University of Arizona
Institute for Mathematics and Education

Elementary Teacher Preparation in Mathematics

February 28–March 1, 2008, Four Points Sheraton, 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
elementary_teacher
Grade level 5
The focus across sessions on mathematical processes/practices was encouraging and also illustrated ongoing work across multiple levels and tasks. This particularly came through in the world cafe sessions

The opportunity to talk through a variety of records from classroom teaching with a diverse group of stakeholders in mathematics education.

I also benefited from participating in several examples of rather elegant mathematical tasks and games that are capable of engaging students in deep mathematical work.
It is always difficult talking across communities and this is especially the case when they are brought into contact so rarely. The unfortunate side effect is that it takes almost a whole day to build up enough collective steam to effectively work together. This indicates that cross community events like this need to be longer or need to be precipitated in some way that will enable participants to ramp up into the work more quickly. The workshop will have an impact on the considerations I make in choosing and using mathematical tasks with students. It will also bolster my confidence in advocating for attention to mathematical processes/practices in instruction.
mathematician
Grade level
Saturday was most helpful because it was more concrete and focused on math for elementary teachers. The world cafe was an especially good session because I got a lot of good ideas and a chance to see some of the variation in approach to these courses. I also think that having an opportunity to look at a pre-service teacher in a classroom (Sheri's presentation) was a very important reminder about the context of the work. It is my general opinion that people learn and accomplish the most when they are grounded in concrete activities rather than talking about general or theoretical issues. I am not sure that there would have been a more efficient way to work through some of the cultural differences between participants, but the opening talk didn't seem to be that helpful. I like Tim and agree that representation is important, but the presentation was too far removed from what I think we needed to do, which was to spend some time defining and clarifying the purpose and expected outcomes of the workshop. I think it would have been better to have Sheri be the opening presentation because it could have grounded and framed the conversation and it might have subsequently been more focused on the pre-service preparation of elementary teachers.

Since you don't ask anywhere else, I will mention here what other things I think would have been good:

1. An explicit discussion about the distinction between math content and math methods courses and alternative models where such things are intertwined or integrated. If we are to get mathematicians involved in teacher education, the hook is usually the content. Different universities have different histories and resources with respect to teacher preparation, and I think we need to have a discussion about how to make content courses that are just content courses effective (we can't expect all people who teach content courses to collaborate with a math educator). I appreciate the sentiment that Kate stated that she can't see how to separate out content and methods, but the reality of the structures of university colleges and departments has this distinction built in to teacher preparation programs. At the same time that we respect the fact that mathematicians are in it for the content, they also need to understand that their piece is an important, but small part of teachers' professional learning. I'd like to see a conversation where we fill in more of the details of this picture and speculate about how mathematicians can contribute to the broader set of professional learning opportunities for teachers.

2. Margaritas at the reception.
I do have some new ideas for our pre-service mathematics courses, but I think I am actually more likely to use the materials I learned about with in-service teachers. I also met some people who I hope to continue to have contact with, and I hope the wiki will become a useful resource for my department and other math depts in NM.
elementary_teacher
Grade level
It was helpful to hear what university math instructors are thinking about. I feel that mathematicians and teachers never get the chance to come together and discuss math education so this was an amazing opportunity.

I also enjoyed the variety of topics that were presented. Since this was a diverse group, most presentations lended themselves to a broad math audience.
Engaging in solving the problems during presntations weren't helpful to me. I felt that we could have used that time more effectively.

Since I'm not a math educator, the World Cafe "centers" weren't releveant to my work.
I feel that I better understand the perspective of math educators (university level) and it's good to see that everyone involved in preparing math teachers have a common goal.
math_educator
Grade level
I feel that I benefited the most from the discussions that came from analyzing student work and videos with other group members. This gave me a real insight into what other mathematics educators thought and how our individual vision or interpretation differed from others in the field. Further, it gave us an opportunity to think critically as a group. The perspectives that were shared helped me to view these things through a different, more critical lens, and helped me to reflect on my own work in similar ways.

There did not seem to be a clear theme to the presentations. I did enjoy and get something out of each one, but the overall goal of these sessions (as a whole) was not clear. For me, it would have been helpful to have overarching goals for the conference (What are we trying to produce or accomplish? What steps are we taking to get there? What evidence is there that we did accomplish this?) that were supported by the presentations. I plan to share much of what I learned at the conference about methods courses with my education department. Much of the information I received will help me to re-conceptualize and improve my methods course in terms of mathematically rich tasks. Further, our communication with the mathematics department needs to improve. In speaking with mathematicians, I have gained some small insights into how to best go about doing that with the goal of improving the mathematics education program.
mathematician
Grade level
I get a lot out of meeting and talking to teachers who are so dedicated to their work. In terms of sessions, I really liked Raven McCrory's session and Sheri Roedel's session. I don't want to be critical of any session. I think opportunities like this help one stay grounded in the work that they do. While I cam back with some specific ideas for activities I may use in courses for future teachers, I think the main benefit is that the workshop made a contribution to my understanding of issues related to the mathematical education of teachers.
mathematician
Grade level
I get a lot out of meeting and talking to teachers who are so dedicated to their work. In terms of sessions, I really liked Raven McCrory's session and Sheri Roedel's session. I don't want to be critical of any session. I think opportunities like this help one stay grounded in the work that they do. While I cam back with some specific ideas for activities I may use in courses for future teachers, I think the main benefit is that the workshop made a contribution to my understanding of issues related to the mathematical education of teachers.
math_educator
Grade level
1) Discussing issues related to mathematics education with both school teachers and mathematicians allowed me to see how others perceive and address issues related to pre-service teacher education and student learning. Not that I agreed with all the views presented but it was good to be exposed to have the oppotunity to view these issues throught different lenses.

2) I learnt a lot from my discussions with others about the structure of their institution's teacher education programs. It provided a renewed appreciation for my own program and also insight into steps that can be taken to forge better relationships with our math dept and school community.
1) I found that a lot of the information that I can readily use came from teh informal discussions with the other participants.

2) There was a lot of cursory discussions about methodology and content - it would have been more useful if we could have spoken explicitly about the specific content (underrepresented and undervalued) and how to better address these issues in content and methodology courses. I think these discussions would have been useful for the mathematicians who are often primarily responsible for the content courses.
The workshop provided useful information with regard to different ways to improve our elementary education program, specifically by creating better connections between the content and methodology courses.
math_educator
Grade level
Interaction with teachers and getting their perspective on how we are preparing teachers--extremely valuable

Ideas for making content courses more effective by blending content and methods

Emphasis on importance of attitudes and habits of mind--that this may be even more important than any content
Perhaps less time on convincing us of the usefulness of certain practices (we are the choir being preached to) and more on how to do them--tools and resources Very strong motivation to work toward many changes: More collaboration with the education dept More work on changing pre-service attitudes toward math; many ideas on how to do this Need to visit elem. classrooms regularly Many, many ideas that need to be digested and turned toward action Many added insights into challenges faced by teachers (much of this came out in individual conversations, but session with Denise and Trudy also gave me many new and compelling insights and reorientations of my assumptions) Depression about the state of affairs at our college :-( --so many things that could/should be done, but I don't know if I/we can
elementary_teacher
Grade level 5
This was my first opportunity to attend a forum like this. It was very impressive to see the collaboration of all the parties that are involved in preparing elementary teachers to be math teachers. It was particularly intersting to hear many of my own thoughts and ideas mentioned. I was hoping to get a better sense of what content would be most beneficial to improve the preparation of future elementary math teachers. I am currently working on devloping a Math/Science Specialist Endorsement and master's program. Listening to the need for a mix of content and methods for math classes will help us to decide and prepare our coursework.
math_educator
Grade level
The best part of the workshop was the conversations with people I would not otherwise meet, teachers, mathematicians and mathematics educators. Several of the sessions were organized in ways that facilitated these conversations. The World Cafe was particularly helpful, but I wish we had had longer in each of those world cafe sessions. It felt like we did not have a common understanding of why we were there, and at times, discussions needed more specificity and clarification. I learned some things about teaching mathematics that will be helpful, esp some of the ideas from Jim Lewis about how he teaches the math for teachers class.
elementary_teacher
Grade level K-8
The most helpful I thought was Sheri's because of its use of video. We each had the same data and it clarified for me the different ways in which each of us perceived it. More such experiences would illuminate, I believe, more areas where the different communities have different perceptions or values about the teaching of mathematics at the elementary and middle school levels. I hope at future events each presenter will be able (required?) to provide video of teachers and classrooms, at whatever level.

Kathy Kostos' comment "I've been in your classroom; how many of you have been in mine?" continues to reverberate for me. Again, video helps us to have more of a sense of the other's reality (tho I wish, like Kate Abell, that we could somehow work actual classroom observations into these workshops). I also appreciated Jim Lewis' suggestion that we begin with a panel of classroom teachers- "welcome to my world"- and I would like to hear the same from other perspectives. Each of us making our practice public as it were.
The research session was least helpful. While I was (and am) interested in the implications of the research I felt that presentation was actually pitched to a different audience (part of the workshop participants, but not all). I've taken statistics, I'm not stupid but I really couldn't make sense of or ask questions about much of the data presented. Given my present situation, I've come away with two big ideas about how to think about my work: Susan Jo Russell's "less is more" idea will work for in service teachers who don't necessarily see any need to change their practice. Just instituting a few routines that will force discussion and reasoning (by both teacher and student) can go a long way in highlighting a need for change. And second, for my own continued growth, I'm intrigued by the idea of math circles and hope to pursue the creation of one here at home. Thanks to all for a productive few days!
math_educator
Grade level
It was my first time engaging in real conversations with mathematicians around the work of teaching elementary mathematics content and methods courses. I picked up a few ideas about how to revive that conversation at my university where the relationship between the two groups is not active. The sessions were good but it would have been better if there were obvious connections between the sessions and some progression in ideas. I recognize now that other institutions struggle with the marriage between mathematics and mathematics education related to the preparation of elementary school teachers. I'm definitely going to try to have a more positive and proactive attitude about this instead of simply criticizing departments of mathematics for not doing things the way we (mathematics educators) think they should be done. If I can influence even the use of the text used for the content course, that will be a step in the right direction.
math_educator
Grade level
It was my first time engaging in real conversations with mathematicians around the work of teaching elementary mathematics content and methods courses. I picked up a few ideas about how to revive that conversation at my university where the relationship between the two groups is not active. The sessions were good but it would have been better if there were obvious connections between the sessions and some progression in ideas. I recognize now that other institutions struggle with the marriage between mathematics and mathematics education related to the preparation of elementary school teachers. I'm definitely going to try to have a more positive and proactive attitude about this instead of simply criticizing departments of mathematics for not doing things the way we (mathematics educators) think they should be done. If I can influence even the use of the text used for the content course, that will be a step in the right direction.
mathematician
Grade level
1) Collegial discussions - we need to get a feel for how the different groups think about things, what they pick up on, what they see as important.

2) Working together thinking through specific things such as problems or looking at student work or student teacher teaching.
Discussions that weren't specific enough. It's important to engage in actual specific substance rather than just spin wheels about general things. I'm thinking about how to get regular collegial interactions going locally among mathematicians, math educators, and teachers. If we think of it as co-professional development, I wonder if a regular group could get funding to have dinner together and look at school student work and at prospective teacher work together, for example. And also solve problems together.
mathematician
Grade level
1. Learning how content/methods courses are structured at other institutions. It would be nice to explore some more models and discuss effectiveness, logistics, etc.
2. Meeting mathematically proficient in-service teachers with an opportunity to discuss specific methods/content issues that arise in my content courses. As a mathematician what I lack with the students is "street credibility": I have never been in a K-8 classroom so it is helpful to have a credible voice echo our goals.
3. The post-graduation mentoring model of the U of C was very interesting, and definitely worth pursuing at my institution.
1. Some of the discussion questions of the presentations were a bit too vague and full of jargon. It seemed as though we needed to establish a glossary in the beginning so it would be clear what people meant.
2. The overall point of some of the presentations was not clear: at the end of the activities and discussions, what were we supposed to have learned/reaized?

It would have been helpful for me to have a discussion trying to identify "high leverage" content topics: in 20 weeks it is clear we are not going to teach them all the content they need to know. But can we identify key concepts with the property that if they learn them well, along with developing more "mathematical habits of mind", this knowledge will facilitate many other concepts to fall into place when they are out on their own.
1. I would like to find a way to incorporate in-service teachers into our 2 content, 1 methods course sequence. I found conversations with them and their perspectives to be very helpful while trying to organize my thoughts around content preparation of pre-service teachers. 2. I would like to explore the possibility of incorporating some of the ideas of the more rigorous course models into the structure of our sequence.
high_school_teacher
Grade level 9-12
a)I was struck by the brilliance of having the first presentation be on representation, for it was a theme that interwove the rest of the workshop. It is clearly a cornerstone of teaching mathematics.
b) I think I reflect my background as someone who is really into mathematics as well as to the actual teaching of math (the theory isn't as interesting). I loved Ginger's Nim game (it helped that I had a great partner and neither of us knew the trick) and Jim Lewis's math problems. I am going to make both available to colleagues. On the high school level, they are such a source of potential enrichment. For me, they capture what mathematics is really all about -- the finding the patterns and then the justifying them. Delicious.
a) I felt that, as a non-mathematics educator, I was rather a fish out of water. Understandably, there were times when the language was unique to that profession (since there were so many people there who understood it) and I didn't feel as though I belonged at all. Perhaps there just needed to be periodic reminders to folks, raising awareness that they were engaging in their own educator-speak.
b) Given my current interests, I was hoping that there would have been more on the the math content for elementary teachers. Given limited time and the over-riding importance of process over knowledge, what key mathematics really could not be excluded from courses with time limitations?
As much as I might have felt like I didn't belong, I treasured the opportunity to learn about what is happening in the field of mathematics education and I really liked meeting so many interesting people. As I move away from my life-long commitment to teaching teenagers (I have just run out of energy), I feel that I still have a great deal to offer to those who are just beginning to educate children. While it is not clear quite in what direction I am going from here, I am so grateful for this opportunity to learn from and interact with superb professionals. It was an honor to be included in this group. Thank you.
math_educator
Grade level
elementary_teacher
Grade level K-5
There were some great ideas that I could use for conducting staff development with in-service teachers. Ideas that I will use include the discussion protocol for critiquing teacher videos, using student representations as a basis for discussion among teachers, and having teachers engage in problem solving with representation and written communication to explain reasoning. The research on mathematics classes for future elementary teachers was not helpful. Although it was interesting to hear about the research process, the findings were not specific enough to be helpful.

The use of games including Nim and Didactique was interesting but not particularly relevant to our curriculum.
This workshop will have little impact on my work. The workshop seemed to be more relevant to teachers in the college environment than to teachers in elementary classrooms. The issues that we face in the classroom are related to the diversity of mathematics learners that teachers (including new teachers) are responsible for, and a lack of teacher preparation in how to handle those diversities.
math_educator
Grade level K-5
Most helpful to me was the thread of discussion that went through the workshop on the habits of mind. Mathematical habits of mind seem to be the most fruitful framing structure when mathematicians, math educators working with preservice teachers, math educators working with inservice teachers, and teachers themselves get together.

The video from Chicago was a good focal point for that discussion to take place, although groundwork was done earlier in the workshop.
All three world cafe presentations, and the case studies in the last session (and doing the math!) were places where habits of mind could be discussed and debated.
I had trouble integrating the information presented from the study of university level math education classes with what we were doing. Although interesting, I didn't feel that it informed my work or the work of the conference.

I think the different vantage points of the groups of participants was potentially powerful but that it took awhile to find the places where those vantage points could be brought to bear.
The habits of mind that mathematicians bring to bear on problems in their work are central to the work of educating students mathematically in elementary school. Precision of language looks different in elementary school than in the community of professional mathematicians. However the importance of precise language to mathematicians underscores the central role that communicating one's own ideas, responding to the ideas of others, and developing--with a community--a justification for mathematical claims, has in elementary school. This is in stark contrast to the vast majority of math teaching in elementary school, which comes to such communication or justification as an afterthought, to get full credit on a standardized test or to answer the teacher's question "fully." I came away from the conference with a fuller understanding of the centrality of this habit of mind and will frame work I do with teachers regarding lesson planning to more consciously bring this element to the fore in our work.
math_educator
Grade level
I was especially intrigued by Sheri Rodel's session on the Chicago program to prepare urban teachers as this is an area in which my institution needs to develop further.

I also enjoyed the roundtables in the World Cafe.
I know have connections with people I did not know previously and can continue a dialog with them. I gained some new perspective on ideas, such as representation, didactique. I need to continue thinking about underappreciated aspects though as I'm still not sure what those are.
math_educator
Grade level
I found working on specific mathematical tasks with other people very helpful. It allowed me to hear others' ways of thinking, especially other mathematicians and teachers rather than only mathematics educators. It also helped me see that we bring the understanding (about mathematics, teaching, and learning) that we have been developing for sometime, and it can be very easy to make the assumption that everybody knows what you are talking about when it may not be the case. The terms and definitions that we use may not be as clear as we think they are.

Also, hearing about how things work in other institutions was very helpful (what kind of content courses they teach, what kind of internships they expect their preservice teachers do, etc.)
I cannot think of any. It helped me think about our teacher development program. I did share some ideas from the workshop with my colleagues.

Grade level
math_educator
Grade level
Each of the sessions helped by raising questions about the work of what prospective elementary teachers need to be well prepared to teach mathematics. The single most pressing question for me is the issue of how many elementary mathematics content courses should preservice teachers take and what should the content of each course be? I find myself wondering if these content courses should "cover" the mathematics topics or uncover the nature of mathematics.

A related set of questions has to do with timing. Does it pedagogical sense to take mathematical content courses two or three years before the preservice teacher begins in her/his own classroom? What does he/she retain in the interim? What kinds of ongoing experiences will keep these mathematical insights alive over time?

Does newly acquired or revistied knowledge translate into effective teaching? Does it matter how math content courses are taught? For preservice teachers who continue to struggle with elementary mathematics and tend to check out of the process, would taking content courses work best once a teacher or student teacher has significant experience with children?

How do preservice students use the mathematics textbooks, during the course and afterwards?

Conversations with the range of perspectives present - those of mathematicians, other mathematics educators, mathematics coaches, teachers - helped me formulate some of these questions. It also helped my awareness of the nature and challenges of their work. Examining and analyzing the documents from their work was very revealing.

The single most useful discussion was that led by Susan Jo on Saturday afternoon.
At points during the workshop, the energy seemed to lag, especially if a presentation was less interactive.

I did not come to the conference expecting answers to questions, rather that questions would be raised and discussions would ensue. The vast majority of the conference sessions, and the opportunities to talk more informally with participants, were stimulating intellectually and informative. The World Cafe format worked quite well.

The conference certainly met my expectations for thoughtful discussions on the challenges of helping preservice teachers learn how to teach and learn mathematics. It raised important questions about the need for the mathematics content preparation of student teachers. The discussions about the use of represtations to model mathematical ideas continues to resonate many days later. Thank you, workshop organizers, for a stimulating set of questions to consider.
math_educator
Grade level
1. The collaboration across disciplines and working with in-service teachers. The contributions made by the teachers, providing an "insider" perspective, was invaluable. As a junior mathematics educator, it served as reminder of where research ought to be focused; in the classroom

2. The variety of presentations
1. This perhaps is in no way a reflection on the workshop, however one of the things I struggled with was the language of talking about mathematics education.I believed that throughout there were times when participants talked passed each other because there does not exist an agreed upon or precise way to talk about issues in mathematics education. I recall, specifically, my struggle in not understanding what a mathematical representation is. As a result, I found it difficult to engage in a conversation. I am not sure how to proceed in minimizing this. I understand that when we talk across disciplines there is this problem, however, it seems to me, even within the discipline of mathematics education, there is a lack of precision in the language used. What can be done? 1. As a researcher, I was reminded of the daily lives of mathematics teachers, and I hope to represent the complexities associated with this work. 2. The new relationships forged during the workshop. I anticipate working with several of the participants on research projects in the future.
mathematician
Grade level
Talking individually with others during breaks and in the evenings was the most helpful thing to me. I also found it helpful to experience firsthand the cultural and communication difficulties that exist between mathematicians, math educators, and teachers. Sometimes I didn't think the speakers were making it clear what they meant by the terms they were using. I sat through several sessions wondering "what are we discussing/doing here?". I would like to have had a bit more of a clear-cut goal. I know there were 3 guiding questions, but many times we seemed to stray far from them. I would have liked to address them more. Difficult to say. I absorbed a lot of ideas, but I'm not sure precisely how I will apply them yet. Part of my new job is learning to do math ed research, so discussing that with people individually helped me learn a lot that I'll need to know to get started. I definitely found it useful and worthwhile to attend.
middle_school_teacher
Grade level 8
Through the discussions with small groups, I was exposed to the opinions of others that allowed me to better understand the need for these kinds of forums. I had walked into this experience expecting answers, instead I gained a new queue of questions. In the end, I didn't walk away with a sense of purpose having been accomplished, or that I was part of an ongoing solution. It would have been good to know that some end product had been accomplished, even if the promise of more conversations to come. (Unfortunately, I had to leave a few hours early, it may have been that I missed out on the fruitation of the workshop.) Since the workshop, I have tried to be more mindful of the factors I consider when preparing my students. As any good teacher, I find myself wanting to learn even more, to better pass that knowledge on to my students. I look forward to more opportunities to experience the idea of mathematics education from a variety of sources. Regarding my math methods course, this workshop had a more direct effect on the types of information and experiences I want to expose those students to in the future. I especially want to address the idea of quality questioning to bring out the mathematician in them and their future students.
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