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Out in left field
In a post on the subject of grade deflation and extended response math tests, he writes:
The Pennsylvania Math Standards on which the Philadelphia public schools base their grades, in fact, include numerous non-mathematical factors: explaining in words, drawing pictures, manipulating objects. Perhaps my daughter's explanations and drawings aren't as elaborate as some of her peers'. Perhaps she doesn't complete hands-on tasks as quickly as others do. And perhaps her shyness and passivity keep her from making oral contributions that "demonstrate superior understanding of concepts, skills and strategies" and from "independently explor[ing] ideas and topics:" two of her report card's benchmarks for grades of 4.
It's of course way too early to say just how strong my daughter's mathematical talents are. But I can't help wondering how many math buffs are being lost in the new system, and what this means for both their future, and that of this country.
This worries me, too.
I went back and found this post Barry G made to the old ktm:
Here's a problem that appears in IMP for 9th grade It is known as the "Haybaler Problem"
“You have five bales of hay. For some reason, instead of being weighed individually, they were weighed in all possible combinations of two: bales 1 and 2, bales 1 and 3, bales 1 and 4, bales 1 and 5, bales 2 and 3, bales 2 and 4 and so on. The weights of each of these combinations were written down and arranged in numerical order, without keeping track of which weight matched which pair of bales. The weights in kilograms were 80, 82, 83, 84, 85, 86, 87, 88, 90 and 91. Find out how much each bale weighs. In particular, you should determine if there is more than one possible set of weights, and explain how you know.”
David Klein, a mathematics professor at California State University at Northridge comments on the problem. “The process of solving this problem made me resentful of the stupidity and pointlessness of it. There is nothing ‘real world’ about it. It is completely inappropriate for kids who likely have not been taught how to solve simultaneous linear equations, or exposed at most to two equations in two unknowns. If I had been given such problems at that age, I think that I would have hated math.”
Consistent with much of the philosophy of “real life math”, the goal of the exercise is to explore strategies and to be able to write about it. This is made apparent by the “student guide” that accompanies the problem. It is essentially a scoring sheet, containing categories, with points awarded for each, such as “Restate the problem in your own words” (4 points); describe all the methods you tried before reaching your solution(s) (4 points); describe the process that lead to your solution(s) (4 points); describe all assistance provided and how it helped you (2 points); state the solution (2 points); describe why your solution(s) is correct, include all supporting data (6 points). Out of a total of 50 points, only 2 are given for the solution. In fact more points are given for describing why the solution is correct.
Be sure to read his post explaining Why teach fractions?
3 comments:
"It is completely inappropriate for kids who likely have not been taught how to solve simultaneous linear equations, or exposed at most to two equations in two unknowns. If I had been given such problems at that age, I think that I would have hated math."
Well, in PSLE Singapore math, you had problems with 3 simultaneous equations (3 books, 2 pencils and 3 pens cost $9.40, 7 pens and 7 pencils cost $7.50, 4 books and ...) but you basically eliminated terms within four to six lines. Then don't forget the problems where beads are transferred to container to container, resulting in a "new ratio".
You can give this problem to 9th graders I think -- but it must be a "challenge" sort of problem, sort of like the Junior Math Olympiads, at the end of the assessment to reward the distinguished. This problem employs permutations, determination of possible multiple solutions on top of simultaneous equations so definitely the rubric is inadequate and too vague to be useful, as well as too inflexible to be useful (ironic, given its vagueness).
It is a theoretically interesting problem, and the tight range of the pairs does restrict the possibilities of individual weights.
What a great find!
I worry that we're going to create a generation (or several generations!) of kids who loathe writing.
People already have writer's block up the ying-yang; now, with all the process writing & the arbitrary grading via incomprehensible rubrics, I fear this will grow worse.
C, who is naturally inclined to like writing, had started to dislike it this year.
His social studies teacher reversed that with his step-by-step research paper assignment.
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