Teacher2Teacher |
Q&A #1659 |
From: Paul
To: Teacher2Teacher Public Discussion
Date: 2003041014:14:22
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 probability. 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 future. 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. --Paul
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