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A Story of Mentoring

During the previous summer, the teacher was making plans for her junior Algebra 2 course the next year. For years, she had been incorporating problem-solving activities into her classes, and she had been thinking about having students work on longer-term projects. Her goal was for students to experience mathematics as something you do, and she wanted them to have the opportunity to bring together lots of ideas and their own creativity while working on a large problem. She also found herself asked on college recommendations to comment on students’ independent and creative work, and felt frustrated that her students did not have enough opportunities to demonstrate what they’re capable of.

The teacher went to the Making Mathematics web site and signed up. She was assigned a mentor, a mathematician from California who was interested in helping high school teachers and students in a mathematics research experience. The mathematician learned about Making Mathematics on an email list. He had mentored undergraduate and graduate students on independent study projects, but had never done any work with high school students. Most of the math majors at his college become teachers, and he was getting more interested in issues in K-12 education. He was excited about finding out what high school students could do on independent mathematical work.

The mentor and teacher exchanged several emails, where she described the text and topics covered in her class, along with some of the activities she used on her own. The mentor helped her think about how much class time she was able to dedicate to the research experience for her students. Together, they read over many of the projects and selected "The Simplex Lock," planning to use it during the second quarter.

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During the first week of school, the teacher led students through some of the introductory activities from the "Mathematics Research Skills" section of the web site. The students worked in groups and individually, learning to pose their own problems, make conjectures, and collect and organize data while exploring a problem. The students, for the most part, enjoyed what they were doing, but they were a little anxious about "getting behind" the other Algebra 2 classes. When were they going to start in the book?

Well, the teacher did have a curriculum to cover, so after the first week, the students started in the textbook. Every week or so, the mentor and teacher communicated by email. The teacher wrote about her class and what they were doing, and the mentor offered support and ideas. The mentor had spent some time working on the Simplex Lock project and looking over the support materials on the web site. He suggested a few of the activities from the "Mathematics Tools" section that would help students with the Simplex Lock project. The class worked on these short activities between chapters in the text, and both the teacher and students enjoyed mixing up the content and activities a bit.

About halfway through the second quarter, the teacher posed the Simplex Lock project in class, using the teaching notes provided on the web site to guide her instruction. Students spent two days investigating the problem in class. They worked individually and in groups, made lists of combinations, and had lots of different strategies for counting. Two students seemed frustrated and overwhelmed by the task and said they didn’t want to write down all the combinations. Talking together, they decided to try and find a way to count all the combinations without listing them all.

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Students had to turn in rough drafts of their work on the project two weeks later. Most students left the work on the rough draft until the night before it was due, and found they couldn’t remember exactly what they had figured out in class or how they had been organizing their data. The teacher was disappointed with their work. She wrote to her mentor, unsure of how to proceed.

The mentor offered ideas for re-engaging the students with the problem, including asking a group who had done one of the better write-ups to share pieces of work (but not their answer) with the class, giving out the rubric on which they would be graded, and talking with students in class about doing this kind of mathematics work. He also offered to be "co-grader" for the projects. He sent a picture of himself and a short biography for the teacher to share with the class, and he offered to answer email questions from any students working on the project. (The students had email access in a computer lab in the school, which they could use during study halls, after school, and during class if the teacher reserved the lab.)

Most of the final drafts of the Simplex Lock project were much better than the rough drafts. Students clearly had become more engaged in the project, and seemed genuinely excited to find out what a mathematician thought about their work. Some students complained that it was unfair they were doing more work than students who had another teacher, but everyone completed the project.

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During the second half of the year, the mentor suggested that students do one more project near the end of the year, and that they pick the topic themselves. Together, the mentor and teacher made a plan for introducing some of the "Research Settings" from the web site to the class. For three or four Fridays, the teacher spent class time introducing a research setting and allowing students to pose and explore their own questions about it.

Near the end of the third quarter, the teacher took her class to the computer lab. Each student signed up on the Making Mathematics web site and applied for a mentor. Students were told that they had one week to select a project to work on (either from the Research Projects or from the Research Settings); that they could work individually, in pairs, or in groups of three; and that the research project would be a major part of their final grade for the course.

Most of the work on the projects took place outside of class. Each week, part of Monday was set aside for groups to work together, for students to ask questions of the teacher, and for email exchanges with their mentors. Some students had email access from home, and communicated with their mentors even more often. During all of this, the class was still trying to finish up the last two chapters in the textbook.

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Final projects were due three weeks before the end of school, so that the teacher would have time to grade them. Each student or group prepared a written report and a 5-10 minute presentation of their work. The presentations took place over several days of class time, with just a couple of presentations each day.

The quality of most projects was so good, the teacher wanted to find a way to share the results and experience with others. The teacher spoke with her mentor, her department head, and the principal about how to do it. They settled on the idea of a Mathematics Fair, presented by her class and attended by the entire school. The students answered questions from other students, from teachers, and from some of their parents who were able to attend the fair. The teacher had a lot to say the next year on those students’ college recommendations.

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Translations of mathematical formulas for web display were created by tex4ht.

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