Oct 31 2012: Yes, using technology may give rise to understanding concepts, hence teachers teach students about using calculators, online graphing tech or SAGEMATH (which I suggest everyone use).
But the question is not the general understanding of math. It's the usage of tech when doing homework. At this stage, homework is used to reinforce concepts and make students apply their new-found knowledge. In this sense, tech plays a smaller role because it can only verify answers.
Oct 28 2012: No, students should never rely on technology for homework. By relying on technology, students create the harmful dependence relationship that flunks boatloads of students on tests simply because they cannot work independently on problems aimed to test the understanding of mathematical knowledge and the development of mathematical thinking. Students should rely on innate abilities to do homework, only using technology on occasion as tools to further expand on mathematical self-discoveries or ideas.
Take the analogy of a mechanic. In his toolbox is a variety of tools that he uses to do useful work. Yet he doesn't carry a wrench in his hand 24/7 nor does he tighten every bolt he sees with that wrench. Similarly, students should not be armed with a calculator and Yahoo! Answers to finish math homework by plugging in numbers and equations into calculators or cut&paste answers online into their homework. In the short-term, they do work, but in the long-term, they aren't doing useful work.
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A reply on Conversation: Debate: Should students rely on technology for their homework?
But the question is not the general understanding of math. It's the usage of tech when doing homework. At this stage, homework is used to reinforce concepts and make students apply their new-found knowledge. In this sense, tech plays a smaller role because it can only verify answers.
A comment on Conversation: Debate: Should students rely on technology for their homework?
Take the analogy of a mechanic. In his toolbox is a variety of tools that he uses to do useful work. Yet he doesn't carry a wrench in his hand 24/7 nor does he tighten every bolt he sees with that wrench. Similarly, students should not be armed with a calculator and Yahoo! Answers to finish math homework by plugging in numbers and equations into calculators or cut&paste answers online into their homework. In the short-term, they do work, but in the long-term, they aren't doing useful work.