Joanne Jacob's roundup of education news is up at the Jewish World Review site.
I had missed the story on "naked math" that appeared in the Chicago Tribune (payment required for access). No, it's not what you think. The math items on the latest state exam are allegedly "dumbed down" by being stripped of their word-problem formats. Some math educators are horrified:
"The message they will send out to teachers is ..., 'Pay attention to this because this is what you're going to be tested on,'" said Philip Wagreich, director of the Institute for Mathematics and Science Education at the University of Illinois at Chicago. "It's not uniformly horrible, but the main thrust is back- to-basics--multiple-choice questions emphasizing routine tasks, rote memorization and computational skills."
And this is a problem why? If kids haven't mastered these skills, how can they master the more sophisticated math concepts? Say what you will about a return to basic skills in, say, reading or writing, but mastery of math is extremely dependent on mastery of rote memorization and computation skills.
Illinois is under the gun to revamp its testing by the 2005-06 school year because of federal reforms that require all states to test every child, every year, in grades 3 to 8 in reading and math. The state's current exam for elementary pupils, the Illinois Standards Achievement Test, measures reading and math skills only in grades 3, 5 and 8...
Depending on which company the state selects, the new test would be an adaptation of the Iowa Test of Basic Skills, the Stanford Achievement Tests or the TerraNova tests.
It is this change that is drawing the ire of math educators, who rallied in meetings and on Internet message boards after the state released its proposed design for new tests in math, reading, writing, social science and science. The proposed tests for the other subjects have not drawn the same controversy, state officials said.
In one letter to State Supt. of Education Robert Schiller, signed by 40 professors and teachers, educators argued that the new test design represents a "radical departure" from the current state math standards and an abandonment of the reasoning and problem-solving skills that have been emphasized in classrooms over the last decade.
Do these educators really believe that the emphasis on "problem-solving" skills at the expense of basic knowledge has produced a generation of math-savvy kids?
For example, 20 percent of the test questions will be "naked math"--number problems that have become a dirty word for math educators who believe the subject is meaningful to students only when it is taught and tested in the context of real-world situations.
Horse puckey. A kid who needs context to understand a computational issue doesn't really understand the issue, and it goes against the entire point of education to claim that kids can't be expected to understand any concepts that aren't tailored to them. Students should be able to understand how to compute (per the example in the article) 7 percent of 350 without having the context of figuring 7% sales tax on a $350 DVD player. There's nothing wrong with showing examples to explain when computation of percentages is useful in real life, but if a student really understands percentages, then he'll know when to use them.
"This [back-to-basics] document ignores the last 20 years of what people have been doing in mathematics instruction," said Zalman Usiskin, director of the University of Chicago School Mathematics Project. "That's when we had students who could add and subtract, but they couldn't make change. They were never taught to tie the two together."
And what do we have now? I don't know about you, but I have yet to encounter a single cashier who could make change without the help of the cash register. I find it hard to believe that anyone who really has the mechanics of addition and subtraction down in their heads would be hard-pressed to make change.
The instructors fear that any change could reverse a steady improvement in math scores, especially in the younger grades. Last year, for example, 68 percent of 5th graders met or exceeded state standards in math, up from 61 percent in 2001.
Perhaps it would impede the improvement, perhaps not. It's hard to see how a back-to-basics approach to math can be harmful.
By the way, this is what they mean by "naked items" for third-graders:
What is the missing number in the following pattern?
94,__, 106, 112
A. 96
B. 98
C. 100
D. 102
This item requires the test-taker to examine the three numbers given in order to figure out the relationship among them. The nice thing about it is that is purely a measure of mathematical skills - relatively little is required in the way of reading skills. It's also very quick and cheap to develop and score.
Here's an open response item, which is what all those educators favor:
On Monday, Joe asked his mother if he could go with his friends to the movies on Friday. His mother gave him a list of chores and said he would have to earn the $5 to buy the movie ticket.
Babysitting his sister: 1 quarter an hour
Dusting: 1 nickel
Making his bed: 2 quarters
Washing dishes: 1 quarter
Cleaning his room: 1 quarter
Taking out the trash: 1 quarter
Sweeping the floor: 1 dime
Folding clothes: 1 dime
Make a plan for Joe to earn $5. List the chores he will need to do each day. Explain in words how you found your answer and why you did the plan the way you did.
Notice the reading load that accompanies this item; that's going to make things very difficult for ESL students and those who are already behind in reading. Notice that a written plan and list, plus an explanation, are required in order for the item to be answered correctly. This is an expensive item to develop and to score, not least because such a wide range of possible answers could be considered correct. Let's not forget that this type of item contains enough content that content balancing will probably be necessary; for every item about a Joe, there will have to be one about a Jill.
Can a test-taker say they hate washing dishes, so they'd plan for Joe to earn the money by doing other chores? Does Joe really have five days of bed-making available (doesn't that depend when on Monday his mom gives him this list)? If so, he can make $2.50 making his bed and then babysit his sister for 10 hours to make the other $2.50. But wouldn't 10 hours a week of babysitting seem like a lot to a kid?
(As Devoted Reader Doug S. points out in the comments: "When I first read the open response question, I thought the best answer was to take at least one nap per day and make the bed after each nap. I wonder how that would be scored? It violates one understanding of how the question should be read, but certainly seems to satisfy all of the stated rules.")
This isn't a bad item, but it is difficult, and it measures a lot of constructs other than pure math ability, and there's a lot of room for a kid to hang himself if he can't read well, can't write well, or comes up with a solution but can't really justify it. Therefore, it's not a given that this is a good item for a third-grade math test; it's not a given that it's a better item than one that simply measures whether a kid can combine 5's, 10's, and 25's to get a total of 500 (which is the actual math skill being measured).
If the point is to know whether a kid understands how to divide 500 by 5, 10, and 25, there are much simpler ways to go about it.
Posted by kswygert at January 19, 2004 09:21 PM