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Participants' testimonials (A)
Selection from in-service program participants' reflections
| The following excerpts come from the reflections that participants in our in-service programs were asked to write at the end of the Summer Institute and after they completed their field experiences. These excerpts were selected to illustrate the range of benefits that participants identified; therefore, you are invited to read the whole set, which comprises of the following items: |
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First impressions expressed by various participants at the end of the Summer Institute (1 page)
Probability of J.B. excited about the project on 8/15/93 was 1/10. The odds that the mood would change by 8/20/93 was 1:9. It just proves that some conjectures are invalid from the start ! It was as it turned out for me a great week. Probability of a successful venture for me in this project is 1. I feel that this result will happen mainly because of the people I have been working with [in this institute] and will continue to work with.
What a week ! I really had a few preconceived notions about what to expect. As a special educator, I felt this was a great opportunity to work with "mathematicians" in school in a collaborative way next year. Traditionally, this has not occurred in [my school]. So I was very comfortable working with my colleagues, but unsure of the role I would play in this relationship.
The tessellation unit opened my eyes and dispelled my beliefs and perceptions about mathematics. Never before had I been asked to think about what is mathematics and what mathematicians do. The tessellation unit stretched my global perspective and more importantly the possibilities in mathematics in relationship to innovative and cross-curricular ideas.
Wow, this was an incredible week. I was frustrated (but not discouraged) engaged, excited, anxious, and stimulated. The experience of becoming a "learner" and then stepping back into "teacher" was invaluable. Having an opportunity to investigate topics with such a diverse group of colleagues was exciting. It's easy to focus strictly on the grade levels in your own building rather than thinking of the big picture. I appreciate the resource materials, bibliography, and the energy of the facilitators. What a great way to start the summer -- planning instructional improvements, reform.
Overall, this is one of the best sessions I have attended on any subject!! I am highly excited about getting back to work to try some things. I also found that much is applicable to the different professional roles I play in a variety of settings.
I felt this summer institute was very useful. I was glad it was over summer because it was a lot of new ideas. I felt all the facilitators did a wonderful job with modeling the inquiry style of teaching. They stayed away from teaching methods. We learned through example. I felt it was very enjoyable and educational.
This was excellent! Each day was well organized and facilitated. The opportunity to experience as a learner followed by reflection was invaluable. The support materials for the tessellation and area units were clear and thorough. I feel that I have come away with a sense of how I can use this in my own teaching.
A week is a long time to sit and work all day/every day, but the whole experience was extremely valuable. One day could never provide enough modeling, discussion, and confidence building as a full week.
It was tiring to sit all day and then have homework at night, but I actually loved the journals. It made the week more personal as I got to know other's thinking. Being able to honestly react/respond to each day kept any pent-up feelings of frustration out of this room. Every day I could approach the activities with a more positive attitude as a result of that sharing.
Believe it or not, I am anxious to come to the advanced institute. I truly want this to become a natural part of my teaching style.
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Final reflection 1 (2 pages) -- veteran middle school math teacher discussing key changes in his classroom practice and how they benefited students.
After 23 years of teaching Mathematics at the High School level and 5 years at the Middle School level using a rather traditional approach, I was very lucky to be involved in the NSF project. The NSF project ­ "Supporting Middle School learning disabled students in the mainstream Mathematics classroom" gave me a whole new life and new ideas to share with colleagues and students. The NSF staff and participants I worked with during the past year were outstanding. The professional attitude and energy shown by all was amazing. In one of my early Journal's, I made the comment that you couldn't teach an old BUCK new tricks. Well I am pleased to announce that this old BUCK did learn some new tricks and I have the utmost confidence that they will make me an even better Math Teacher.
I feel that one of the most valuable tools that I will be using for the rest of my career is that of Cooperative Learning. This played such an important part in the teaching of all the Units that we did. Using Cooperative Learning in the classroom is a must for all Educators in the future. I feel this method is very valuable for L D students. Working in small groups, they don't feel so intimated and are more willing to share ideas.
One of the things that surprised me the most about teaching the Units was that every student was actively involved in the project. There was no daydreaming and lack of interest. The students that would have been bored in a traditional setting were actively involved in this process. Also by using the inquiry method of teaching, I was amazed at what the students came up with for ways to arrive at the solution. In most cases they were very original and even enlightened me on many different approaches to solve the problem at hand.
Using the inquiry approach to teach young adults can be very rewarding for the teacher as well as the student. I was amazed at how into each activity the students were. They seemed to have more at stake in the group activity than they would have in just a typical lecture situation. As a teacher I was elated at the different approaches that each group took to solve the problem at hand. As each group shared their approach to the entire class, I think it made everyone in the class have a better understanding of the problem at hand. Very often when you see the solution of a problem from another viewpoint, you understand it more clearly than if presented by just one approach. The only thing that concerns me about the inquiry method is the fact that many times it takes so much longer to complete. But after being involved with this method of learning, I feel the students learned the task in a much more solid fashion that in the traditional mold. Thus it is very easy for me to conclude that it is far better for a student to really learn well a few things that will have a lasting effect than to hastily learn a lot of things that will not have a lasting effect. I feel that the L D students really functioned well in this type of setting because they were involved in the actual learning process. It is easy to see that if you keep any type of student busy, interested and on task, they will learn much more and retain it for a longer period of time.
As we were doing the N S F project units, the students seemed to enjoy Math. They were talking about what they were doing to other students in other Math classes. Other Math teachers told me that their students were asking "why can't we do what Mr. B.'s classes are doing?" Let's hope some of these other teachers will wake up before it's too late and try some other approaches besides straight lecturing. Don't get me wrong, lecturing still has a place in the classroom, but it is about time that the old traditional lecturing Math Teacher climbs out of their shell and breathes some of the new fresh air and sees some of the new rays of sunlight on the horizon.
One thing we have to be careful of in this new approach to teaching Math is that we don't lose individual accountability. Sometimes in a group activity a student does not participate and will still receive a good grade from the entire group. There is nothing wrong with this on occasion, but we must remember that each individual in the group must be accountable for understanding the task at hand.
Another very important feature of this project was that I feel that my students discovered the true meaning of a Mathematician. Rather than just doing problems 1­31 Odd on page 354 in the textbook, they found out that Math is much more than doing a few boring repetitious problems. I also feel they learned to think and talk like Mathematicians. Some of them were excited about Math for the first time and wrote about it in their Learner's Log. Yes Learner's Logs! I never thought that writing a sentence or a paragraph would be valuable in a Math class. But like I once heard [another teacher] say, "it is really enjoyable to read what some of my students are thinking." I found that some of my students who were to bashful to contribute in class were very willing to write about what they were feeling. This proved valuable to me in trying to find different ways of trying to satisfy every child's needs in the classroom. But, I still must admit that I am not very fond of writing in a Journal. I think this is OK as long as I don't relate this to my students.
All in all I felt this was a very rewarding and exciting experience for me. It has changed my whole approach to the teaching of Mathematics. I am very excited about trying to improve on the methods I learned last year working with the N S F project. I would like to thank the N S F Staff for showing such enthusiasm and so willing to share everything with us. I feel that through the years many teachers have been unwilling and afraid to share with their fellow teachers. The sharing that took place during the project was truly amazing and worthwhile. I am positive that all of us involved became better teachers because of it.
Thanks again for letting me be a part of such a valuable contribution to the teaching of young adults.
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Final reflection 2 (1 page) -- special education teacher discussing some of the mathematical goals reached as a result of teaching mathematics through inquiry and the benefits if this approach for LD students more generally.
I think I was most surprised by the fact that the students thought of some of the activities as being fun. I haven't heard eighth grade students refer to math as being fun in the past! Most of the time they were interested and extremely involved in the activities. They really seemed to enjoy working with partners. I guess I thought of the tessellation activities as being fun too!
I think the inquiry approach allowed us to address higher level thinking skills. [...]
I also believe that this approach was beneficial in showing the students that problems can be solved in different ways and that often there are a variety of approaches. This was most evident during the area/perimeter unit when the students worked on finding the area of complex figures. At first, they wanted to know exactly what steps to follow. As the unit progressed, they looked at these problems as puzzles that they could solve! They enjoyed sharing their results with each other and seeing the various ways that these problems could be solved. Also I think we were somewhat successful in teaching them that real problems take time to solve. This is where my AHA experience occurred. I used to think that many of "my kids" weren't capable of solving complex area problems like the fish. Boy, was I wrong! When I saw how proficient most of the students were at finding the areas of complex figures, I was truly amazed!
One drawback may have been the fact that some of the students were frustrated by the fact that Frank and I wouldn't provide immediate assistance or answers whenever they perceived material as being too difficult for them. We would tell them to continue to work on the problem in their group or with their partner, and we would offer some guidance, but for some of the students that wasn't enough. These students were very concrete learners who perceived math as being very exact. Most of them also felt that there was only one way to solve a problem. As the year progressed, I think many of them became more comfortable with the inquiry approach, but at times they were still somewhat frustrated. [...]
To summarize, I think that our students probably think of themselves as being more capable mathematicians. They are willing to tackle difficult problems, which will be to their advantage as they continue in math.
I think that all of our student benefited from this approach to math. The only students who did not benefit were the ones who refused to do any work or those who faced other issues outside of school that interfered with their academic progress.
As an L.D. teacher, I have always felt that I have been sensitive to the needs of my L.D. students. However, working on the Grant this year has allowed Frank and I to deal more successfully not only with our L.D. students' needs, but with the needs of all the students. I can't stress how important I feel manipulatives and visuals are in helping students visualize difficult concepts. The hands on activities that we did were great! Such activities enabled the students to visualize things that many of them couldn't have visualized otherwise. The group activities and think, pair, share activities were also excellent. These activities provided opportunities for the students to exchange ideas, to learn to listen to each other, and to value each other's ideas. Group activities and partner work were also beneficial in that the students were able to help each other perceive and understand difficult concepts and problems.
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Final reflection 3 (1 page) -- middle school math teacher discussing the changes in her planning process and the benefits of collaborating with colleagues.
As I reflect over the past school year, I feel a lot of satisfaction and pride in the work that we have done. I feel my students have faired well this year in their growth towards being better mathematical thinkers. And also, I feel the obligations of the curriculum have not been ignored in the process of changing my teaching strategies and my approach to the curriculum. I feel that my teaching has a much more global viewpoint in that I now tend to think about good activities to teach from rather than topics to teach. I have grown to have confidence that from activities, the topics will emerge and that the curriculum will be tended to in a very different way than those sequenced in the chapters of textbooks. The result of this all is a very positive outlook to refining my experiences next year and thinking about new units to try in the immediate future. [...]
I feel that there are endless ways that my learning this past year will inform my practices next year. I have learned and refined notions of planning and goal setting in the writing of units. The process of collaboration in writing of units gave me new insight into making ideas come to practice in the classroom. Having a circle of professionals to bounce around ideas with helped me to learn a lot about the possibilities that mathematical exploration can take. Hearing various viewpoints in the planning process helps me as a teacher to see how various students might react to plans before they are actually implemented in the classroom. I feel the collaboration process has expanded my viewpoint towards lesson possibilities for students.
The work we professionals did in our group planning sessions paralleled for me the group activities we engaged the students in. The weekly planning times where ideas were exchanged and dialogued seems to me to be the adult version of the conjecture/proof group discussions the students have done this year. I guess I see adult collaboration paralleling student collaboration in the classroom as an important notion. Teachers immersed in the units and teachers immersed in the strategies sensitizes the teacher to student situations and dilemmas. Taking on the role of student while being teacher is a very powerful model to effecting change in my opinion. Talking about changing is less dynamic than experiencing it. The experiences of the summer institute and the sharing of experiences with other school teams inspired me to keep going and assured me that the other "student teachers" were facing similar challenges. [...]
In summary, I am very pleased with our work this year. I think I have grown personally and professionally during this time. I have appreciated the collaboration and support of the grant staff in our endeavors. I think the work begun in this grant has great implications for the future. I hope there can be a way to continue to educate teachers and spread the notions we have refined during these times. I know that I will never be able to turn back to any rote traditional style ever again. I took a risk getting involved this year and did so without the explanation that other new teachers got when visitations to schools were done. I am glad I did not miss this opportunity. I hope we have added to your success in our time with the grant. We did try hard. Onward and upward...
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Final reflection 4 (2 pages)-- pre-service math teacher discussing what she learned about the teacher's role in teaching mathematics through inquiry.
How can I even begin? What have I learned? There have been so many things since the first day of the summer institute that have had a major impact on my growth in the understanding and approach to the learning and teaching of mathematics and that will have a major impact on my teaching practices in the future. Not everything has been learned for the first time, but many things have been reinforced and emphasized, and I have developed a better understanding of them. And this is what learning and teaching is really all about. Learning, growing, reshaping, developing, extending, always pushing for a better understanding. What I have been reminded of over and over in the last few months is what students and teachers can do when they are given the right tools. They have such potential. They are growth waiting to happen. We all need someone to push us, to ask us to extend and to explain, to guide us in the right direction, not to just "tell" us the right answer or to "tell" us how to do something. Our students need teachers who are willing to be "awed" by them (as Judi has mentioned), willing to be awed by each new discovery, even if others have discovered it before, because for these students it is the first time. My instructional philosophy has not completely changed­­rather it has grown and extended. Now I have more than just a philosophy, I have some of the tools to carry it out.
I think probably the most important thing that I learned this semester is the importance of the teacher taking on the role of a facilitator/observer/practitioner in her own classroom. A teacher needs to get to the students' level, to figure out what they are thinking, to almost get inside their heads, to anticipate what they will struggle with and what they are really having problems with. Through my tutoring and observation experiences, I have come to realize once again the incredible amount of flexibility, insight, and creativity that students have when given the opportunity to show it. I have also come to realize how little of an effect just telling students the answer has on real learning. They may be able to spit the answer back to us that day or even the next day. But do they really understand it, have they really learned it? Again and again I have thought about how much students need to be encouraged to think about things and to figure them out, how much they need to be pushed to extend and to think and to explain their thinking in words. I have realized that before, I often thought students had a good understanding of something if they gave the right answer. Now, I have noticed myself pushing the student I tutor to explain, explain, explain...to really show me that she understands. It is hard to explain our thinking, but it is necessary. I am reminded of how hard it was for me to explain a point I was trying to make about tessellations to the rest of the people in my group at the summer institute­­something that was completely obvious to me. Yet, by being pushed to explain and extend, I understood my own thinking much better. I have also been reminded that students are not going to remember everything that we teach them, but if we provide them with memorable and meaningful mathematical experiences we can lay a foundation for further learning and for better understanding later on. I didn't understand everything there was to know about derivatives when I took calculus in high school (and I still don't). However, a wonderful foundation was laid for my further learning later on. This is what we should be doing as teachers, laying the foundation for further learning, helping our students become learners, realizing that there are many other experiences that will shape their understanding and learning. But we need to provide them with challenging and meaningful experiences, turning them on to learning, so that the "growth waiting to happen" will happen.
I have learned so much over these last few months, and this learning is continuing each day­­each new discussion that we have about the inquiry process, about students' learning­­about their thought processes is helping me to come to a much better understanding of the entire inquiry process: how it works or does not work in some cases and why, what is necessary for inquiry to take place, the importance of setting the stage and the role of the planning process, and most importantly, the crucial role of the teacher as a facilitator of the whole "learning through inquiry" process. I have also come to a better understanding of learning disabilities through my observation experiences in blended classrooms and through discussions in one class with the math teacher and in another class with the special ed teacher about different students. I feel that the inquiry approach to teaching mathematics is good for all students. I do not believe that it is going to solve all problems over­night. However, it just makes more sense to me for the teacher to play the role of a facilitator, helping students raise their own questions, encouraging students to ask why, pushing for understanding, asking students to extend their thinking, creating a need for what students learn, helping them make connections, creating meaningful contexts for learning to take place. Real understanding has got to be better than memorization! [...]
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