University of Arizona
Institute for Mathematics and Education

Mathematicians in Mathematics Education

March 20–22, 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
math_educator
Grade level
I listed myself as a mathematics educator because that is my current mission. However, I "grew up" as a mathematician who researched in the areas of geometry (Worm Problem of Leo Moser), Generalized Inverses, and Numerical Linear Algebra (Rook's Pivoting). I gleaned some great ideas from every session. The overview of mathematics education by Deborah reminded me of the concerns and challenges for the mathematician who wants to teach teachers (K-12). The interesting discussions about mathematics and algorithms from the classroom were stimulating, and remind us mathematicians that things aren't always as easy as we think. There is a lot to be learned about how best to "educate" K-12 teachers. I personally think it is not the knowledge that is so critical, but rather the training of how to think about mathematics and that we should control it, not vice versa. Changes attitudes among teachers is an awesome task. George I could not get "into" the text review process. I think if it has been more about K-8 texts, I would have been "all over it." Such workshops always change how I think about mathematics and couching anything and everything in a concrete or semi-contrete setting. Teachers need to "see" what we do, and often mathematicians don't want to (or can't) show them the picture.
mathematician
Grade level
The overview of all the ways in which mathematicians can become involved in math education issues, and the perspective of the various aspects of mathematics knowledge for teaching, which gave me a useful language to describe some of what we want to accomplish in our content courses for pre-service teachers. Also the chance to interact, discuss, and think about math education issues with others who are as passionately interested in it as I am. I also thought the discussion on the various ways to represent the fraction division problem, and the discussion about mapping an algorithm to the use of manipulatives was really interesting. Watching the video on the teacher demonstrating the fraction problem (adding a positive fraction to a negative fraction), where the problem was in the "artwork." On the whole, getting bogged down in the discussion of how to teach a topic, rather than focusing on the things you have to think about when thinking about how to teach. (In other words, we needed to be one level removed from where we were working to really get to the issues we were supposed to be focusing on.)

Feeling rushed, not enough time to process everything, and rushing through the consulting/ reviewing textbooks and standards part was frustrating.
I will better be able to describe my goals for my pre-service content courses, and I have a much clearer idea of what I want to accomplish in materials I develop for those courses. I hope that in the long run the workshop will enable me better to identify ways in which I can become involved in math education issues, and to be more effective in my involvement. I hope to build on some of the connections made at the workshop, and to use ideas generated to develop my own, currently very limited, expertise in the area.
mathematician
Grade level
Probably most important was nmeeting the group of mathematicians who attended the meeting. Both of the activities -- viewing teaching practice and materials on fractions and the practice at reviewing materials were enlightening as to what was involved. Thinking about the intricacies of teaching fractions led to the more surprising insights but both were useful. I appreciated the fact that both were activities (not lectures) and that both were focused -- at least at the outset --before the audiences began to diversify the issues. I think the discussion was very good and well handled. The schedule was somewhat tight and despite the opportunities at lunch and during the evening there still wasn't enough time to talk to all of the participants as much as I would have liked. The biggest impact will be on new contacts made. I'm also more prepared to talk to middle school/ elementary school teachers about there practice. Specifically I have some additional ideas for the types of homework problems that could be placed on WeBWorK to aid these teachers.
mathematician
Grade level
The workshop gave me a new and very different perspective of what it takes to analyze school mathematics from many views: mathematics, materials, and standards. I also believe that the mathematics community needs to be serious about involvement in teacher training and in enhancing in-service teacher knowledge and opportunities. The short time frame made us move to different/new topics before the items at hand were fully digested. It was a lot for a quick workshop. But it was extremely valuable. I have a wider view of both the needs and opportunities for mathematicians to be involved in mathematics education. I will begin trying to bridge the divides at home.
mathematician
Grade level
Probably most important was nmeeting the group of mathematicians who attended the meeting. Both of the activities -- viewing teaching practice and materials on fractions and the practice at reviewing materials were enlightening as to what was involved. Thinking about the intricacies of teaching fractions led to the more surprising insights but both were useful. I appreciated the fact that both were activities (not lectures) and that both were focused -- at least at the outset --before the audiences began to diversify the issues. I think the discussion was very good and well handled. The schedule was somewhat tight and despite the opportunities at lunch and during the evening there still wasn't enough time to talk to all of the participants as much as I would have liked. The biggest impact will be from the new contacts I made. I'm also more prepared to talk to middle school/ elementary school teachers about their practice. Specifically I have some additional ideas for the types of homework problems that could be placed on WeBWorK to aid the students of these teachers.
mathematician
Grade level
* Discussions of the mathematics in specific examples, such as the procedure for dividing fractions, or for graphing equations, was positively eye-opening.

* Focusing on just 2 strands was a good compromise.
* Interacting with various "stakeholders" (parents, schools, principals, politicians, publishers) is tricky. There wasn't much specific advice/examples of how to do this.

* The workshop was too short! Just as we learned how much there was to do, it ended. (This could be largely ameliorated by followup activities, perhaps another workship in 6-12 months, or possibly nothing fancier than a mailing list to keep us active and in touch.)
* Provided a framework for defining myself as a mathematician interested in mathematics education, including specific contributions I can make. * Provided a framwork for establishing "MIME" as a respectable field!
mathematician
Grade level
Unfortunately, I missed the most important day due to illness. So I'll have to say the chance to meet and hear (a little, in my case) from people (esp. Ball and Bass) whose informative, thorough, accessible, and sensible writing on mathematics education I've admired for a while now. Also connect with people with similar concerns and desires to contribute. N/A It has given me (and will continue to, I hope) both a broader view of the "landscape" and some food for thought on concrete, specific ideas for my work with teachers.
mathematician
Grade level
The most helpful aspects were: (1) interacting with the other participants; (2) the videos of teachers and students in classrooms. It was great getting other people's point of views and hearing about their experiences, and it was a real eye-opener to see the issues that arise in teaching these concepts in the classroom. If possible, it would be great to post the videos on the web with the commentary of the participants. There were many subtle things noticed by different people, and the videos would be more effective and useful with these comments. It might have been more useful to have less material and cover what remained in greater depth. As it was, we didn't have enough time to cover all the stated material, and a few times it seemed like we ended discussions before they were done (though not necessarily before enough had been said!). Also, it might be useful to be a bit more specific in where to go from here, and have some things mapped out to explicitly build on what we've done. I've been in several workshops with good goals, but as no 'next steps' were listed we never seemed to continue. I hope to build on this workshop in several ways. I have plans to talk to people in teacher training programs, and the inputs from the other participants and what I learned from reading the materials and seeing the videos will help frame these conversations, making them (I hope) more productive and useful. I am definitely more aware of the issues. I hope to participate in future discussions of curriculum and standards.
mathematician
Grade level
1. There was an impressive range of both macro perspectives on math education and more micro interactive sessions digging into the fabric of the work that mathematicians might do in a few strategically chosen areas.

2. There was a great diversity of participants with a great appetite to learn things to help their work in their various environments, and a strong sense of professional community and networking took hold as the workshop progressed.
Readings and other resources could have been provided earlier As an organizer, I was impressed to see many new faces, particularly young people, and a strong expression of need for some community building such as the workshop provided. This convinced me that the MIME concept has a well grounded rationale, that IME is a natural environment for it, and that it is well worth pursuing.
mathematician
Grade level
For me the two most helpful aspects of the workshop are: 1) I learned about some problems in school matmematics education, such as the problem of mathematical knowledge of teachers and methods of teaching mathematics to kids
(throuhg the discussions about teaching fractions with different models);
and 2) I knew more mathematicians who are interested in mathematics education.
It is difficult for me to find a least helpful thing or two. Perhaps, a little bit less time on criticism of textbooks so that more time could be spent on discussions of programs and curriculum issues? Or on possible initiatives or actions for collaboration? I plan to maintain a webblog where I would share my ideas or points of view in mathematics education for teachers, and things that what I learned during the workshop of course will be reflected in my webblog. Then we will see, perhaps, something more substantial will emerge. Also, our department plans to add a masters program for secondary teachers (jointly with a branch campus) and as the current graduate chair what I learned at the workshop will help me in realizing this plan. And big thanks to the IME for organizing the workshop.
mathematician
Grade level
The opportunity to meet other mathematicians with similar interests and the exercises and activities at the workshop were the most helpful aspects for me. The workshop was too short for the work planned. More time for planning, and becoming acquaintanted with the experiences and interests of the participants would have improved it. I hope to build on the workshop experience as a mathematician engaged in lesson study.
mathematician
Grade level
The session on evaluating curriculum and standards was helpful. It was good to hear about how standards are constructed and to hear advice on best practices in evaluating text materials.

At the top of the list was just making connections with mathematicians interested in mathematics education.

The strand on mathematical knowledge for teachers was also interesting.
However, regarding the diagram at the top right on expressing 5/6 divided by 1/3, although it does "contain" a mathematical description of the operation, the diagram contains more irrelevant information than useful information, and this should have been recognized as a way NOT to present ideas to students.



The session on the National Math Panel report should not have been skipped.
It would have been better to cut short some of the discussions on the text material to make time for this.

The exercise on comparing the magnitudes of fractions could have been skipped to leave time for the material on the NMP report.


The workshop will help me better evaluate text material. It has given me some good connections with other mathematicians in mathematics education.
mathematician
Grade level
First of all, the article by Deborah Ball, Heather Hill and Hy Bass that we read prior to the workshop was very helpful to me.
I thought that the "people" resources were, and will continue to be, quite useful. For example, I expect to follow up with Deborah and Hy on specialized content knowledge and the assessment tool they developed.
Although I have not reviewed books for a number of years, the list of key questions that we developed will be useful the next time I review a book, even if the book is not for K-12 students.
I would have liked to have more of a focus on secondary mathematics education. So I would suggest that subsequent workshops be targeted for elementary education or secondary education or that there be some concurrent breakout sessions during a combined workshop. In the next few years, I expect to complete a book to be used in a course for secondary mathematics education majors that serves as a transition between the calculus sequence and the advanced theoretical courses. I also will have a role in the development of workshops for secondary mathematics teachers. I expect that the identification of specialized content knowledge necessary for teaching secondary mathematics will inform the development of the content for both projects and I can imagine using the assessment instrument to evaluate the effectiveness of the course and workshops.
mathematician
Grade level
* Understanding how my mathematical expertise can be used productively in mathematics education.

* Networking with important mathematicians and mathematics educators and hearing their opinions on where we should focus our efforts.


*I would've liked to spend some time discussing professional development.

* This workshop will have a big impact on my work. Especially determining which aspects of mathematics education to focus on that will better serve me and the profession.
mathematician
Grade level
The presentations by Debra Ball and Roger Howe both gave insight into the challenges of
understanding (and teaching) elementary school mathematics.
It was all very good. Various activities could have been shorter. The point was really to give us the flavor
of the work, not to complete a job.
I hope to be able to work directly with pre and in-service teachers at some point. Additionally, I would like to consult on "standards."
mathematician
Grade level
1. understanding in depth the complexity of teaching concepts like fractions. Roger Howe, Deborah Ball and Hyman Bass did an outstanding job explaining the issues in depth.
2. Insight on what is involved in working with Mathematics educators and teachings in developing good text books and evaluation materials.
All aspects of the workshop were very helpful. A better understanding of what the issues are will help me work with Mathematics educators and teachers and will enable me to better explain to others what the issues are and convince them about their importance.
mathematician
Grade level

The discussions were very useful for me, as it reinforced my beliefs of mathematics education by talking with other mathematicians and gave my further insight into the issue of what I can do as a mathematician by talking with mathematicians that have been working on mathematics education for many more years than myself.

Another thing I really liked was the quality of the facilitation. Both Deborah Ball and Bill McCallum modelled what a classroom discussion should look like (since the conference felt very much like a class).

n/a
I realized that I need to continue to develop a sense of what I am focusing on when participating in mathematics education.... That's a very awkward sentence.... What I mean by that is, when I am participating in mathematics education (discussing curriculum, planning my lessons, running a professional development class for teachers, etc.) I have a very bad habit of lumping everything related to math ed into one big lump as opposed to step back and ask "am I commenting on the mathematics of this activity? or the pedagogy? or the grammar?" As it was pointed out in Bill's session, we all had some sort of problem/issue with the book's definition of function- but to put that problem/issue into words is a skill I realize I need to further develop.
mathematician
Grade level
Evaluating and critiquing materials were very useful. The discussions and framework we developed gave us a guideline as to how to evaluate the materials in a very constructive way.

I really learnt a lot about the K-12 educational system in US from the talk on landscape of US mathematics education. And also from the end of workshop discussion on the state required mathematics content knowledge for high school students.

I couldn't think of one. I learnt more about the roll of Mathematics educators and how as a Mathematician I can help the cause. I will actively seek opportunity to use my knowledge to better the Math education in K-12 students and beyond. Now I am more aware of the difference between teaching knowledge and content knowledge of mathematics, which will make me a better teacher and an active listener.
mathematician
Grade level
- It was professionally reassuring to be surrounded by mathematicians who have thought deeply about, and invested significant time in, K-12 mathematics education. I believe that having a network of mathematicians who are engaged in these sorts of K-12 mathematics activities will be useful to me personally, and to the mathematics community as a whole.
- I would have preferred spending less time on the basics of the mathematics curriculum (e.g. adding fractions, multiplication) and more time on the meta-issues in K-12 math. These meta-issues would include things such as: Which curricula have been proven to be effective (and, conversely, which have not)? What is it about the educational systems used in other countries which could possibly be incorporated in the US educational system in order to improve mathematics understanding? - I will use some of the contacts I have made through the MiME workshop to help clarify and hone various K-12 mathematics activities in which I am currently involved.
mathematician
Grade level
I really enjoyed the Friday session conducted by Deborah Ball. She did an excellent job of illustrating the mathematical knowledge needed for teaching through the examples that she presented. Her idea of "unpacking" the mathematical concepts and procedures at the elementary school level was very enlightening. I'd like to see this kind of work extended to the mathematical material covered at the middle and high school levels. I plan to use many of these ideas in the mathematics teacher preparation courses that I teach at the university.

I also liked interacting with other mathematicians who are interested in mathematics education at the precollegiate level. Having the list of names and e-mail addresses will be helpful.
While I know that state standards are important, my eyes tend to glaze over when I read them. I prefer to stay involved in working on teacher preparation, and not spend my time working on writing the general statements that appear in these standards. I'm not criticizing the workshop at all for covering this important topic. It's just that for me, it was the least helpful in terms of my own interests. As I mentioned above, as a result of this workshop, I plan to put more emphasis on trying to develop the mathematical knowledge needed for teaching in the work that I do with prospective teachers at both the preservice and inservice levels.
mathematician
Grade level
1. Discussing mathematics in the context of education-specific examples such as subtraction algorithm.

2. Making comparisons among the texts defining the same context.
1. Discussing the opportunities for mathematicians as consultants. 1. Further thought put into designing curriculum and professional development to specifically target mathematics teachers need. 2. Opened my eyes and gave me ideas for publication outlets in math education.
mathematician
Grade level
The most useful part was the sense community that was formed among the several participants. It was clear that all of us were interested in the issues of mathematics education and wanted to know what more we could do. As a beginner I felt comfortable knowing that I was not the only beginner, and also felt secure that there were many others, those who were much more experienced, whose career paths I could like to follow.

I also found the specific focus on two strands very useful. I only had vague ideas of what I could do, these sessions made my ideas a bit more focused and concrete.
I would have liked it to be a bit longer. Everything we did was useful and I would not wish to have any strand discussed any shorter. However, those of us who are beginners were still left with the task of figuring out for ourselves what our next steps should be, and I for one would be very grateful if I could have gotten some more guidance in that direction. As we discussed in the last half an hour of the workshop, I think a group project or two started in this workshop could have helped us immensely. I do not have a clear view of how things will develop yet, but I expect that I will often see the people I met in the future, and hopefully embark upon some joint projects. I do have some ideas about what to do next, especially with respect to teaching possible courses for pre-service teachers, and regarding reviews of textbooks. Thank you!
mathematician
Grade level
The most helpful aspect of the workshop was networking. I met several people who are "in my boat" in that they are mathematicians by training, but are starting to focus more on mathematics education. It was great to meet contacts with my perspective from other parts of the country.

Also, Deborah Ball did a wonderful job pushing a roomful of mathematicians to think hard about mathematical knowledge for teachers and how best to present material.
I like the fun, informal atmosphere of the meeting by all the leaders with one exception. Hyman Bass and Bill McCallum kept the event fun and fresh, with jokes and self-deprecating humor. While Deborah Ball was excellently prepared and very sharp, she occasionally came across as though she couldn't be wrong. Instead of giving the feeling that she was working with us, sometimes it felt like she was talking at us, which rubbed some people the wrong way and made some situations more tense than they needed to be. I plan to submit a proposal to IME for a workshop to help train mathematicians how to work in the research field of mathematics education. This is something I have been considering for several months, but did not know exactly how to go about making the shift. This workshop might ultimately shape my future career, moving from pure mathematics to mathematics education.
mathematician
Grade level
The presentation by Deborah Ball was fabulous. We could have had another full day with her.

The opportunity to meet with fellow mathematicians also interested in Mathematics education. It's a hard conversation to have in many departments. So, this opportunity was a real treat.
Reviewing textbooks. Although an important role we can play as mathematicians, not quite what I wanted to do. I was hoping for more practical and political advise for working with the community ... fellow colleagues, parents, teachers, students, and kids. This workshop gave me much needed background information on math education literature. I hope to follow up on this more. A reading list would have been great. I also think I'm more confident about taking on this work. I hope this institute will grow into something well-respected --- that is, being affiliated with it will mean something towards tenure and credibility when doing math education activities.
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