Circulation of West High School Calculus Exams in 2001

Lee Sensenbrenner:

As a sophomore at Madison West High School, Danny Cullenward tookCalculus 1, a yearlong advanced math class that put the only B on theotherwise straight-A student's transcript.

The same happened with Sam Friedman, the former captain of West's mathteam. Friedman, who is now at the University of Chicago, got two B's incalculus at West but went on, as a high school student, to get an A inadvanced calculus at the University of Wisconsin.Chris Moore, who is a junior at West and is already ranked among the top 30high school math students in the United States, also had trouble in his highschool course. He got a B when he took calculus as a freshman.

UW Professor Janet Mertz knows of all these cases, and cited them in aletter to administrators. She argued, as other parents have for more than ayear, that something is not right with the way calculus students at West aretested.

It's unfair, she wrote, and it's hurting students' chances to get intoelite colleges such as the Massachusetts Institute of Technology, for whichMertz interviews student applicants.

Fuzzy Math at West High: A Capital Times Editorial:

For more than a year, a group of West High parents have beencomplaining about the way calculus students at West are tested. This week theywent public -- voicing their concerns before the Madison School Board.The first complaint came from Joan Knoebel and Michael Cullenward, M.D., onbehalf of their son, now a senior at West. They decried the fact that KeithKnowles, West's calculus teacher, reuses old tests or parts of old tests thatare available to some -- but not all -- students.

According to the formal complaint, "students have obtained copies fromolder siblings, prior students, through study groups, private tutors, or by awell-defined grapevine." The school itself does not keep the tests on file.

School district administrators contend that Knowles did nothing wrong andthat there's no evidence to conclude that having access to old tests washelpful to students.

Doug Erickson:

George Kelly, English chairman at East High School, said teachers share thesame interests as committee members -- to ensure that students have access tothe tests they've taken and to make the playing field level for all students.But he said a districtwide policy would be cumbersome.

"There's a larger issue here," Kelly said. "How much micromanaging does theboard want to do in instruction and evaluation?"

West parent Joan Knoebel said Tuesday that the district continues to avoidthe real issue that her family raised, which is that a particular teacher atWest is not following the test return policy already in place at that school.Although she would like to see districtwide guidelines, she has neversuggested that the problem is widespread.

"(The district) is attacking this globally, when what you really have isone teacher who, in my opinion, is acting unethically," she said. "They'reusing an elephant gun to shoot a starling."

Joan Knoebel:

Common sense tells us that students with an advance copy of a test have asignificant advantage over their classmates. Assessment is meaningless underthese circumstances.This is the basis of our complaint. And this isn't just about one teacherat West. The decisions in this case emanate throughout the Madison SchoolDistrict.

What's the teacher's job? To teach the principles of calculus and to fairlyevaluate whether his students learned the math. He undoubtedly knows the math,as some former students enthusiastically attest. However, because old examswere not available to all, the only thing his tests reliably measured is whoma student knows, not what a student knows.

And -- this point is critical -- he also couldn't tell whether the tests heconstructed, or copied, were "good" tests. A good test is one a well-preparedstudent can complete successfully during class time. Think of it this way.Assume there were no old tests to study -- all students were on a levelplaying field. The teacher gives a test. No one finishes or gets a high score.Did no one understand the material? Possibly, but many of these hardworkingstudents come to class prepared. The better explanation is that there was aproblem with the test itself; for example, it was too long or too complex tofinish within the time limit.

This mirrors the experience of students who didn't study the old tests.Unfortunately, they were sitting alongside classmates who'd seen an advancecopy and could thus easily finish within the class period.

Ten years ago, West High enacted a test return policy. Why? Because thiscalculus teacher, among others, wouldn't give the tests back. The policy was acompromise to give families a chance to review tests, but only underconditions that gave teachers control against copies being handed down.

This calculus teacher had a choice: offer in-school review, as is done atMemorial High, or let the tests go home under tight restrictions, including awritten promise not to copy or use them for cheating. After this policy washammered out, he elected to return his tests unconditionally yet continued tore-use his tests. The district says that was his prerogative.

What was the administration's job here? To conduct a fair formal complaintprocess and to ensure that assessment is non-discriminatory. The "outsideinvestigator" the district appointed is a lawyer who together with her firmroutinely does other legal work for the district. Had we known of thisconflict, we wouldn't have wasted our time. In reality, the administration andits investigator endeavored mostly to find support for the foregone conclusionthat a teacher can run his class as he wishes.

We greatly appreciate our children's teachers, but with all due respect,autonomy does not trump the duty of this teacher, the administration and theboard to provide all students with a fair and reliable testing scheme.

The only remedy the district offers is to let students repeat the course,either at West or at UW-Madison at their own expense -- $1,000 -- andsubstitute the new grade. This isn't a genuine remedy. It punishes studentsfor a problem they didn't create. Furthermore, it is only truly available tothose who can afford UW-Madison tuition and the time.

What was the School Board's job? To tackle public policy -- in this case,non-discriminatory assessment. With one brave exception, the board ducked, andchose to protect the teacher, the administration and the union -- everyoneexcept the students.

The solution is easy. If teachers are going to re-use tests or questions,safeguard them using the test return policy or make an exam file available toall. Otherwise, write genuinely fresh tests each time.

After 14 months of investigation and a 100-plus page record, it's worsethan when we started. Now the district says that this teacher, any teacher,can re-use tests and give them back without restriction, and that it isperfectly acceptable for some but not all students to have copies to preparefrom.

For six months, we sought to resolve this matter privately and informally,without public fanfare. Confronting the dirty little secret of the calculusclass didn't sully West's remarkable national reputation, but openly paperingit over surely does. Simply put, this teacher didn't do his job. Theadministration and six board members didn't do theirs, either. "Putting kidsfirst" needs to be more than just a campaign slogan. -->

In the Madison West High calculus class, tests are the only way astudent is evaluated -- not by quizzes, homework or classroom participation,just tests. The teacher admits he duplicates or tweaks old tests. He knew somebut not all students had copies, yet he wouldn't provide samples or an examfile.

Common sense tells us that students with an advance copy of a test have asignificant advantage over their classmates. Assessment is meaningless underthese circumstances.This is the basis of our complaint. And this isn't just about one teacherat West. The decisions in this case emanate throughout the Madison SchoolDistrict.

What's the teacher's job? To teach the principles of calculus and to fairlyevaluate whether his students learned the math. He undoubtedly knows the math,as some former students enthusiastically attest. However, because old examswere not available to all, the only thing his tests reliably measured is whoma student knows, not what a student knows.

And -- this point is critical -- he also couldn't tell whether the tests heconstructed, or copied, were "good" tests. A good test is one a well-preparedstudent can complete successfully during class time. Think of it this way.Assume there were no old tests to study -- all students were on a levelplaying field. The teacher gives a test. No one finishes or gets a high score.Did no one understand the material? Possibly, but many of these hardworkingstudents come to class prepared. The better explanation is that there was aproblem with the test itself; for example, it was too long or too complex tofinish within the time limit.

This mirrors the experience of students who didn't study the old tests.Unfortunately, they were sitting alongside classmates who'd seen an advancecopy and could thus easily finish within the class period.

Ten years ago, West High enacted a test return policy. Why? Because thiscalculus teacher, among others, wouldn't give the tests back. The policy was acompromise to give families a chance to review tests, but only underconditions that gave teachers control against copies being handed down.

This calculus teacher had a choice: offer in-school review, as is done atMemorial High, or let the tests go home under tight restrictions, including awritten promise not to copy or use them for cheating. After this policy washammered out, he elected to return his tests unconditionally yet continued tore-use his tests. The district says that was his prerogative.

What was the administration's job here? To conduct a fair formal complaintprocess and to ensure that assessment is non-discriminatory. The "outsideinvestigator" the district appointed is a lawyer who together with her firmroutinely does other legal work for the district. Had we known of thisconflict, we wouldn't have wasted our time. In reality, the administration andits investigator endeavored mostly to find support for the foregone conclusionthat a teacher can run his class as he wishes.

We greatly appreciate our children's teachers, but with all due respect,autonomy does not trump the duty of this teacher, the administration and theboard to provide all students with a fair and reliable testing scheme.

The only remedy the district offers is to let students repeat the course,either at West or at UW-Madison at their own expense -- $1,000 -- andsubstitute the new grade. This isn't a genuine remedy. It punishes studentsfor a problem they didn't create. Furthermore, it is only truly available tothose who can afford UW-Madison tuition and the time.

What was the School Board's job? To tackle public policy -- in this case,non-discriminatory assessment. With one brave exception, the board ducked, andchose to protect the teacher, the administration and the union -- everyoneexcept the students.

The solution is easy. If teachers are going to re-use tests or questions,safeguard them using the test return policy or make an exam file available toall. Otherwise, write genuinely fresh tests each time.

After 14 months of investigation and a 100-plus page record, it's worsethan when we started. Now the district says that this teacher, any teacher,can re-use tests and give them back without restriction, and that it isperfectly acceptable for some but not all students to have copies to preparefrom.

For six months, we sought to resolve this matter privately and informally,without public fanfare. Confronting the dirty little secret of the calculusclass didn't sully West's remarkable national reputation, but openly paperingit over surely does. Simply put, this teacher didn't do his job. Theadministration and six board members didn't do theirs, either. "Putting kidsfirst" needs to be more than just a campaign slogan.

Lee Sensenbrenner: Former Students Defend Teacher:

After hearing West High graduates who had returned home for winterbreak defend their former calculus teacher, the Madison School Board decidedit would seek the advice of department heads before potentially changing anypolicies on math tests.

Noah Kaufman, a freshman at Dartmouth College, told the board Monday nightthat complaints against calculus teacher Keith Knowles -- who parents sayrepeated exam material without providing universal access to the old tests --were "entirely unreasonable.""Had I memorized numbers and calculations from old exams, and passed themoff as my answers, I would have failed my class, without question," Kaufmansaid.

"Mr. Knowles did not use the same questions on different tests. What he diddo was ask questions that involved similar applications of the concepts. Allof these concepts were explained thoroughly in the textbook, as well as by Mr.Knowles himself.

"A student could have access to the concepts and examples of applicationsby simply doing the homework and paying attention in class."

Doug Erickson:

arents of a Madison West High School senior urged the School BoardMonday to make sure that teachers who recycle exams from year to year also tryto keep copies of the old tests from circulating among students.

Either that, or a sample test should be made available to all studentsequally, said Joan Knoebel.She said her son, Danny Cullenward, and other students were at adisadvantage during several semesters of advanced math, because the teacherrecycled tests even though he knew that some but not all students had accessto old copies. Danny said that when he privately asked for help, the teachertold him to find old tests but refused to supply them.

Said his mother: "Exams should be about what you know, not who you know."

She said her son, a National Merit Scholarship semifinalist, becamesuspicious when some students breezed through the exams while he struggled tofinish on time.

Posted by Jim Zellmer at May 6, 2004 4:48 PM
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