>There is a major philosophical difference inherent in this discussion. >Your philosophical belief as evidenced by the value that you place of >already created charts and posters is that there is a finite set of facts/ >information, that can be learned (generallly by memorization). Sometimes >people are not aware of the philosophical beliefs which they are acting >upon.
My point was more that many things that can be done in a low-tech way.
>My philosophical belief is that information is fluid, always changing, >infinite. That techniques that illuminate knowledge are of more value than >the specific facts and information.
>In otherwords the "decimal name/fraction name" facts are not nearly as >important as the techniques that the students develop to determine them,
I agree with this. As a software engineer, I have a strong interest in processes, techniques, algorithms and patterns. I'll go further in saying that a student can learn to develop his or her own algorithm or process in experimenting with a calculator. But I'll also state that much of this can be done without a calculator.
You stated that students could learn patterns/algebra using calculators given specific operations to perform. This could be done without calculators (we did this sort of thing when I went to school too). It could be done with the teach asking for volunteers or with the students working in small groups with at least on student strong in mental calculations in each group. For some, the calculators have the advantage, and for others the group approach has the advantage.
>If I felt the need to have a chart relating >this information I would expect each student to create their own.
Can fourth graders relate to rational numbers though?