A Math Forum Project

Elementary Problem of the Week: Mentor Information

I. Goals and Objectives

The Math Forum's Problems of the Week are designed to foster the growth of a mathematics community on the Internet. Mentors contribute to the elementary mathematics community by volunteering to reply to solutions submitted by students in grades three to six. Students discover the joy of exploring challenging math problems with someone outside their regular classroom. Both students and mentors enhance communication skills as they discuss their problem-solving techniques.

II. The Mentors

Mentors for the Problems of the Week include:

• classes of elementary, middle school, and high school students with their teachers;
• pre-service teachers;
• college students and professors;
• retirees who like problem solving and interacting with young children;
• others with a love of mathematics and a willingness to share their experience with elementary school students.

Classes or individuals who are mentors will need to have access to the Internet during the week(s) they are mentoring. A Web interface has been designed to aid in managing the submissions and responses. A word of caution: when there are many responses, mentoring can involve a good deal of work.

Because of the increase in participation over the past year, we are offering limited mentoring this year. We have had as many as 600 submissions during one week, though 200-300 are more typical. When you fill out the Mentor Registration Form you may specify the maximum number of submissions you feel equipped to handle.

We are also looking for "cavalry members." These are people who are willing to support the lead mentors by responding to students on an as-needed and as-available basis. (This means that you'd be welcome to write back to students just about every week, but we might make requests for help when we really need it!)

III.  Benefits for Mentors

There are many reasons why students can profit from being mentors. First, they can learn how to create good and interesting problems. Second, they will see that there can be more than one way to solve problems. Third, they will learn to assess student work and analyze common mathematical errors and misconceptions. Finally, they will use the Internet as a learning and communication tool.

It has been our experience that after they have assessed the work of other students, mentors' own subsequent explanations have shown improvement.

Through the mentoring experience teachers and other adults gain practice in assessing student work, are afforded the opportunity to work with different learning styles, and experience teaching in a world-wide environment. Participation can also be used to enhance a professional portfolio.

Ruth Carver designed the Elementary Problem of the Week for third through sixth grade students. At first, she looked for mentors in grades seven through twelve, college students, student teachers, etc. Then, at the suggestion of Gail Lauinger, a fourth and fifth grade teacher at Mendocino Grammar School in Mendocino, CA, mentoring was extended to classes of elementary students who regularly used the Problem of the Week. Gail teaches her students assessment criteria - after doing problems they create assessment criteria for grading them - see her Teaching "Assessment Criteria" to Elementary Students.

IV. Responsibilities of Mentors

When you sign up to be a mentor, specific instructions are sent to you. In brief, mentors who wish to be responsible for a particular week are encouraged to find or develop the problem to be used. They will grade and respond to individual student responses, highlight a few student submissions and write summarizing comments.

Teachers who wish to have their classes serve as mentors should also plan to spend time developing an assessment rubric with their students.

Cavalry members are only responsible for grading and responding to individual student submissions.

V.  Other Help Needed

If you would like to be a part of the Elementary Problem of the Week but don't have the time to commit to being a mentor, we are always in need of good problems. Send your problem suggestions to Lisa at webmaster@mathforum.org . For an idea of the types of problems we have used in previous years, check out some of our past problems.

VI.  Rewards for Mentor Groups

A biography of the current mentor group will appear each week linked to the Elementary Problem of the Week Web page. Photographs and links to school Web pages may be included when available. In addition, mentors will receive letters of recognition and certificates.

VII.  Comments from Former Mentors

  Lisa Lavelle:

After showing my students the web site, I asked them to bring in some clever problems they either created themselves or had fun with in the past. I asked that they be problems they thought would intrigue students in elementary school. About half the students in each of the classes (I led mentoring for two different weeks) brought in problems. We then got into groups of three or four and critiqued the problems. The entire class voted after the critique, and we submitted our top three choices to Ruth, giving her options in case she thought our favorite would be too difficult (see December 9-13, 1996 for our top choice).

Next, each student took home the chosen problem to work out on his or her own. The next day in class we discussed the solution and how we had each arrived at it. This included a discussion of what was needed for a correct answer and what we might look for to consider highlighting a solution (our "assessment rubric").

As solutions came in the next week, I doled them out to my students to begin composing responses. I scheduled a day in the computer lab later in the week when most of the solutions had come in to give them time to respond, and I also lightened up on the homework assignments that week anticipating that they would need a little extra time to wrap up their responses.

My job was to cut and paste responses, create a list of correct participants, and prepare the highlighted solutions section (a job that is no longer necessary because of the software we are using). During this process, I also did a little editing of a few of my students' responses and gave them grades based on their responses and participation outlined above. Most of them did very well with only a few not giving complete responses or turning in their responses in an untimely fashion. The grade was approximately equivalent to a third of a test.

We had a lot of fun, and it was a great way for me to see some talents I hadn't seen before. I learned a lot about the assessment process, as did my students, and I'm looking forward to mentoring again this year.

  Gail Lauinger:

Last year my fifth graders solved the problem the week before it appeared. Then I gave each group copies of the responses submitted (less than 10) and each group did a three pile sort. They then wrote criteria for the best solution, needs work, not there piles. The best became our rubric which we posted along with the best solutions. The class then wrote to each respondent. They were disappointed in that they didn't get any acknowledgement back from any group.

This was a wonderful opportunity for them to discuss work that was not done by anyone in our class. We do anonymous reads but they always recognize styles within the class so the discussions are constrained.

  Caroline Brennan and her 8th grade math class:

Being mentors for so many students around the world was a wonderful educational experience for my 8th grade students. We discussed the posted problem after the solutions starting coming in, and we noticed that many students forgot to give their answer in square feet. Many students arrived at 800 feet instead of 800 square feet. We thought we should have emphasized that the answer was to be given in square units. This may have helped many students to arrive at the correct solution. My students felt badly about not including the answers with 800 feet but after a little discussion they decided that the next time those students work with area they will remember to put square units. Thank you for giving us this exceptional learning opportunity.

Shannon, Marilyd, Kim, Christine, Paul, Ryan, and Mrs. Brennan

Comments from the mentors:

Shannon wrote:   Being a math mentor has taught me that math can be fun. I found that the most enjoyable thing about being a mentor was helping people and telling them their answer is correct. I thought it was hard to tell people their answer was almost correct or wrong. Having a paper to look at while doing my responses helped me make less errors. All in all, my mentoring experience was a good experience.

Marilyd wrote:   What I liked the best about mentoring was having the opportunity to go on the Internet and answer responses from other people. What I didn't like was telling the other people that they were wrong. I really enjoyed doing this and I look forward to doing it again.

Christine wrote:   I thought that being a math mentor was fun but also a lot of hard work. I liked being able to correct students' work but I thought it was frustrating when someone got the answer correct but forgot to put square feet. They got the hard part correct but left out the easy part. I thought that I was being mean when I had to mark their answer "incorrect". I also got upset when some students didn't show their work. Now I know why teachers get upset with you when you make silly mistakes. Some of the mentoring was strenuous because we had so many responses to correct. I really enjoyed doing this project.

Kim wrote:   I thought mentoring was fun. It was interesting to find out the names of the different places that sent in answers. It was neat to tell them that they were wrong and then explain what to do in steps. When we got into the program on line it was easy to answer the responses. This experience was fun and interesting.

Paul wrote:   Being a math mentor gave us the chance to interact with others. It also helped others and us with our math. We had the chance to use the Internet as well as help others. I had fun doing this project and I know my classmates enjoyed it as well.

Ryan wrote:   I liked being a math mentor. I liked doing this because I felt like a teacher. I hope to enjoy this experience again some time in the near future.

VIII.  Online Registration

If you are ready, you may complete the Online Registration Form now. Please check our Problem of the Week calendar and consult your school calendar before you select your preferred dates.

IX.  Contact Person

If you have any questions or comments after reading the information or at any time during the mentoring process, please contact Lisa:

Lisa Lavelle <webmaster@mathforum.org >
Elementary Project Coordinator
The Math Forum
Swarthmore, PA 19081