University of Arizona
Institute for Mathematics and Education

Using Cases to Develop Knowledge for Teaching Mathematics

February 14–16, 2008, Tucson, Arizona

This page is for the organizers of the workshop, and contains all evaluations received so far through the IM&E's electronic submission system.

Background Most useful Least useful Impact on my work
mathematician
Grade level
The outstanding work of the Director and staff of the IME as well as Rebecca McGraw who served as local organizer were big factors in the success of the workshop. I hope to use Dan Chazan's materials at my institution when they are available. I think that they will turn out to be quite useful.
math_educator
Grade level
I thought the sharing of the materials was the most interesting I wanted more time to see what other people were doing. That seemed too short to me I look forward to working with my team to develop cases that relate to the materials that we saw.
mathematician
Grade level
1) Working with people in different fields, i.e. math educators and HS teachers. 2) Listening once again to their prejudices about mathematicians -- we are such an elitist, uncaring, isolated bunch, etc. etc. This has to be done. 1) Having to hear about existing projects in much more detail than necessary. I know people want to present their hard work, but each group should have really about 20 minutes to get things across to the entire group -- they can go into more detail in breakout sessions. 2) Listening once again to their prejudices about mathematicians -- we are such an elitist, uncaring, isolated bunch, etc. etc. Haven't we gotten past this yet? On my mathematics teaching and research, honestly not much. On my increasing interactions with math educators and teachers, a lot. I get an increasing sense of how hard it is to teach "elementary" math, from a combination of content, pedagogical and social issues.
mathematician
Grade level
Talking to people who have different perspectives. The product driven mode. Not much of an impact in my work per se. It helped me reaffirm some values and ideas about managerial styles and concepts of collaboration.
middle_school_teacher
Grade level 8th grade
The second day of the workshop was great. The discussions that went on regarding ∏ was very enlightening. I never realized how detailed people get when trying to define 3.14... Because of this topic I have found myself reading up on the history of pi and being very careful on how to define it to my students. The people in the group were very interesting to work with. I feel that everyone learned from each other. When we switched topics to Mathematical induction, we were able to put together an outline for a further case study. This is still a work in progress. I found the entire workshop to be beneficial. Returning to my class after attending the workshop I found myself excited about teaching math again. I was allowing the negative feelings of teachers to get me down and I was forgetting about why I love to teach. This workshop made me realize that I have so much to learn and so much to teach that I should never forget the impact of having a good math education does for my students. I find myself reading more on math and signing up for a math class during the summer.
math_educator
Grade level
During our small group discussion and work, the mathematician comments helped greatly in developing the case. This was insightful because he claimed to know little, if anything, about pedagogy. In his words, "I am a sage on the stage." I consistently felt rushed to produce a product, which did not give time for critical reflection about the structure of the case and its application to my teaching situation. The case I worked on and the others that were discussed will help me be more explicit regarding giving directions, using mathematical language, and teaching concepts as well as skills.
math_educator
Grade level
During our small group discussion and work, the mathematician comments helped greatly in developing the case. This was insightful because he claimed to know little, if anything, about pedagogy. In his words, "I am a sage on the stage." I consistently felt rushed to produce a product, which did not give time for critical reflection about the structure of the case and its application to my teaching situation. The case I worked on and the others that were discussed will help me be more explicit regarding giving directions, using mathematical language, and teaching concepts as well as skills.
math_educator
Grade level
The most helpful part was getting to work in sub-groups on materials targeted at a very specific audience (mathematicians/math grad students). This was helpful because I think in the process we developed a potentially useful model for how to take cases that are created for one community (K-12 teachers at some grade level, for example) and generate supplementary materials to support people from another community to learn from the case. This isn't really an "aspect" of the workshop, but it would have been useful for me if as a group (or in sub-groups) we had devoted time to discussing what it is that someone has the opportunity to learn from particular cases. To me this seems like a very important part of the case production/marketing process. Implicit in many of the conversations was the the idea that people would learn things about teaching, things about how students learn, and perhaps things about mathematics, but we were not explicit about this (and I think that being able to convey that information to potential users of the cases is something we should be prepared to do, especially if we're trying to convince mathematicians to use them). Those of us who work with teachers often make a big fuss about how lesson plans should include learning objectives and it seems like we should expect the same of our case materials. Perhaps this could be a topic for some future workshop-- maybe with a specific focus on a few "types" of knowledge such as pedagogical content knowledge, content knowledge, and mathematical knowledge for teaching. Maybe by doing that we would also learn a bit more about how to communicate the importance of these kinds of knowledge to those who do not has extensive experience working with teachers (and have therefore seen the need for these kinds of knowledge in action). I think the part about having a possible "model" for how to adapt case materials for use with mathematicians or mathematics graduate students is the part that will have the most impact on my work since that those are the folk I work with most.
math_educator
Grade level
I found it helpful to see a variety of things that people, from across the country, are working on with cases and their use with various groups of people. I also found the working groups to be stimulating and productive. We could have used more time in our groups to complete the work we had begun. I will look with new eyes to the prospect of using cases with various groups, including my colleagues who are mathematicians.
math_educator
Grade level
It was interesting to hear from various people, from across the country, are doing with using cases with various groups of people. I also found the working group stimulating and interesting. We could have used more time in our working group to complete the work we had begun. I will look with new eyes at ways to use cases with various groups, including my colleagues who are mathematicians.
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