime factorizations of Gaussian Integers, but near certain in the

Other:  Hyperbolic trigonometric functions, boolean algebra, text,
geometry and basic programming.

Computer-based algebra systems like Mathematica can do everything
mentioned above, and then some.  Many math professors don't understand
all its capabilities, but there is absolutely no chance that some
student will be willing to pay $500 for such power.  Overall, most
students won't have the state of the art system, but they will have
one that can do most of what I mentioned above.  It's up to you to
decide how to handle these issues.


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