To tell you the truth, I don't really have a problem with my state's math standards (here and here). I do, however, have a serious problem when the standards become the target rather than the scope through which we aim at the target. So what's the target? What should be the point of math education today? It has become very clear to me that it has never been easier to find correct answers to anything rooted in computation. With WolframAlpha, GeoGebra and all the other resources available, there probably isn't a question we could ask a student where they couldn't quickly look up an answer. When I first started teaching, the big question was whether or not we should let our algebra students use a calculator. A lot of the "veteran" teachers were dead set against it because they "gotta add, subtract, multiply and divide, for cryin' out loud." But the calculator would allow a student to speed up all the calculations (read arithmetic) and get to the "math." Well can't the same be said for WolframAlpha or GeoGebra? Don't these tools give students access to certain problems where previously they would have been bogged down by calculations they couldn't complete?
I remember when basic skills were being able to perform the four operations over the Real Number system. What's a basic skill look like today? Is algebra the arithmetic of the 21st century?
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I couldn't agree with you more. I think we are witnessing the emergence of Algebra as the standard of math knowledge and understanding for every student. We should be incorporating these tools into our curriculum rather than prohibiting them. I heard a great teacher once say that calculators are absolutely necessary for teaching multiplication when everyone else was demanding that students memorize the facts. The teacher insisted that the calculator would help the students get the answer right every time, whereas the answers that the students produced from memory are often suspect.
It seems to me that you are somewhat missing the point of the veteran teachers argument against calculators. Yes, technology can speed up calculations; however, they can also be used prior to understanding the calculations themsleves. How is a student going to understand more complex issues if they do not even understand multiplication? Many of us can recognize an incorrect answer because we have some number sense and can computationally estimate the answer. Do students that solely rely on calculators have this same ability?
The bottom line is that technology is a tool that can be used to teach or to speed up computations that one already understands. Technology should not be used in place of learning.
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