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Tests Dumb Down Math: Too Much Emphasis on Basic Skills
As the state completes plans to expand its standardized testing program, prominent math educators are criticizing the proposed design, arguing that it will dumb down math instruction by focusing disproportionately on basic skills at the expense of analytical thinking.
"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."
The fact that the phrasing of test questions could stir such an uproar underscores the growing cynicism among teachers who fear that the relentless push for better test scores and standardized curriculum is harming classroom instruction.
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.
The State Board of Education is expected to decide this month which of three major testing companies will win the bid to handle the assessment program, which will cost $18 million a year.
As part of the process, state officials are asking that the revised tests measure not only how well students meet the state's learning standards, but also how well they measure up against national norms. That would allow individual school districts to use these results instead of administering national tests.
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.
Irate educators rally
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.
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.
Reinforcing life's problems
A question about percentages should not ask students to compute 7 percent of 350, they argue. Rather, students should be asked how much sales tax John paid on his new $350 DVD player--same math problem, but one that reinforces how the skill is used in everyday life.
"This 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."
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.
Critics also faulted the state for hiring an out-of-state consultant to design the tests instead of relying on the feedback of Illinois experts whose teaching will be shaped by this new generation of standardized tests. Wagreich, for example, was involved in creating the ISAT math test in the late 1990s, and Usiskin helped create an earlier state test.
State officials said criticism of the proposed math test is "just plain wrong." And given the time constraints imposed by the federal No Child Left Behind Act, it would have been impossible to return to the exhaustive collaboration with local educators that led to the creation of the ISAT, they added.
"The state test never reflects everything a child should know," said Lynne Curry, director of planning and performance for the state board. "This will not dumb down the curriculum. Good instruction is good instruction, and good tests are good tests, but these are not the same things. In a large-scale assessment, we're looking at an efficient way of measuring what kids know and are able to do at a point in time."
Teachers agree that, in an ideal classroom, tests would not dictate the scope of what children are learning. But now, especially given the pressures of No Child Left Behind, that ideal too often is abandoned.
"Even good teachers are going to be forced to teach to the test," said Angela Andrews, a national award-winning math teacher who works with struggling 1st graders in Naperville District 203. "And teachers who don't have a great passion for math will definitely give in because it's much easier to teach lower-level math skills, to have the kids memorize math facts. It's so discouraging to have worked so hard over the years and see this happen."
At the heart of the debate over the proposed math test is the heavy reliance on "number sense" questions and the expected elimination of open-ended questions where students must write out their answers and explain how they solved a problem.
Math experts said the inclusion of two open-ended questions on the ISAT had a dramatic impact on the way math has been taught in the last five years because teachers knew their students would be tested on their analytical skills.
But state officials said the questions were enormously expensive to score, compared with the computerized scoring of a multiple-choice exam. Curry said including two open questions for every grade on the 2006 math test would cost an extra $2.3 million a year, on top of the estimated $600,000 to distribute and score a multiple-choice math exam.
Officials also contended the questions didn't change results or provide any additional insight about students' math aptitude. Schiller is expected to make a final decision on whether to include open questions on the math and reading tests during a meeting Tuesday. According to the proposed test design, computation questions--covering concepts such as fractions, decimals, addition and division--will make up nearly half of the test for students in grades 3, 4 and 5. Questions that explore probability, statistics and data analysis will represent only 5 percent of the test for these grades.
Tests to be 10% analysis
In grades 7 and 8, about 60 percent of the test will focus on algebra and geometry, with 10 percent devoted to higher-order analytical skills.
Curry said the design reflects changes proposed by a committee of math educators who reviewed the proposal by the state's test-design contractor, AccountabilityWorks, during two meetings last spring. But some teachers involved in that process said the changes were superficial at best and failed to fix the fundamental flaws.
"The response to this was universal: We were horrified," said Sue Pippen, a 30-year suburban math teacher and one of 10 educators who reviewed the test framework. "What is valued should be tested because what is tested is what is taught. We felt it was a major step backwards."
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Proposed test design shifts problem-solving emphasis
Proposed Illinois math tests focus on computational or "naked math" questions, and reduce the number of "open response" questions--those that require students to think through a problem and show their work. Teachers and other critics say the change could lead to a dumbing down of math education in Illinois.
THIRD GRADE EXAMPLES
'NAKED MATH'
What is the missing number in the following pattern?
94, (underscore)(underscore), 106, 112
A. 96
B. 98
C. 100
D. 102
'OPEN RESPONSE'
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.
EIGHTH GRADE EXAMPLES
'NAKED MATH'
Which would result in the largest number?
A. 10(2nd power) + 30(2nd power)
B. 10(4th power)
C. 19 x 21 + 29 x 31
D. 25 x 36
E. 40(2nd power)
'OPEN RESPONSE'
You have six oak boards left over from a variety of projects. You plan to use these boards to make a bookcase. The boards are all one foot wide and vary in lengths as shown. Draw a diagram and label the dimensions of your bookcase. Explain in words how you designed your bookcase. Determine the total amount of shelf space. Explain in words how you found this amount and why the procedure you used is an appropriate solution process.
1' x 6'
1' x 8'
1' x 7'
1' x 4'
1' x 51/2'
1' x 71/2'
Source: Illinois State Board of Education
— Tracy Dell'Angela
Critics: Tests dumb down math
Chicago Tribune
2004-01-04
http://www.chicagotribune.com/news/local/chi-0401040332jan04,1,4350375.story?coll=chi-news-hed
INDEX OF OUTRAGES
Pages: 380
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