While these students are very different, they both have one thing in common-they have special needs, needs that are often difficult to meet in a traditional classroom setting. The Math Forum's Problems of the Week provide a unique opportunity for students to develop their problem solving and mathematical communication skills and to be mentored by an individual removed from their usual educational setting. Students have a personal relationship with a mathematician who judges them by their work alone, not by who they appear to be.
In the ten years since the program's inception, Problems of the Week (PoW) has evolved and expanded. This is the current process: After a student submits an answer, a mentor reads the submission and gives the student feedback in six categories-the completeness and correctness of their mathematics, the completeness and clarity of their communication, and how methodical and reflective they are in their problem solving. In each category, the student is judged to be a novice, apprentice, practitioner, or expert. Those achieving at least practitioner in all six levels get their name posted on the solution page for that problem.
A Program with Multiple Uses
Many teachers (and students) use the PoWs as a source of rich, non-routine problems. Some teachers have their students submit answers as practice for state tests, which increasingly include open-ended response questions.
A local middle school math supervisor told me recently that when parents come to her asking for advanced textbooks and harder work for their children, she first suggests the Problems of the Week as an appropriate resource. The student can work as far ahead as he or she is able and will receive help and feedback.
Many students are not working beyond their peers, but could, with a little prodding, move ahead more quickly or explore topics in more depth. Meeting this need is obviously difficult in the classroom because of the time it takes.
A less obvious benefit is that the PoWs offer an opportunity that many students have never had-that of being judged by their work alone. When I read student submissions, I know nothing about those students other than their name, age, and where they go to school (and even then we don't know that they're telling the truth!). Students can list the name of their current math class, but that's optional. I don't know whether they're considered good students, speak English as a first or second language, or are physically disabled. I know nothing of their skin color, socioeconomic status, home life, or friends.
PoW is an example of the truth of the famous cartoon published in the July 5, 1993, issue of the New Yorker in which one dog (sitting in front of a computer) says to another dog: -On the Internet, nobody knows you're a dog." When I am working on PoW, I only know what I read in the students' submissions.
For David and Natalie, the two students mentioned in the beginning of the article, having their solutions included on our site gave them status as mathematicians and that helped their peers to see them in a new light. I would not have known that either of them is any different from anyone else if their teachers had not written to me. I simply chose their submissions as good examples that I wanted to share with other students.
Because the product that I see from students is sent electronically, I don't have any idea how easy or hard it was for them to type their solution in or how long they spent working on a particular submission. Another big factor for some students: penmanship doesn't count! The only time I get additional information about a student is when one of them revises after I respond to a submission. Then I know how that person reacted to and incorporated my suggestions, but that's it.
A Safe and Flexible Environment for All
It should be noted that the distance-learning nature of the PoW can be an advantage not only for students, but for mentors as well. One of the Math Forum's mentors, a retired math teacher, relies on a wheelchair and no longer works in a traditional classroom. Armed with his computer and his Internet connection, however, he can still help students and continue to foster a love of mathematics in everyone he mentors.
Sometimes, adults submit answers to the PoWs. While some of these adults are simply people who love doing math and can't get enough of it (and sometimes get recruited as mentors!), I've talked with several people who were doing the PoWs because they were preparing for their GED or going back to school.
PoWs also give teachers the chance to explore mathematics that they're not familiar with or don't remember. Teachers often use the PoW archives, which has a mentor's comments highlighting different solution paths and common errors that students made as well as a selection of student solutions. Again, the online environment supports the teachers' learning without judging them. Teachers and other adults feel safer in the distance and anonymity of PoW, just as students with special needs do.
As is often the case, aspects of a project like the PoW that benefit students with special needs also benefit all students. As we look closely at meeting special needs, we can use the opportunity to reflect on our teaching in general.
Annie Fetter is the Problem of the Week supervisor.