Jonathan at http://infinitesums.com/ wrote: "... There were no in class examples like it. Though I did mention that the largest exponent has control of behavior throughout the course of the material. ... Now the conundrum: is this a good test question because it showcases who internalized the concept completely? Or a bad test question because the answer is so obvious to me, the seasoned veteran, and hahaha can you believe these inexperienced teenagers are no match for me?"
0) Thank you Jonathan for sharing this information. 1) There need not be an example for every eventuality of any given math concept for we must leave room for students' brains to remain active and at edge.
2) Mentioning something does not necessarily mean students grasped it but it would be better if the students be expected to pull the leading term out and use limits over and over again to internalize the inevitable rule. I noticed that the student did not show the limits approach in the sample shown, which means she/he just memorized the rule rather than understood its essence.
3) I think the question is good question for it helps us as well as the student to reexamine the essence of the concept at hand.
4) A former student of mine discovered a cool method to deal with these kind of problems while taking one my tests on the same subject. He figured that given any problem of this nature, he would have to always write both numerator and denominator Polynomials in such a way that they would always be in descending order and he would supply zero coefficients if necessary to match the upper and lower Polynomials degree-wise. This enabled him to always have only one rule to work with, namely that of equal degrees. He presented this to the class and everyone adopted it and started calling it Gordy's method. Pass this along to your students and let me know how it plays out.
0) Thank you Jonathan for sharing this information. 1) There need not be an example for every eventuality of any given math concept for we must leave room for students' brains to remain active and at edge.
2) Mentioning something does not necessarily mean students grasped it but it would be better if the students be expected to pull the leading term out and use limits over and over again to internalize the inevitable rule. I noticed that the student did not show the limits approach in the sample shown, which means she/he just memorized the rule rather than understood its essence.
3) I think the question is good question for it helps us as well as the student to reexamine the essence of the concept at hand.
4) A former student of mine discovered a cool method to deal with these kind of problems while taking one my tests on the same subject. He figured that given any problem of this nature, he would have to always write both numerator and denominator Polynomials in such a way that they would always be in descending order and he would supply zero coefficients if necessary to match the upper and lower Polynomials degree-wise. This enabled him to always have only one rule to work with, namely that of equal degrees. He presented this to the class and everyone adopted it and started calling it Gordy's method. Pass this along to your students and let me know how it plays out.
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