In the middle school >I am trying to get that kind of student to take responsibility for what >they learn/don't learn by using a sort of "mastery" approach wherein I >let them work on assignments in a chapter at their own pace until they >think they are ready for chapter test; if they pass the chapter test I'll >let them move on to the next chapter but not until they do. I do not >give them calculators because they are working on 4th to 8th grade >material (in an 8th grade class); I encourage them to get their own, and >use them in class, but don't let them use them on tests, of course.
This is a very good point you make. I would like to change the focus again(I believe Gary tried to point this out). Maybe if calculators are going to be used then we need to change what we are asking for. Computation has a perpose(less so now then say a hundred years ago) and students need to have some sort of understanding of what is going on but wrote arithmatic year after year after year(traditional elementary math) is really counter-prductive IMHO. Why not ask interesting questions in which students can use the calculator to explore and maybe the arithmatic will come into play as the exploration is continued(you would be surprised how often this happens). I am not saying do away with arithmatic, just to incorperate it into interesting problems and situations that can be done with the calculator(and the brain).
> >I don't think it is just fear of the new or unknown that keeps people >from going ahead rapidly into using technology extensively. It may be >that for some people (and society) there are big benefits from more >technology and for others (and society) there will be some losses. As >technology is so increasingly present we need to encourage students to >learn to use it without taking away the incontrovertable benefits of >learning to manipulate numbers and symbols with the brains that are able >to design and use new technology.
As the standards say we need to decrease the focus of minipulations and arithmatic drill not do away with(see above)
I believe that the best quantitative >and qualitative research in mathematics education shows that procedural >and conceptual knowledge develop together, and that people (in general) >need algorithmic experience in order to develop numerical understanding.
Your talking about over a hundred years(the last few decades of declining effectiveness) compared with less then 10 years of "standards" focus. hmmmm. How about giving it a chance? You might be surprised.
Remember: 1) we didn't grow up depending on calculators,
Why do people always say if it is good enough for us it is good enough for you? Has the calculator been around forever(maybe 20+ years). Who is to say that if it were around 20 years before you came along you wouldn't have a different oppinion? Just because you were not dependent on a calculator when you grew up does that mean the rest of the population wasn't? I just don't see this as a relavent point for students today!!
2) our >educational system is highly regarded around the world,
Uhhhh. How long ago was this? When you were going to school? Is it really still high regarded? Maybe I read different news papers then you do?
3) and we have >produced a highly creative and productive society with it.
What percent of our society would fit this? 10%? 20%? Is it really highly productive? I don't know.
If there >are voices that caution us not to throw the baby out with the bath waters >of reform, there may be good reasons for it.
Are we saying to do away with other methods? I think it is to de-imphasise not get rid of. If you read the standards you can see that clearly stated.
Scott Powell University of Hawaii University Labratory School 1776 University Ave. Honolulu, Hi. 96822 firstname.lastname@example.org