My thoughts follow this part of his message: > > The following exercises related to this skill are: > > 8. Estimate. Then use the square root table in Appendix B to approximate: > sqrt(0.003266 x 10^-18) > > 16. Simplify: 4sqrt(20,000) > > In Lesson 108, #6 emulates #8 above and #14 emulates #16. > > Et cetera until the ideas are cinched. Thank you, but I consider this
> to be primarily *conceptual* and exactly the level of conceptual and > computational competence that I expect students to have coming into the > university. Do you disagree? > > Wayne.
I think I would agree that the students would achieve a level of computational competence. But I would appreciate it if you could clarify some things for me. You must have a copy of Saxon's book (or your memory is way better than mine). Here's what I remember from the lesson I alluded to in my earlier post: the discussion did start with square roots of two and three digit numbers, but when numbers with more digits were introduced, I recall the instruction went along these lines (again, please correct me if I am mis-remembering).
To find, say, sqrt(500000000), the student was instructed to count the number of zeros (in this case there are 8). So the square root will have have 1 appended with half that number as a factor (i.e., 10000). the other factor will be sqrt(5), so the sqrt(500000000) = 10000*sqrt(5). If the number of zeros is odd, say, sqrt(700000), then take half of the largest even number of zeros (2 in this case is half of 4)) and append 1 with that number of zeros and multilply by the other factor still in under the radical. So, sqrt(700000) = 100*sqrt(7).
I don't remember the book providing any rationale for taking half the number of zeros to find a square root. If what I remember is correct, I cannot call this a conceptual development - the book is simply providing the student with a set of rules to be memorized and remembered.
Now, if I had been teaching this lesson (with or without a calculator), I would've made darn sure the students understood where these rules were coming from - maybe lots of teachers would. If that happened, then I think I'd feel more comfortable with the "conceptual competenece" part of your sentence. The teacher I observed that day back in 1985 shed no light on it. She simply read the rules from the book. Given the "warm body" criteria some school districts are forced to employ when it comes to hiring math teachers, I wonder how many of those would be able to fill in the gap left by the author. -- Mark Klespis, PhD Associate Professor of Mathematics Sam Houston State University Huntsville, TX 77341-2206 936.294.1577 - office 936.294.1882 - fax http://www.shsu.edu/~mth_mlk
"Everyone has a photographic memory. Some don't have film."