>Since I appear to be the only actual K-4 teacher who is currently reading >and responding to the list I would like to respond to this comment. This >is somewhat how the calculators 'are' used in our K-4 classrooms.
I've taught my son K-5 math so I have some experience though not math classroom experience.
>The students play games such as "Beat The Calculator" inwhich they race to >perform mental calculations more quickly than the calculator.
I assume that you put a person with the calculator against someone performing an operation mentally. This type of competition could be done without calculators as well by having several students compete. What you're really comparing is the speed and dexterity of one student against the mental speed of another.
>As a fourth grade teacher I also permitted students to figure out the >"decimal name" for various fractions. An interesting side effect to this >was that students performed this operation so frequently that by the end of >the year they could tell you pretty accurately the "fraction name" for a >decimal. (This type of inverse learning is typical when students use the >calculator.) This is a portion of "number sense", the ability to look at a >fraction and give it an approximate "decimal name" or look at a decimal and >give it an approximate "fraction name", is hard to find in the general >population,, but was common for the fourth grader who had been working with >the calculators.
In the fifth grade text that we used, the material involved converting back and forth among decimals, fractions, percents, ratios and proportions (in the section on Ratio, Proportion, and Percent); some simple relationships between fractions and probabilities in the Statistics, Graphing, and Probability Section; and the relationship between linear plots and fractions (slope).
Also, simply posting a conversion chart between fractions and decimals could accomplish the same purpose.
>Again, since I am actually in the K-4 environment and not just an outside >observer, I have at least 10 years worth of real classroom experience and >evidence that calculators 'are' infact beneficial in learning math. I will >however qualify that by saying, at least in our school district, students >are not using them as a crutch. It would be irresponsible of me, or any >other teacher for that matter to deprive students of opportunities to >think, and trust me when I say K-4 teachers would be the 'last group on >earth' to do this.
The text we use has lots of exercises with calculators although we seldom use them. We do have calculators around the house (arithmetic, reverse-polish and algebraic) that our son knows how to use. I like the idea of being able to go back and forth and agree that calculators are an easier way to do this. But we typically grind it out using division or going over the actual operations to find the inverse.
When I was in high school, I had two programmable calculators and I used them to program games and other mathematical trinkets (along with using them in science classes). My personal feeling is that teachers should have them available as tools as they may have particular students that could benefit from them. I'm interested in the debate because the curriculum committee that I'm on is stalled (at the school board level) over this issue. We have a ten-year-old curriculum that staff wants updated, and we also have a new set of standards from the State of NH (kind of a summary of NCTM and fairly readable). We would like to use the standards, especially as that's what the state's standardized tests will probably test on.