### The Challenge Problem

Every Friday, the sheet comes home in my son's backpack: "If Sue is a truck driver who needs to deliver 57 cases of Diet Coke to Greensboro, but every 14 miles along the way she gets thirsty…."

Although my 35 years' absence from Algebra I makes me a poor judge of difficulty, I've talked to enough scientist dads and engineer moms to know that when the middle school Math Department calls these weekly assignments "challenge problems," they're not kidding.

By my son's teacher's estimation, about 50 percent of her students can solve these demons on their own. My son, who may have a tendency to over-generalize from a small sample, claims that four or five students in his class of 25 actually "do the math" themselves.

But assuming that the teacher is correct, what is the Math Department's expectation about how the other 50 percent will approach this homework? Some, they assume, will get assistance from their parents. Others will seek extra help from the teacher. Still others will collaborate; they will work together. All of these options are deemed acceptable.

What happens in practice? Those fortunate enough to have a scientist dad (like my son) or an engineer mom give their parents a chance to brush up on their algebra. A few students stay after school for teacher assistance. Some work together. Too many spend the lunch hour before math class copying someone else's answer to the problem.

That such copying is cheating and that such cheating is wrong-these concepts are clear to me (and, thankfully, to my son). But I do wonder how clear they are to the many students who engage in this activity. If the math is beyond them and they must have someone else walk them through the steps in order to solve the problem, how far is that from simply copying the steps? Where does collaboration end and cheating begin? And if collaboration is acceptable on these challenge problems, what is wrong with it on the everyday homework, or even on a test?

A 1998 survey at Rutgers University asked students, "On what aspect of academic integrity are you most unclear?" In overwhelming numbers, the respondents said "collaboration."
Rutgers Professor Donald McCabe, a leading researcher on academic integrity, conducted a nationwide survey of college students in 1999. He found that fewer than one in four students believed collaborating on an assignment was cheating, even when the instructor had specifically disallowed it. In an interview with Synfax Weekly Report, McCabe said, "Many students have convinced themselves that they learn more when working in groups (which is probably true), and thus, this is an acceptable strategy no matter what directions the instructor has given."

If such confusion seems disingenuous, consider the lack of unanimity reflected in these statements on collaboration, taken from various university honor codes and class syllabi:

• In science, collaboration is the norm. We stand to gain much knowledge and understanding and to perform better quality work by collaborating and sharing with others. I strongly encourage you to find one or two other persons in the class with compatible personalities with whom you can study, to whom you can pose questions that test your own ideas and understanding, and for whom you can explain and answer questions, thereby deepening your own understanding.
--Physics Class at Elizabethtown College

• Unless specifically permitted or required by the instructor, collaboration will usually be viewed by the university as cheating. Each student, therefore, is responsible for understanding the policies of the department offering any course as they refer to the amount of help and collaboration permitted in preparation of assignments.
--Honor Code, Carnegie Mellon University

• Collaboration on homework is permitted to an extent. Specifically, students are allowed to discuss the possible solutions to a problem. However, handing your work to someone so that they may see how a problem is worked or guiding a person through the problem step by step is not within the spirit of the collaboration policy or the honor code of the university.
--Collaboration and Honor Code Policy, University of Florida

Sisela Bok, whose book, Lying, is a modern classic on the subject, told U.S. News online, "People are very confused about what is meant by cheating." The article then continues, "The rules just aren't that clear, particularly given the growing number of schools that stress teamwork."

Perhaps part of the problem is fostering a "rules" approach to the subject. It is virtually impossible to write academic integrity rules that cover every permutation of cheating—especially as the technological gadgets of the dishonest now rival those of the CIA. Ban crib sheets, and you will not have covered beaming answers between Palm Pilots or answer-encoded pencils.

Though the technology has changed, the problem is an old one. I remember the director of the community center where I once worked telling her staff, "If we make a rule not to throw a brick through the window, the next kid will throw a stone."

The important thing is for kids to understand the reason behind the rules. For example, rather than trying to define collaboration and specifying which types are allowed, wouldn't it be better to talk with kids about what we hope they will learn from an assignment and from working on it together? If this challenge problem is meant to engage students in dialogue about math, let's distinguish that from other problem sets that are meant to give them practice with operations, or from tests that are meant to determine their individual mastery of the subject.

Such a conversation might also raise some questions for the adults involved about what we are asking children to do. What is the point of assigning a problem that 50 percent of the students will be unable to do on their own? How should we grade homework that we know many students needed help to finish? What sort of habits are we fostering by sending home assignments that presume the participation of parents?

• Might there be a relationship between these requirements and the troubling trends we see?

• Parents writing their children's college application essays
80 percent of college-bound youngsters reporting they had cheated in high school (Who's Who Among High School Students survey)

• More than 30 percent of college students finding nothing wrong with plagiarism (McCabe study)

If we could answer questions like these, we might eliminate some of the confusion young people are feeling about the nature of integrity at school and beyond.

Miriam Schulman is the director of communications for the Markkula Center for Applied Ethics.

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