Click an item in the table below to go directly to
a specific questionnaire and/or participants' responses to a specific item:
Note: The following menu includes ALL the questionnaire responses
received from Implementation A participants. Ratings on the readings (item
#11 on this questionnaire) have not been included for space considerations.
Click the arrow icon to return to this menu:
 |
| ENTIRE Questionnaire |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 1. Introductory lesson |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 2. Cardtrick experience |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 3. Problem solving issues |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 4. Tessellation experience (D2.1 + D3.1 + D3.3) |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 5. Assessment issues |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 6. Inquiry approach issues |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 7. Teaching strategies issues |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 8. Student case-study |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 9. Teaching and learning of a specific math topic |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
| 10. "What have I learned" paper |
1, 2,
3, 4, 5, 6, 7,
8, 9, 10 |
| Other comments |
1, 2,
3, 4, 5,
6, 7, 8,
9, 10 |
Participant 1
P 1
|
1. Introductory lesson
This class didn't have the appeal of the others, but I'm not sure how
it would be better exactly - I left the class with the impression there
would be a staggering amount of paperwork and discussion of aspects of math
which seem rather obvious it needs to contextual, students learn differently,
etc.) - I guess this is the hardest point, though - laying the foundation.
Maybe just an overview of the syllabus instead of a detailed one would have
been better for me. |
P 1
|
2. Cardtrick experience
I thought this was great - I don't really have any suggestions for improvement
- I liked the way you presented it and proceeded through the entire lesson.
It was very useful, as were the writing assignments. |
P 1
|
3. Problem solving issues
The hiking problem didn't turn me on too much, even though it was a realistic
situation and something I'm interested in, I didn't feel like it was real
to the class. Maybe because in most situations, I think most of us would
rely on a couple basic facts and our definition, and not do all the math
we did (which made a "realistic" situation unrealistic). |
P 1
|
4. Tessellation experience
This was one of the best learning experiences I've ever had - the high
point of the course, and though some of the writing seemed like overkill
at the time, I think every part of it was extremely valuable! I would
recommend working in a pair outside of class to everyone. |
P 1
|
5. Assessment issues
This didn't have a big impact on me - is there some way to model assessment
more concretely or get us involved in assessing... Maybe as part of the
case study, we should think about how we'd assess our student within the
confines of our situation and how we'd go about it in an "idea"
situation. |
P 1
|
6. Inquiry approach issues
The classroom stories were interesting - too bad so many people were
absent from our class. Actually, these are probably all readings where class
should do - maybe some others could be replaced. |
P 1
|
7. Teaching strategies issues
This was interesting to think about, though I felt like we dwelled on
it too long in class. This is a point at which I think we may have spent
time reflecting on the class when we maybe could have spent time more effectively
actually doing something else. I know reflection is necessary, but
I also think it can be overdone. The NCTM standards all make a lot of sense
to me, but I'm having some problems connecting them to experiences or having
them within those experiences. |
P 1
|
8. Student case-study
This was a very valuable project ... very good to get us thinking about
how we can better understand our students because as teachers we will be
responsible for a whole class full of students and ideally should understand
a case-study worth of material about them - so this was great practice!
At the time, I felt like it should have been introduced earlier, but the
timing worked out fine. |
P 1
|
9. Teaching and learning of a specific math
topic
This was a very interesting project - the best thing about it was reading
the articles which gave anecdotal themes - the Lampert article was the best
and I think that the more theoretical and journal pieces had some merit,
but nowhere near the value for this assignment as did the reports of real
experiences - so I'd suggest more of those. The Lampert and Research
Methods book article really got us thinking and excited about multiplication.
Once again, the timing was perfect - I was glad we didn't have more time
and also thankful to get it done before the very end of the semester! I
didn't find it useful to do points and annotated bibliography for every
article - felt I was repeating myself. |
P 1
|
10. "What have I learned" paper
I approached this will reluctance, even though I think it is an essential
way to draw closure... I'm just a little "reflected out." By the
time I was done with it, have gone through all my old papers and highlighting
them, it almost turned into fun. It was useful even though slightly tortuous.
As you can see, I have mixed feelings! |
P 1
|
Other commentsThis is the best course I've encountered
yet in this program! Your teaching models the kind of teaching we talk about
achieving, the reflection component got us started on that word of reflective
teacher, the organization was magnificent - a good example of how open-ended
learning and discussion can occur in a highly organized structure. The journals
got a little old - they were more interesting and useful the first half
of the semester - could it be changed part way through the semester? Maybe
have all of us hand in lesson plans we're doing or ideas we'd like to try.
I know this could have been chosen as an option by people, but I didn't
think of it till just now - journal could be a form specifically for sharing
teaching ideas, strategies, activities, etc. |
Participant 2
P 2
|
1. Introductory lesson
This was good. It started us off thinking about our relationship to math
through questionnaire. I really didn't know what to think of the class at
the time - I didn't realize the first day how dynamic and exciting it would
be! |
P 2
|
2. Cardtrick experience
I love it. I liked how it introduced us to other people's feelings about
math when we tried it on other people. It was a good lesson in teaching,
exposing us to pain of letting other discover solutions. |
P 2
|
3. Problem solving issues
I liked this because it was a practical application of problem solving. |
P 2
|
4. Tessellation experience
I loved this experience and hated it too! It was great to struggle. I
liked every part of it except the 2nd reflection paper, but I've already
mentioned that in class. |
P 2
|
5. Assessment issues
I found the discussion a little less stimulating than some we've had
as a class. Not very many people seemed to have prepared for class that
day and they weren't talking. Maybe you should require the preparation as
a writing assignment. I thought it was useful to prepare for the discussion. |
P 2
|
6. Inquiry approach issues
I loved reading from your book. I think it would be better to have a
more common experience. I was frustrated that I didn't get to read the Olympics
article because there weren't enough copies. |
P 2
|
7. Teaching strategies issues
It was good to see all the strategies in a list, but I'm not sure it's
something I'll take with me like I will the tessellations experience. The
NCTM discussion was good because it gave us a place to discuss our hopes,
dreams and fears about using them. |
P 2
|
8. Student case-study
I thought it was very valuable because it got me to focus on how I see
my students and what are some ways to examine their learning styles and
their actual learning. It was fun and interesting! |
P 2
|
9. Teaching and learning of a specific math
topic
From my search in the Research ideas for the classroom book -- Early
childhood I came across several references which I did not have time
to search out and which I wouldn't have had time to share in our short
presentation. Maybe you should include them in the next folder (look on
bottom of page 145 for them). I wish we could've had more time to present.
It went by so quickly. The estimation and number sense article was very
difficult write. It is the only factual writing we did and it was rough
switching from writing reflections to writing facts. |
P 2
|
10. "What have I learned" paper
Good way to organize gained knowledge through course experience, however,
felt redundant because I have been doing this in all my reflection papers,
so it felt like doing it again, saying things I've probably said. Perhaps
it's more valuable for people who have been learning how to reflect in this
course? |
P 2
|
Other comments
It was excellent. I was thrilled to see you model the type of teaching
you were instructing us about. You made us think. I appreciated the challenge
and I valued the respect you gave to our thoughts, feelings and comments.
I felt myself reaching a point where I wasn't coming up with many new
ideas for my what I've learned paper. I don't think you necessarily expected
new ideas, but I think it would be nice to have a conference with you (about
1/2 year) where we discuss together what I've learned. This would still
require preparation. I am not suggesting this to get out of writing a paper.
It's just that I think throughout the course I've been writing very detailed
reflections and it feels like I keep repeating myself when I'm writing them
in another paper. Also, we didn't have the chance to talk one-on-one and
this could be a nice way of getting together to talk about an individual's
learning! One other suggestion: this course requires the use of a lot
of paper. Maybe when you do the next course reader you could make the copies
back-to-back (2-sided) instead of one-sided. It would save on paper and
make the reader much less heavy! |
Participant 3
P 3
|
1. Introductory lesson
I don't remember too much about the first day of class. I remember that
we filled out a questionnaire about our feelings about mathematics. I think
we talked about our answers in the large group. We also watched a video.
I like the idea of the questions especially because you told us you would
use them to try to get to know us better. |
P 3
|
2. Cardtrick experience
I really enjoyed the card trick experience. I was frustrated for a short
amount of time, but the feeling of discovery was well worth it. The fact
that you told us that you would keep doing the trick until we all
got it. You were confident that we could get it which made us try even though
we were frustrated. I liked the way you split the group when some of us
had figured it out. It kept those of us who had solved it, challenged. Those
who hadn't were able to discuss together what they thought. |
P 3
|
3. Problem solving issues
I was frustrated with the hiking problem at first. I remember that you
asked us to start and expected that we would say that we didn't have enough
information but we didn't. I don't really like problems like these and I
think that the class would not miss anything if this exercise was cut. I
am having a difficult time remembering the purpose for the activity, and
that is why I feel it would not be missed if were omitted. |
P 3
|
4. Tessellation experience
I did enjoy the tessellation experience. I liked working on our own at
home and then working in small groups. I thought that the experience did
go on a little bit too long, but as we discussed it was difficult to pick
something to cut to make it shorter. |
P 3
|
5. Assessment issues
I remember reading the articles and I especially liked the Clark, Clark
& Lovitt article. I don't remember much of a discussion about assessment.
I would have liked to talk about assessment more thoroughly because it is
a very interesting, practical, and necessary part of teaching mathematics. |
P 3
|
6. Inquiry approach issues
I enjoyed reading the classroom stories, but I did not think we had a
very stimulating discussion about them. Perhaps thinking of the stories
in terms of our tessellations experience hindered our conversation. If we
were more free to discuss the situations, it might have been a more meaningful
discussion. |
P 3
|
7. Teaching strategies issues
I think I missed your intent on this assignment. I handed in my thoughts
on the different teaching strategies and you said that I did something different
from what you intended. I looked back on the various teaching strategies
I thought you used in the class and what you did specifically. I learned
a lot when I tried to define what your role was in all the exercises I experienced
as a student. |
P 3
|
8. Student case-study
This was a valuable project, but I wish that I didn't focus so much on
one child. I understand that your point was that you should be able to focus
on one child so we can know how to observe all our students. I wish we talked
more about strategies to determine each student's capabilities when there
are so many students and only one teacher. How can individual attention
be given to those who need extra help without the others doing traditional
pencil and paper computation? |
P 3
|
9. Teaching and learning of a specific math
topic
I enjoyed this project very much. It was extremely helpful that you were
able to give us articles that might be helpful. I think this is where the
most practical application came from. Not only did I learn strategies to
implement my own topic, but I was excited to learn what the other classmates
found about their topics. I wish we could have talked more about how to
find the kinds of lessons where discovery and inquiry approach are used,
etc. |
P 3
|
10. "What have I learned" paper
I had a difficult time writing this paper. I think I felt a little bit
constrained by your detailed description of what you expected from this
assignment. I tried to write what I felt the assignment meant to me and
then reread what you described. I then tried to edit what I wrote to be
more like what you described but I don't think I did exactly what you had
in mind when I wrote the first time. I learned a great deal, but I got frustrated
revising it to fit into your description. I know you were worried about
being too vague, but sometimes being too detailed is just as confusing. |
P 3
|
Other comments
Many of the readings which I circled neutral were because I did not find
time relevant to elementary mathematics. |
Participant 4
P 4
|
1. Introductory lesson
The math metaphors assignment & math autobiography helped me to reflect
on my own mathematical experiences/philosophies on math. The math survey
was helpful in finding out my own views on mathematical learning at that
point of my life, & now helps me to see what I've learned in the past
3 months from this course.
*I liked that everything (course syllabus/objectives) was presented in
an organized, "mathematical" way. (It helped to organize my thoughts!) |
P 4
|
2. Cardtrick experience
I liked the challenge to solve the cardtrick. It was a great hands-on
experience ... especially learning to do the cardtrick and trying it on
others was fun & helped me to see math in another way. Even the feelings
I got while determining the solution were valuable to my own learning &
helped me face my own weaknesses. Eventually I had to accept my own weaknesses...
(Ex. thinking at one point that there was a possibility that I may have
failed in solving the problem.) |
P 4
|
3. Problem solving issues
I liked the NCTM curriculum & eval. standards "Problem-Solving"
section - it helped me greatly to understand more the level I was teaching
at. The hiking problem activity was interesting because I was actually absorbed
in it as if I was really planning the trip. The small group discussions
were definitely beneficial & less intimidating to solve the problem.
I liked all of Schoenfeld's articles on problem-solving - helped me to put
things into perspective & understand the categories of knowledge &
behavior. |
P 4
|
4. Tessellation experience
I liked the entire challenge to understand the definition of tessellation.
I liked that it began to work my right-brain activity as well as sharpen
my left-brain... Therefore, during my inquiry process, my critical thinking
skills were enhanced & I was able to develop conjectures to prove them
right or wrong. I disliked the frustrations, but learned a great
deal from them. The tessellation unit should be kept in your agenda for
next year's class. |
P 4
|
5. Assessment issues
I liked that we were again given the opportunity to reflect on our tessellation
experience to think of valid ways in assessing students' learning. I was
able to assess my own learning throughout the process. The "Walk down
memory lane" helped me to see "assessment" under a different
light because I didn't realize how much I actually learned. Your unpublished
manuscript on inquiry approach was beneficial because it helped me to apply
the main points to my own teaching and experiences. I wish I could've read
more about "assessing" students in elem. school. It would've
helped me to find new ways to assess math learning. |
P 4
|
6. Inquiry approach issues
As I mentioned above, your manuscript was very helpful & I was able
to develop stronger inquiry techniques. The analysis of classroom stories
was valuable to me (dialogue of students/teacher) because I was able to
understand how important it is to use the inquiry approach to teaching (posing
problems, etc.) |
P 4
|
7. Teaching strategies issues
Excellent! Helped me to reflect on my own teaching strategies & alter
them to make them more effective. By looking back on my own experiences
(at my site & in this class) I was able to develop new strategies which
I'm excited to use in my own classroom. I found reviewing our strategies
in class was one strategy to reinforce our own developments. Listing what
we have discovered only reaffirms our teaching methods and beliefs. |
P 4
|
8. Student case-study
This was a valuable project & learning experience. It helped me to
learn more about children's learning behaviors & taught me "to
observe" in a realistic situation. I liked that my discoveries on this
one child affected me in many ways. I had a great time & besides got
to know the child more than I had planned in doing so. Suggestion: perhaps
encourage your students to begin observing earlier in the semester. I noticed
Danny and became particularly interested in observing him and was lucky
to use him in my case-study. |
P 4
|
9. Teaching and learning of a specific math
topic
The timing of this project was perfect! I was able to organize my presentation
more effectively only because I applied what I have learned from my site
to the topic I researched. And later, I was able to reapply it (research)
back to my site experience. I would have liked more time during the presentation
because there were so many interesting things to talk about. Perhaps you
can begin the presentation a week earlier & extend the time for each
presentation? I would highly recommend for required reading (the
whole book, not only chapters) the book, Research Ideas for the Classroom:
Early Childhood Mathematics, by Jensen because it helped me to understand
the basic foundations of early mathematical learners/learning. I was able
to develop lesson ideas just from reading that book. |
P 4
|
10. "What have I learned" paper
A great way to end the session. Only reinforces in me how much a "reflective"
person I've become... |
P 4
|
Other comments
Raffaella, I just want to thank your for being such an inspiration. Through
this course, I've learned so much about myself - that I don't hate
math anymore & that it's pertinent in understanding the world, that
I have the confidence in problem-solving (which I never had before),
that I've become so "reflective" that I can actually appreciate
what I do & how I think ... There are so many more ways this course
has benefited me. You've done an excellent job in planning & you're
diligence/persistence in teaching me only motivates me. (Motivations which
I could always have before...) To be honest, this was the most productive
course I took this semester!! Thank you so much!
Any suggestion? Yes! Perhaps integrating more creative activities,
besides, this world is becoming more visual. Ex. In presentations, require
students to bring in charts, visuals, objects, because it makes math so
much more fun than it's perceived. |
Participant 5
P 5
|
1. Introductory lesson
I really found it valuable to write up a questionnaire about what I felt
about math and students' perspectives of "good math teacher" and
people's perspectives of "good math student." It got me to really
think about what I liked and disliked about math. It stirred up a lot of
memories, which I think can be valuable when teaching others. Remembering
may help me to relate to others. |
P 5
|
2. Cardtrick experience
I liked it because it was a challenge, but I disliked feeling frustrated.
I also got aggravated and distracted in a big group. I do better in small
groups because I am not distracted. Again, though, I felt it valuable to
discuss all of our feelings about it so that we might be able to relate
to feelings of future math students. |
P 5
|
3. Problem solving issues
I liked trying to solve this in small groups and then bringing back ideas
to the large group. I felt when we started with the large group that we
were getting nowhere because we couldn't agree on where to start with anything.
In a smaller group this was easier. |
P 5
|
4. Tessellation experience
I liked it because it was a new challenge for me. Sometimes I got frustrated
with whole group trying to agree on definition. So I then took a step and
just observed the different perspectives. I found this very interesting.
I think it is difficult to talk as a group. I don't know how you could improve
this aspect. |
P 5
|
5. Assessment issues
I don't really remember this lesson and looking back in my notes is not
helping me. I guess from that, I didn't get as much out of it as I did the
other lessons. |
P 5
|
6. Inquiry approach issues
I wished I could have read the Olympics as well as your study unit with
the two students. I was lucky though to be able to read Learning and
Living Mathematics. I think all of these readings should be required.
They gave me so many ideas and helped explain the inquiry approach more
thoroughly. |
P 5
|
7. Teaching strategies issues
I really enjoyed this because it made me realize how much I had learned
during the course of the semester, which was a lot. It really summed things
up for me and gave me ideas for my own pedagogy. Maybe not talk about it
as long as we did. I could be thinking about something else. I felt it might
be easier to talk first and then write about it. |
P 5
|
8. Student case-study
I really liked this project. It force me to observe my students very
carefully. I don't know if I would have observed them as thoroughly as I
did for this project. Since then I have found myself looking at all students
observing them all much the way I did the other student, or at least as
much as possible. I think sharing the next class examples of what you want
will help them. I realize that this was the first time you had students
do this. I think it was very beneficial. Definitely have your students do
it again next year. |
P 5
|
9. Teaching and learning of a specific math
topic
Very valuable once again!! It is too bad we couldn't spend more time
on this or the project presentations. I like the fact that all presentations
were different and that there were not too many constraints on how we were
to do our presentations. I liked all of our reading except for Quality
and the research article Educational Studies in Mathematics. Both
were interesting but not as helpful as the others in a practical sense.
There were a of resources. We could have gone on about it but time did not
permit. Hopefully, we got the important points across. |
P 5
|
10. "What have I learned" paper
I don't know because I have not written it yet. I suspect though, like
"walk down memory lane," that I will get more out of it than I
anticipate. |
P 5
|
Other comments
I felt that most all readings to be very helpful. Obviously, some were
more helpful than others. I liked the fact that I could see some correlations
between the readings and what I am seeing in the classroom. I know that
this was not the case for everyone, but it was for me. With that in mind,
it was possible for me to develop my own pedagogy with NCTM Standards always
in mind. I used to sometimes get aggravated with math, but now I really
like it. I love the inquiry approach and really learned so much about myself
as a student and as a "future teacher of mathematics" in your
class. I wish we could continue with you more next semester. I also think
the writing and working in small groups was a wonderful part of your class.
Don't change this! Thanks for everything! |
Participant 6
P 6
|
1. Introductory lesson
The main thing I disliked was the time mix-up. Not much you could do
about that though. Other than that, I think it was fine. I thought the Math
Surveys were a good introduction to the course. |
P 6
|
2. Cardtrick experience
I loved the cardtrick experience. I liked learning the trick and teaching
it. It was very interesting to me - figuring out the different ways of doing
the trick. I liked it because there were lots of neat math things about
it. |
P 6
|
3. Problem solving issues
I guess the "hiking problem" activity seemed kind of strange
to me. I think the one day it just seemed to be sort of tacked on at the
end. I guess I would suggest trying to do this all in one day if possible.
I thought there were some good discussions on problem solving. I guess,
although I understood the purpose for the hiking problem activity, but it
seemed kind of repetitive going through it in class and then working on
it again in small groups. I think we should have kept going without you
giving us the additional information as a whole class. I think you should
have let each group either make assumptions or come up with questions on
their own. Perhaps you could provide some other resources, like almanacs,
etc., to find temperatures and conversions rather that discussing as whole
class. |
P 6
|
4. Tessellation experience
I liked being an observer for this experience. I really liked the interactions
in the different groups and the individual work people did at home. I think
this was crucial! |
P 6
|
5. Assessment issues |
P 6
|
6. Inquiry approach issues
I think this was hard because so many of us had read the one story and
some people were missing. Perhaps you could let people know what others
were reading in case they wanted to discuss it with someone else ahead of
time - or if they knew they were the only one reading a particular story
maybe they would be better prepared to give a brief synopsis of the story.
Perhaps have those reading the same story discuss it as a group. Maybe you
could give a grid line for some different ideas to discuss. |
P 6
|
7. Teaching strategies issues
I really liked the NCTM sections on Discourse. I thought this
was a valuable review/discussion of the teaching strategies used. |
P 6
|
8. Student case-study
I got a lot out of this project - mainly I think because I had the chance
to tutor a student 1-on-1. I learned a lot! By really focusing on how she
was thinking and figuring things out. Even without the project, I would
still have learned a lot through tutoring - but I think it really benefited
me to record her thoughts and my suggestions and sort of transcribe a couple
of sessions.
Perhaps you could work more with the cooperating teachers or with students'
elem. ed. advisor to help them out in what they needed to do for this project.
There seemed to be a lot of questions and concerns from other students in
our class. |
P 6
|
9. Teaching and learning of a specific math
topic
I think what has been most interesting for me about this is to listen
to many of the elementary teachers and their excitement and interest in
teaching different math topics in creative ways. |
P 6
|
10. "What have I learned" paper
I learned a lot from going back through my papers and journals and highlighting
what I have learned. This was a good culminating experience and emphasized
how important the role of the teacher is in the classroom based on inquiry.
I had commented on this a number of times throughout the semester. |
P 6
|
Other comments
I feel that I really did get a lot out of this course - even though I
would have liked to have a few more secondary teachers to talk to. It was
definitely worthwhile - I appreciated having a rather "unique sole"
during the tessellation activities.
What I think was especially neat for me was seeing how a couple of the
elementary teachers' math anxiety affected them - how it changed or didn't
change over the course of the semester. This was so interesting to me based
on my work last semester on Math Anxiety.
Although I wonder what this class would have been like if it was made
up of 11 secondary teachers, I'm very glad that I had this rather unique
opportunity. I really enjoyed the class!! |
Participant 7
P 7
|
1. Introductory lesson
The survey was a good way of getting to know us as math learners and
for us to think about ourselves in that way. I wasn't overly impressed by
the connections video - I can't remember much of it. The outline for the
entire semester was wonderful! |
P 7
|
2. Cardtrick experience
I loved this! I remember my roller coaster emotions - frustrated, upset,
mad at you for making us do it -- elation!!, feelings of confidence
and amazement. These emotions were valuable lessons! |
P 7
|
3. Problem solving issues
I liked doing a real world problem and found that it's the most useful
kind to do and teach. I have already incorporated this type into my
lessons. The readings stressed the important concepts and the discussions
did also. I would only suggest less reading as it was a heavy load. |
P 7
|
4. Tessellation experience
I liked this long term experience - we had the time to explore so much.
For some it may have been too long and I felt this way at times too.
However, the depth of discovery & learning couldn't have been achieved
otherwise. It's important as a teacher to experience what students go through
too. |
P 7
|
5. Assessment issues
The readings and discussions seemed to address this topic at the time
but as I think about it now I wish I learned more or spent more time on
this topic - I'm not sure what I know about this & need to review my
readings and notes. |
P 7
|
6. Inquiry approach issues
I really enjoyed seeing other people's lessons and knowing why they did
what they did. This is always helpful. This approach seems common sense
to me - I find it a natural way to teach. |
P 7
|
7. Teaching strategies issues
I liked that you taught the way NCTM prescribes. The learning of math
I had this class as well of teaching is evidence of how well you taught.
I really believe in NCTM standards and plan to review them for each lesson
I plan. |
P 7
|
8. Student case-study
We should have started this sooner! Being in the classroom 2.5 days and
not having math on some of those days was constraining! Had I started earlier
I may have had more observations! |
P 7
|
9. Teaching and learning of a specific math
topic
Readings were quite useful! The presentations are extremely helpful -
we are learning many topics at once and listening to our peers and what
they've learned is a great way to approach these topics. The discussions
so far have been quite enlightening! |
P 7
|
10. "What have I learned" paper
Excellent way for me to review all I learned and as I wrote in my paper,
"solidify" my knowledge! |
P 7
|
Other comments |
Participant 8
P 8
|
1. Introductory lesson
To be honest, I don't remember much about the 1st class. However, I do
sort of remember the NCTM video and I thought that was a worthwhile video. |
P 8
|
2. Cardtrick experience
I liked the way we got to help each other figure out the trick. I didn't
like how - when someone figured out the trick - they got to leave the room.
I would suggest that when someone gets it they be allowed to offer 1 suggestion. |
P 8
|
3. Problem solving issues
I really liked the hiking problem. It was very interesting and practical.
The readings on problem solving were also very helpful. |
P 8
|
4. Tessellation experience
I really liked the hands-on parts with the manipulatives and the small
group discussions. I would suggest that the time frame be cut back. 4 weeks
is a little long. |
P 8
|
5. Assessment issues
The readings were all very long & time consuming. I sort of felt
like I was reading about the same thing over & over again. |
P 8
|
6. Inquiry approach issues |
P 8
|
7. Teaching strategies issues
I thought that identifying teaching strategies was a good idea. It's
a good way of assessing if the class got the main points of the lessons
that we were supposed to get. |
P 8
|
8. Student case-study
This was extremely valuable. It gave me a lot of insights into what my
students were doing and thinking. I think the timing, structure & requirements
were fine. |
P 8
|
9. Teaching and learning of a specific math
topic
This was a very interesting project & it helped me get many ideas
for teaching. The timing was really hard though because it fell in between
other presentations & papers. (and Thanksgiving) It was hard to coordinate
things with my partner. I did not particularly get too much out of the "Quantity"
article but the other articles were very helpful. |
P 8
|
10. "What have I learned" paper
This was a good way of putting a closure on the class. However, at the
same time this was due I had 3 other papers due. Although, we couldn't really
do it at any other time so I guess it was a good thing. |
P 8
|
Other comments
If possible, I would try to cut down on some of the writing. For example,
instead of having both a journal and another written assignment try to connect
the 2. It was really hard trying to keep up with all the assignments. Otherwise
I think everything was good. I liked the small and large group discussions
and I especially liked the "hiking problem." |
Participant 9
P 9
|
1. Introductory lesson
I missed this class due to the registrar's scheduling error. |
P 9
|
2. Cardtrick experience
I thought the card trick a lot. I think it went very well because you
let us develop at our own pace (saying we would all "get it"
and when we felt we "got it" we could move to the next
step.) I think you gave or didn't give clues at the appropriate times. (Keep
it!) |
P 9
|
3. Problem solving issues
I thought this was a good activity because it allowed us to be the knowledge
base and reflect on our own experiences in developing problem solving strategies,
as opposed to being told how to do a problem. (Keep it!) |
P 9
|
4. Tessellation experience
I enjoyed the tessellation experience. It was good to hypothesize and
investigate (on our own) issues we felt were interesting. However, I became
bored and tired after three weeks of the same activity. I also thought
that walk down memory land assignment was lengthy and a bit much. (Change
it!) |
P 9
|
5. Assessment issues
I thought the article by Clarke, Clarke & Lovitt were useful, especially
used as a supplement to our class discussion about the various ways to assess
students. (Group projects, oral means, journal, etc.) |
P 9
|
6. Inquiry approach issues
I thought the readings were really good. They allowed me the opportunity
to see what type of environment I had been in as a student, as well as what
type of environment I want to create as an educator for my students. (Keep
it!) |
P 9
|
7. Teaching strategies issues
I really gained a lot from this activity. It was good to see what other
strategies people were able to come up with, and to see whether you had
commonalities or differences. It allowed me to incorporate other strategies
and techniques into my own pedagogy. (Keep it!) |
P 9
|
8. Student case-study
This project was especially difficult for me. I liked the general idea,
but for younger children it is virtually impossible to generate the type
of information you wanted from them. (Change it!) |
P 9
|
9. Teaching and learning of a specific math
topic
I thought this activity was good, because once again, we were allowed
to choose topics that were of interest to us. The readings that you provided
us with were really great because they gave us a starting point for our
projects. Also, working with a partner helped a great deal, as we were able
to bounce ideas off of one another. The timing of the project was also very
appropriate. (Keep it!) |
P 9
|
10. "What have I learned" paper
Haven't done it yet, but I can comment on this evaluation piece. It was
hard for me to really remember everything we have done over a 3 month period.
Perhaps, you could provide students with a small evaluation inventory
after each lesson, and then just compile the immediate feedback you're given
and make the appropriate changes, as opposed to waiting unit the end of
the semester.
(added later) I think this final reflection piece was a good idea.
It allowed me the opportunity to identify things that were instrumental
as both a student learner and as a teacher. (Definitely keep this activity!) |
P 9
|
Other comments
I enjoyed this course, perhaps because I really enjoy math. I found that
many of the activities were beneficial, and I feel I learned a great deal.
The only thing that I would really change may have been the journal entries.
I think they're a good idea, but requiring them every week made it
just that, a requirement. There were some weeks where I really didn't have
(what I felt) was anything of importance or exciting to say, and I felt
I was just writing to write. Perhaps, if you require five or seven entries
over the semester more people would get something out of it, both in readings
as well as writing them. |
Participant 10
P 10
|
1. Introductory lesson
I liked describing math as a metaphor because I felt that you allowed
us to voice our personal experience (past, present frustrations) in an honest
way so that your could probably get us over that mental hump when we came
to an activity we thought was too hard or difficult. |
P 10
|
2. Cardtrick experience
I loved the cardtrick experience maybe because I just became enthralled
with Solitaire or maybe finding a simple pattern was exciting for once and
to be able to pull the "trick" off was fun in itself once I mastered
handling the cards in a comfortable way. |
P 10
|
3. Problem solving issues
I liked the readings very much because I feel that many of us are "conditioned"
into a certain state of helplessness if we don't solve a problem with the
correct number of steps. God forbid if we find a short cut because it would
throw the great math minds into a whirl. Everyone should be allowed to solve
mathematical problems according to their comfort level any other way would
be a violation of their individual uniqueness. |
P 10
|
4. Tessellation experience
One word for you. Draining. Very exciting initially however as it dragged
into the third lesson I couldn't keep up my enthusiasm. I think the lesson
should not spend so much time on coming up with conjectures and then having
the students present what they already know is too repetitive and redundant. |
P 10
|
5. Assessment issues
I like it to a point in applying it to tessellation, but as I said earlier,
continuing on tessellation was like beating a dead horse and I disengaged.
It basically was outlining what we had done in the past three lessons to
see if we left anything out, hadn't reflected enough, or could come up with
new ways of determining such a lesson wasn't in vain. |
P 10
|
6. Inquiry approach issues
I liked the fact that we were or had become "manipulators"
of math instead of the other way around. The different intellectuals levels
within the classroom (mainly, H, S & K) who were so enthralled kinda
put me on edge during the class. |
P 10
|
7. Teaching strategies issues |
P 10
|
8. Student case-study
Since I had so many problems finding a placement, although I'm sure this
bad luck won't strike another student, I think that the student case study
should be dropped and what should be added is an assessment of our teacher's
style in comparison with ours. I found it to be invaluable since I was working
with Pre-first and they didn't work on math dittos or any recorded test
sheets. |
P 10
|
9. Teaching and learning of a specific math
topic
I found it incredibly insightful on a personal level because my topic
(algebra) had never been explained or expressed in such simple stages. I
was like the majority of students racking our brains to make it fit the
framework of something or rather a separate part of math that was "special."
The readings were extremely helpful and I found myself grasping for equations
that I couldn't solve in the past and now do them now that I knew the true
story. |
P 10
|
10. "What have I learned" paper
You never realize how much work we've done for this class until you sit
down and truly look at your notebook with all the scribbled insights along
the margins. |
P 10
|
Other comments |
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