Devoted Reader Hovav S. sent me a link to a Stanford Report article (an official Stanford University publication) entitled "How Urban High Schoolers Got Math." What both Hovav and I find fascinating is that the word "got" is open to interpretation here:
A group of disadvantaged Bay Area high school students who learned mathematics by discussing open-ended problems in mixed-ability groups outperformed wealthier teenagers placed in tracked, traditional classes, according to a new School of Education study. Their performance on state-mandated tests, however, was less encouraging.
See what I mean? They're outperforming wealthier teenagers on the one hand -but the results aren't showing up on the state exams. So did they really "get" the math? Let's see:
Students from a school called "Railside," a pseudonym for an urban school with a 77 percent Latino, African American and Asian/Pacific Islander population, entered freshman year achieving at significantly lower levels in mathematics than students at the other two Bay Area schools, according to the study's tests. These more affluent schools included "Hilltop," the pseudonym for a rural school with a half white, half Latino population, and "Greendale," a school in a coastal community with an almost all-white student body...
Within two years...Railside students were "significantly outperforming" the students at the other two schools in tests designed by the study. By junior year, 54 percent of Railside students said they enjoyed math "all or most of the time," compared to 29 percent of students at the other schools...
Certainly, it's not a bad thing if students are enjoying math a great deal - that's a worthy achievement for any school.
Keith Devlin, a consulting professor in mathematics, said the study's results do not surprise him. "Good teaching is not just about teaching the tools, but teaching students how to use the tools," he said. "Learning math is about developing our mental capacity to a point [that] when faced with a new problem involving mathematical thinking, we know how to go about solving it. You can't get away from drill, rote and practice, but then you have to develop the skills for using the tools well."
So far, so good...
...the results include a caveat: Although Railside students performed well on the study's tests as well as end-of-year exams administered by the high school district, they fared relatively poorly on the state's standardized tests.
What gives? Jo Boaler, the education professor involved in the study, reaches the pat conclusion that that standardized tests must be biased. Not only is that the easy way out, but it doesn't even make sense. Doesn't wholesale bias against minority students rest on the assumption that those students were deprived of the chance to learn anything having to do with the construct being measured? But here, they're learning math. They like math. The test items don't know the ethnicity or family income of the examinee. Why is bias the chosen explanation, as opposed to the more-believable concept that even though these kids are learning math, there's still more on the tests that they aren't learning?
Of course, to really answer that last question, we'd have to know how the state tests differ from the study tests that show these students doing so well? If that were clarified in the article, then the reader could make his own conclusions. Without that information, the reader is left to wonder whether the study items are any good.
Boaler argues that the state tests gauge English-language comprehension as much as mathematical competency. "The tests use complicated terminology, terms that kids have never heard of and, when you put them into schools like this one with [English] language learners and minority kids, they don't do well," she said. "For example, kids came out of these tests asking, 'What's a soufflé?'"
I agree that items on math tests should stick to measuring math constructs, but it's not unheard of to have English comprehension items in there as well. What's more, why are minority kids not expected to learn this complicated terminology, especially the native students? It's great that they're learning math, but if the tests suggest that they're not learning English, isn't that something we'd want to know?
Bottom line, though, is that keeping English comprehension to a minimum on a math test is preferable.
Brad Osgood, a professor of electrical engineering with a courtesy appointment in education, does not question Boaler's results. However, he added, if the study's findings do not match up with the state's, each party may have to find middle ground. "You need technical skills, there's no doubt about that," he said. "But no curriculum is a replacement for inspired teaching. If this helps teachers get excited, that's a good thing."
Not a bad way to reach a compromise. Certainly better than assuming the state tests are worthless. If the kids are excited and want to study math later on, that's spiffy.
Hovav also mentioned that Boaler's articles are pretty dismissive of standardized tests. She gives examples of her math items, vs. SAT-9 items:
Consider, for example, two of the questions from our assessment, directly assessing the mathematics in the California standards...
1. Here is a rectangle. The sides are 2x + 4 and 6 units. [Image omitted]
a. Find the perimeter of the rectangle. Simplify your answer if possible.
b. Find the area of the rectangle. Simplify your answer if possible
c. Draw and label a rectangle with the same area that you found in part b, but with a different length and width.
2. Solve the following equations:
a) 5x - 3 = 101
b) 3x – 1 = 2x + 5
...By contrast, consider this question from the SAT-9 test for students of the same grade:
'A cable crew had 120 feet of cable left on a 1000-foot spool after wiring 4 identical new homes. If the spool was full before the homes were wired, which equation could be used to find the length of cable (x) used in each home?
F 4x + 120 = 1000
G 4x – 120 = 1000
H 4x = 1000
J 4x –10000 = 120
Now we have something to work with. Boaler's items are clear, straightforward, and require no additional English comprehension outside of mathematical terms. The SAT-9 item does require students to understand the context and know what spools and cables are. I have to say I like Boaler's items better, and I find this amusing, because her items are much more like traditional math items that focus on narrow applications and strict rules. The SAT-9 item, on the other hand, fits much more with the "progressive" math ideology that says all concepts must be displayed in a context to show that students can apply rules in different situations. Of course, for them to be able to do so, all students have to understand the English in the item.
If Boaler's argument is that we should do away with all the frou-frou surrounding math instruction and math items and make sure students are heavily drilled in mathematical concepts, I'm all for it. I agree with her item analysis much more than I agree with her allegations of stereotype threat.
Posted by kswygert at February 8, 2005 09:34 AM