Participant 1 (elementary)
P1
|
1. "What is math?" experience
A good way to have students begin thinking about/rethinking their perceptions
of math. Starting with a small group experience on the first day was a good
ice-breaker. |
P1
|
2. Cardtrick experience
Don't tell students they can't leave until they figure out the trick
-- unnecessarily intimidating and anxiety producing. I liked the way this
problem illustrated that different approaches or methods can lead to the
same result. |
P1
|
3. Problem solving issues
This was a great experience. I hope to use something similar in my classroom.
Just remember that the students may have diverse lifestyles. What is a legitimate
issue for some may not be for others, and some students may be reluctant
to share some personal information with the group. |
P1
|
4. Area experience
This series of lessons was very helpful. It illustrated the many ways
available to approach a problem. The fish problem allowed us to use different
methods and tools to begin thinking about area, and pointed out that absolute
precision is not always required for a usable answer. The experience of
developing a formula for a particular figure really made me think about
process. |
P1
|
5. Inquiry approach and NCTM Standards issues
This was my favorite part. I found the classroom stories very interesting
and useful. The midterm was helpful to focus on why an inquiry approach
is educationally important in addition to being appealing. |
| P1
|
6E. Teaching of arithmetic session
Good modeling of what you expected from the group sessions. I liked the
"mental math" part, followed by student explanations of their
process of strategy. Another example of the many differences. |
| P1
|
7E. Teaching and learning of a specific math topic
Good practice for the students to have to be able to synthesize and communicate
information. I'd recommend encouraging students to come up with more suggestions
for classroom activities. It was helpful to have this assignment due when
it was - we had enough exposure to class to help us understand and synthesize
the materials, but it wasn't so late in the semester that it occurred at
the same time as our other final projects. |
P1
|
Other comments
More time to share math-related student teaching experiences. More classroom
accounts, examples of NCTM standards in practice, examples of inquiry approach.
I liked having some of the classes with the secondary students. Also, more
examples of problem solving activities would be helpful. For group projects,
consider making some time available to meet with group members during classtime.
It's very hard to find times to meet with students' diverse class and student
teaching schedules. |
Participant 2 (elementary)
P2
|
1. "What is math?" experience
At first this seemed a very difficult assignment. It was like defining
literacy. However, when I thought about it, I came up with many metaphors
for math. I liked the math autobiography idea. I may ask my older kids to
do that for me. |
P2
|
2. Cardtrick experience
Wonderful! I didn't like not being able to talk or to discuss our thoughts.
It was fun showing and teaching it to adults who liked or disliked math
or who felt they were good, OK or poor in math. I loved cardtricks anyways.
They are a sure way of getting a child's attention. |
P2
|
3. Problem solving issues
Stressful! The assignment was too vague. Some of us did not know how
much this counted towards our grade and therefore went out of our way to
find out the information. It was hard to compare since different people
took different things into account and calculated for different amounts
of time. This activity needs some guidelines. The questions with calculating
the area of the fish was fun, interesting and very thought provoking. Keep
it! |
P2
|
4. Area experience
It seemed long and when 2 groups chose measurement and geometry, I was
afraid more area was in store. I liked working in a group to make a poster
instead of writing another paper for finding the area of a star. It was
harder to come up with a generic area equation and to reconstruct the star
than we thought it would be. We learned a lot from this unit. |
P2
|
5. Inquiry approach and NCTM Standards issues
Excellent. Your articles are very helpful. It sounds like you try to
create a Rogoff-style community of learners. The video clips seemed to drag
a bit or I was very tired that day. Living and Learning Mathematics
should be a required text for elementary student teachers. It gives excellent
examples of incorporating math in the children's lives. |
| P2
|
6E. Teaching of arithmetic session
The fraction lesson dragged a little, but our discussion of how we figured
out the answer was helpful and valuable. I also enjoyed Luca's recordings.
They showed what a child can do. |
| P2
|
7E. Teaching and learning of a specific math topic
Very useful. Some readings were more useful than others of course. I
would have liked to see a list of books (children's literature books), manipulatives
and games which could be used to teach a topic instead of just 1 suggestion
of each. I had mixed feelings about getting a manipulative without any explanation.
We did find a way to incorporate it though in our presentations. Working
in groups is always very hard, but working by ourselves would have been
a nightmare. Presentations were very useful and we tried many of the techniques
you modeled for us. Some were successful; others flopped. It was too bad
the secondary teachers were not included in this. Please coordinate this
with Joanne, so that everything isn't due in the same week. |
P2
|
Other comments |
Participant 3 (elementary)
P3
|
1. "What is math?" experience
I liked this because it helped me to see my true feelings and thoughts
about math. |
P3
|
2. Cardtrick experience
I really enjoyed the cardtrick experience, it showed me that no matter
how frustrated you may get, if you keep trying you can finish anything,
do well at anything. |
P3
|
3. Problem solving issues
Loved this, especially our projects. It got us involved and was something
of interest to class. It was neat to see the difference in people's findings. |
P3
|
4. Area experience
I liked this because for myself it showed me that I do know something
about math, that I am understanding what is going on. |
P3
|
5. Inquiry approach and NCTM Standards issues
This was very useful, by doing the midterm I got to see exactly where
the standards really do fit into the classroom, which is very important. |
| P3
|
6E. Teaching of arithmetic session
This I liked because it helped me to see how I process information and
allowed me to compare this to others. |
| P3
|
7E. Teaching and learning of a specific math topic
It was valuable but also difficult for myself because I chose a topic
I had no interest in, but wanted to learn from it. I learned a little. But
feel I learned more from other people's presentations. The project was at
a time when I had a huge paper due, which left not as much time for this
project. But is was a positive experience. |
P3
|
Other comments |
Participant 4 (elementary)
P4
|
1. "What is math?" experienceOverall
I thought it was a good introduction to the course. It gave me an opportunity
to reflect on what is math to me. What I liked and disliked about it. My
experience learning math. It was a good starting point to how I would like
to teach math. Suggestion: Maybe the instructor could share more about her
own experiences learning and teaching math. |
P4
|
2. Cardtrick experience
It was excellent. It gave a good experience on the learning process of
math in general. |
P4
|
3. Problem solving issues
The readings were good. It gave me a better understanding of problem
solving. Suggestion: Maybe we should do it in group - to problem solving
something in our everyday environment. Not everyone would want to buy a
pet. But I did like the activity anyway. |
P4
|
4. Area experience
It was a good experience to see how math knowledge can be constructed.
Suggestion: We needed more time for the group discussion before the presentation. |
P4
|
5. Inquiry approach and NCTM Standards issues
The analysis was good. It gave us opportunities to reflect on the NCTM
and it's application to classroom teaching. Suggest: Video presentation
on classroom practices. |
| P4
|
6E. Teaching of arithmetic session
I like the sharing and discussion we had on the topic. It gave a lot
of insights. Suggest: It would have been better if the activity was more
interactive (while doing the fractions). |
| P4
|
7E. Teaching and learning of a specific math topic
It was a lot of work. But it was worth the effort. The discussion and
sharing was useful. I liked the exposure to teaching at different grade
level. |
P4
|
Other comments |
Participant 5 (elementary)
P5
|
1. "What is math?" experience
I liked that we were able to reflect on our experiences and fears
about mathematics. |
P5
|
2. Cardtrick experience
I liked that we had to take an activity that we explored within the context
of our classroom and attempt to gather knowledge about the structure and
content of the activity outside of the class. |
P5
|
3. Problem solving issues
The experiences that we explored helped me to understand the importance
of activities that were open enough to allow for variation amongst students
in regards to their interests. |
P5
|
4. Area experience
One sentence: there are many ways to look at a problem as well
as solve a problem. These processes are adopted by students to facilitate
their growth and understanding. |
P5
|
5. Inquiry approach and NCTM Standards issues
Do not underestimate what your children can achieve. |
| P5
|
6E. Teaching of arithmetic session |
| P5
|
7E. Teaching and learning of a specific math topic
The topic was valuable because it allowed us to synthesize the readings
with practice. |
P5
|
Other comments |
Participant 6 (elementary)
P6
|
1. "What is math?" experience
I thought that this was a great way to begin the course. I think I might
have challenged the students to try to use the posters as a way to find
ways of depicting what math is without listing sentences or formulas. But,
this may also restrict the actual goal of letting students come up with
their own meaning. My intent was to think creatively about math -- which
people usually don't do. |
P6
|
2. Cardtrick experience
OK, even though this proved to be a frustrating experience for me, it
really opened my eyes to lots of subtle things about the nature of learners
and learning. I actually enjoyed the trick once I finally got it. The best
part was having this knowledge and then torturing another person with it!!(haha)
But, it will have a real affect on my teaching in terms of how competitive
learning is; how different student approach learning (solo or in groups);
how students make sense of things, etc. I want to value all of this diverse
learning and I hope I can do it! |
P6
|
3. Problem solving issues
This was really cool -- especially the "cost of a pet" activity.
I want to really focus in on real-life experiences in my classroom and these
were really important activities for me. Again, it also reinforced the diversity
in thinking and problem solving skills among our small group. |
P6
|
4. Area experience
I enjoyed this experience because it allowed us the freedom to figure
it out on our own. The only thing is that we have prior experience stored
away in our minds so I wondered what other types of scaffolding I would
do in order to make this productive in a classroom of "first-timers."
But, the point of the activity came across and it will help me to understand
my students' when I can see the learner in myself. I have to say that I
hated when you chose the groups to work with for this project (area of a
diamond) -- I know that learning to work in a group is a real issue but
my group drained me of any will to want to participate! (sorry) |
P6
|
5. Inquiry approach and NCTM Standards issues
I have to say that I want my classroom to reflect inquiry approach in
all areas. The standards are good but somewhat overwhelming because they
conflict with standardized testing. I know that the tests won't go away
but I worry that I won't have enough time to establish the type of learning
the standards require. That doesn't mean I'll fall in to "teaching
to the test" -- I'd better not! |
| P6
|
6E. Teaching of arithmetic session
More video clips of the "Bike Path" classroom would be very
helpful - not traditional ones, we already know what doesn't work! |
| P6
|
7E. Teaching and learning of a specific math topic
I really enjoyed my topic and the readings were wonderful. They got me
all excited about the real possibilities -- I always have a million ideas
but always wonder if it would work or not. (I realize the value in things
not working...) Reading about real-life experiences to shape a math unit
really focused my "million ideas." It also made the poster presentation
easy to put together because I was so into it. I would perhaps structure
it so that groups perhaps give actual examples of how a specific topic would
be taught and reasons for it. I felt some of the presentations lack that
so I felt a bit lost. |
P6
|
Other comments
I found the Luca stories inspiring for my own student teaching experience
-- gave me great ideas. |
Participant 7 (elementary)
P7
|
1. "What is math?" experience
I enjoyed this lesson. It was only the beginning of my reflections about
math - but it was a great start. It would be interesting to compare those
thoughts with "end of the course" thought. |
P7
|
2. Cardtrick experience
Right now, I'm trying to remember if I can still perform the trick! I
had fun and also became frustrated at points. I think that was key in getting
me to reflect on my own learning of mathematics. I think it was quite worthwhile. |
P7
|
3. Problem solving issues
This was extremely valuable (the pet activity). Math is useful in daily
life and it varies depending upon one's experiences and situations. This
activity proved that everyone views the world through unique eyes, i.e.
getting a cat means different things to different people. |
P7
|
4. Area experience
I like the fact that we could work together. I think that learning is
social and we learn through interaction. This lesson was particularly helpful
in teaching us that people attack "problems" in varying ways. |
P7
|
5. Inquiry approach and NCTM Standards issues
Very helpful -- I was unsure of the inquiry approach, and now I believe
it is the way to teach mathematical concepts. |
| P7
|
6E. Teaching of arithmetic session |
| P7
|
7E. Teaching and learning of a specific math topic
This project was meaningful and valuable. I liked sharing our research
with the class and gaining knowledge from classmates' research. To do all
of it myself would not be possible in such a short amount of time. Another
helpful aspect was that you provided us with readings beforehand. |
P7
|
Other comments
#6 - I feel that this entire book is helpful! We used it for our project
also. The NCTM standards are definitely worth reading for this course. I
agree with their philosophy of teaching math - and the standards are helpful
in thinking and reflecting on teaching math. |
Participant 8 (elementary)
P8
|
1. "What is math?" experience
I thought this was a useful project. It made us really think about what
math is to us because we had to put it down on paper. |
P8
|
2. Cardtrick experience
I disliked the competition feeling that went along with trying to figure
the trick out, but I understand the value of such an experience. |
P8
|
3. Problem solving issues
I think this is a very important topic to address. The pet activity was
fun and showed how school work can relate to real life interests. |
P8
|
4. Area experience
This activity was good because it showed that there are many ways to
solve the same problem. |
P8
|
5. Inquiry approach and NCTM Standards issues
This activity (the midterm) was good because it showed more practical
and concrete examples of how the standards can be put into practice. |
| P8
|
6E. Teaching of arithmetic session
This was valuable because it showed specific techniques for a specific
topic. |
| P8
|
7E. Teaching and learning of a specific math topic
I appreciated that we did not have to spend a great deal of time getting
the research materials on our own. The presentations were helpful to me.
I like having the handouts (key points, annotated bibliography) as resources
for the future. |
P8
|
Other comments |
Participant 9 (secondary math)
P9
|
1. "What is math?" experience
Great kick-off - the math bio is also a big part of this I think. |
P9
|
2. Cardtrick experience
Good experience - some tough reflection came out of it - I wish we could
have explored more how to deal with "slow vs. fast" learners and
types of "teaching" or not tracking in order to cope with differences
in learning speeds. |
P9
|
3. Problem solving issues
Good exercise - makes you think about the time involved in doing or giving
an assignment like this one. |
P9
|
4. Area experience
Loved it, it's a great way to introduce our basic concept of what area
is and the technologies (formulas) we use to find it. |
P9
|
5. Inquiry approach and NCTM Standards issues
This really helped me to focus on Inquiry as a process separate from
"good teaching" or "teacher involvement" - both of which
are necessary to, but not exhaustive of the approach. |
P9
|
6. Teaching of probability sessions
Liked this in principal but by the end I was "running out of steam"
- suggest you put this earlier - maybe in place of lessons on "negative
x negative = positive" |
P9
|
7. Final project |
P9
|
Other comments
Pertaining to #'s 19-21 I would keep the "idea" but update
as newer/better materials are released - also would recommend examples of
what you would consider poor material without any input from you to see
how students react by themselves to the extremes |
Participant 10 (secondary math)
P10
|
1. "What is math?" experience
I really liked that the experience made me evaluate my own views of mathematics.
Without this self-exam I think that I might have been more pessimistic about
math than I like to think. |
P10
|
2. Cardtrick experience
I didn't like that everyone had to figure out the cardtrick before we
could leave. It made me very nervous. I didn't want to be the one
to hold up the class. |
P10
|
3. Problem solving issues
Everything was well planned. The amount of work given was fair, up until
the end. I think a little too much writing was crammed all together. Better
quality could have been gotten by spacing big assignment out. |
P10
|
4. Area experience
I really like that it was an idea I might be able to use for my own classes.
I think the kids would consider it a lot of fun. |
P10
|
5. Inquiry approach and NCTM Standards issues
The inquiry approach is okay as long as the kids are motivated to do
it. I think an approach that is a little more structured might be
better for students who are slower or are afraid of math. |
P10
|
6. Teaching of probability sessions
I liked that we could compare different resources on the subject. It
made it more interesting, and gave me more ideas to use in my own teaching. |
P10
|
7. Final project |
P10
|
Other comments
I think that most of the readings given were very useful. The introduction
to the NCTM Standards could be cut out, I think because it is easily understood
without it. The probability section asked for a lot of reading, but I think
it was well worth it. |
Participant 11 (secondary math)
P11
|
1. "What is math?" experience
loved, focused class for entire semester, GREAT! KEEP! |
P11
|
2. Cardtrick experience
saw what it was like on both sides of learning teacher vs. learner, very
interesting, wave of education one teaches another teaches another. Give
hints, show different ways of looking at things. |
P11
|
3. Problem solving issues
Didn't really like, though I suppose it teaches a lot about differences
in ideas of what having a pet means and will cost. I never truly understood
its purpose. |
P11
|
4. Area experience
Enjoyed exploration and discussion it provoked. Opened my eyes to how
different students think. It was a really long experience, maybe
too long. Not certain what to cut out though. |
P11
|
5. Inquiry approach and NCTM Standards issues
From readings I never truly grasped what to look for, but through watching
how students/teachers interacted and based this NCTM standards or grading
scheme. The discussion really opened my eyes and focused me in my views
and desires. |
P11
|
6. Teaching of probability sessions
Good, but not certain of final focus until the end - all dropped on us.
Suddenly create your own based on what we have learned on top of everything
else. Timing would have been better sooner, middle of semester lots of writing
now. |
P11
|
7. Final project
Preview of what we did in classroom helped refocus and organize thoughts
and experience. |
P11
|
Other comments |
Participant 12 (secondary math)
P12
|
1. "What is math?" experience
I think this is of extreme importance because it sets the stage to reevaluate
our conceptions of mathematics and this foreshadows what is to come in the
course. |
P12
|
2. Cardtrick experience
More than anything it allowed me to revisit my own unpleasant experiences
as a student. Beyond this I was able to evaluate this experience as an adult
and apply it to the behavior of my prospective students. |
P12
|
3. Problem solving issues
Most importantly, gave some insight into the power of math over daily
situations and this opened my mind to a number of different situations that
I can provide for student to develop this skills. |
P12
|
4. Area experience
Really allows students to get as mathematicians do, make similar decisions,
have true understanding of area. |
P12
|
5. Inquiry approach and NCTM Standards issues
This was important because I think that it gave us the idea that this
movement is truly effective and supported. Important for us to analyze situations
so that we can begin to construct our own experiences with goals in mind. |
P12
|
6. Teaching of probability sessions
At times, I was a bit discouraged, possibly from the topic at hand. I
think it would have been helpful for us to actually teach a lesson in probability. |
P12
|
7. Final project
There is a lot I have learned and I consider this project to give be
quite a bit of latitude which is perfect!! |
P12
|
Other comments
I had a hard time justifying getting rid of any of them!! |
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