email@example.com (Herman Rubin) wrote: <much snipped> >>I heartily disagree here. Everything that I have witnessed as a >>teacher tells me that there is a very strong correlation between good >>arithmetic skills and the ability to proceed further in mathematics.
>Have you even considered teaching in such a way that arithmetic skills >are not required for a satisfactory performance? The old-fashioned >geometry course did this; it used to be the introduction to mathematics.
I haven't taught geometry for seven years, but when I did there was almost no arithmetic until the second semester. And the bulk of that came in a unit that dealt with areas, surface areas, and volumes (there was also a little arithmetic in a unit that introduced right triangle trig functions). What I noticed was that those students who had the most difficulty with logic and proofs also had difficulty with computations and were the first to grab their calculators (yes, I allowed them).
> I don't know if there is truly a cause and >>effect relationship, or if those who have one aptitude also tend to >>have the other. But I cannot envision how having good arithmetic >>skills could be detrimental, but I am absolutely certain that a lack >>of them is!
>There is probably a correlation.
>Try teaching algebra and geometry WITHOUT requiring the use of >arithmetic. Having good arithmetic skills may be a problem, in >that it can make it harder to grasp the concepts.
I have taught geometry without using arithmetic. On the other hand, I see much of algebra as an abstraction of arithmetic. Perhaps that is my blind spot here, but I cannot envision explaining much algebra without a solid arithmetic base to build upon. I certainly have never seen it done at either the secondary or collegiate levels. (And it is probably pertinent to reiterate that at my alma mater, secondary math ed students are in the math department, not the College of Education. All but the student teaching class involved straight math majors and math ed majors. That was the primary difference in the two programs.)
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| Thomas W. Cowdery When I die, I want to go peacefully in firstname.lastname@example.org my sleep like my grandfather did. email@example.com Not screaming like the passengers in his car. ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||