Vignette/Standard Alignment
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Keith
Feb 7, 2008, 12:01:49 PM2/7/08
to MthEd608Winter2008
To what extent do you think these vignettes supported the Standard
they were being used to exemplify?
they were being used to exemplify?
Tenille
Feb 11, 2008, 11:33:55 PM2/11/08
to MthEd608Winter2008
I think that some of the vignettes represented their respective
Standard better than others. For example, I thought that the vignette
associated with the Learning Environment Standard did a decent job of
illustrating the Standard as a whole---it captured the entire Standard
in one vignette. I think the same characterization could apply to the
vingettes for Reflection on Student Learning and Teachers'
Mathematical Learning Experiences.
There were two vingettes that I felt exemplified part of the Standard
failed to encompass the entire Standard. I thought that the vingette
for Knowledge of Mathematics and General Pedagogy did an excellent job
capturing the importance of mathematical knowledge, but I thought that
the vingette did not explicate the importance of pedagogical
knowledge. I also thought that the vignette for Teachers as
Participants in the Observation, Supervision, and Improvement Process
exemplified the benefits of collaborating with a supervisor. However,
I thought that it lacked disscussion of how deep personal reflection
can improve our teaching. Perhaps the other vignettes associated with
these Standards exemplified the ideas that I felt were missing from
these vignettes.
I did not think the vignette for Teacher Knowledge and Implementation
of Important Mathematics exemplified the Standard well. Maybe I just
didn't see all the connections that the vignette was trying to make.
What do you guys think?
Also, did anyone else think that the vignette for Reflection on
Students' Learning sounded familiar? I don't have my articles with me
here at home, but I'm pretty sure that this vignette was used to
exemplify classroom discourse in Professional Standards for Teaching
Mathematics (1991). Am I remembering correctly? If so, I think that
it illustrates how great teaching can encompass multiple standards.
Standard better than others. For example, I thought that the vignette
associated with the Learning Environment Standard did a decent job of
illustrating the Standard as a whole---it captured the entire Standard
in one vignette. I think the same characterization could apply to the
vingettes for Reflection on Student Learning and Teachers'
Mathematical Learning Experiences.
There were two vingettes that I felt exemplified part of the Standard
failed to encompass the entire Standard. I thought that the vingette
for Knowledge of Mathematics and General Pedagogy did an excellent job
capturing the importance of mathematical knowledge, but I thought that
the vingette did not explicate the importance of pedagogical
knowledge. I also thought that the vignette for Teachers as
Participants in the Observation, Supervision, and Improvement Process
exemplified the benefits of collaborating with a supervisor. However,
I thought that it lacked disscussion of how deep personal reflection
can improve our teaching. Perhaps the other vignettes associated with
these Standards exemplified the ideas that I felt were missing from
these vignettes.
I did not think the vignette for Teacher Knowledge and Implementation
of Important Mathematics exemplified the Standard well. Maybe I just
didn't see all the connections that the vignette was trying to make.
What do you guys think?
Also, did anyone else think that the vignette for Reflection on
Students' Learning sounded familiar? I don't have my articles with me
here at home, but I'm pretty sure that this vignette was used to
exemplify classroom discourse in Professional Standards for Teaching
Mathematics (1991). Am I remembering correctly? If so, I think that
it illustrates how great teaching can encompass multiple standards.
Janellie
Feb 12, 2008, 10:08:54 PM2/12/08
to MthEd608Winter2008
In general, I think the vignettes did a good job at displaying the
ideals in each Standard. However, I would not be able to pick out the
standards just by reading the examples. I feel the vignettes are
meant to support the standards, not replace them. Also, it would be
hard to show all the elements in a standard by just one vignette. I
would probably not be able to come up with ones that were any better
(without making them seem unrealistic).
That said, I believe some vignettes did a better job at supporting the
standard than others. In particular, the Standard about Teachers as
Participants in the Improvement Process did a pretty good job of
showing how teachers can work together with supervisors and evaluators
in improving their teaching. In the vignette, the teacher gave input
and listened to the ideas of the supervisor as well. They were a team
and it seemed as if they met often, as the Standard would suggest.
One of the other Standards that I was impressed with was the
Reflection on Student Learning. The teacher in the vignette was
constantly observing and gathering information about the students as
the Standard suggested.
The vignette I had the most difficulty connecting with its Standard
was the one under "Teacher Knowledge and Implementation of Important
Mathematics." Perhaps I just did not understand what was meant by
"implementation". The first standard we were given dealt with teacher
knowledge of pedagogy and mathematics, so what is different about this
one? Perhaps this standard is talking about how teachers present
information to their students. It does say "The primary emphasis in
this Standard is on the teaching of mathematical content and
processes." The vignette talked about what the students did, but it
did not help me understand the Standard at all. So, my QUESTION,
perhaps is, what exactly is this standard trying to get us to
understand?
ideals in each Standard. However, I would not be able to pick out the
standards just by reading the examples. I feel the vignettes are
meant to support the standards, not replace them. Also, it would be
hard to show all the elements in a standard by just one vignette. I
would probably not be able to come up with ones that were any better
(without making them seem unrealistic).
That said, I believe some vignettes did a better job at supporting the
standard than others. In particular, the Standard about Teachers as
Participants in the Improvement Process did a pretty good job of
showing how teachers can work together with supervisors and evaluators
in improving their teaching. In the vignette, the teacher gave input
and listened to the ideas of the supervisor as well. They were a team
and it seemed as if they met often, as the Standard would suggest.
One of the other Standards that I was impressed with was the
Reflection on Student Learning. The teacher in the vignette was
constantly observing and gathering information about the students as
the Standard suggested.
The vignette I had the most difficulty connecting with its Standard
was the one under "Teacher Knowledge and Implementation of Important
Mathematics." Perhaps I just did not understand what was meant by
"implementation". The first standard we were given dealt with teacher
knowledge of pedagogy and mathematics, so what is different about this
one? Perhaps this standard is talking about how teachers present
information to their students. It does say "The primary emphasis in
this Standard is on the teaching of mathematical content and
processes." The vignette talked about what the students did, but it
did not help me understand the Standard at all. So, my QUESTION,
perhaps is, what exactly is this standard trying to get us to
understand?
erin...@byu.edu
Feb 13, 2008, 8:50:46 PM2/13/08
to MthEd608Winter2008
AS A WHOLE... FINISH THIS PART WHEN YOU ACTUALLY FINISH READING.
In particular, I felt that the "Knowledge of Mathematics and General
Pedagogy" vignette did a fairly good job of illustrating the
standard. It seemed evident to me that this teacher certainly did
have a sound understanding of the mathematics her students were
working with, and she seemed able to handle her students' problems
(Are there more multiples of 8 or of 3), which indicates forethought
of potential student strategies. She handled her students question
appropriately by turning it around and giving it back to the rest of
the class. The tasks was obviously motivating enough to encourage her
students to explore further. When I first read it though, I did not
think it was a very good example of the first standard; it was only
when I went back through the detailed explanation line by line,
seeking for evidence of the standard in the vignette was I able to see
the connection. I guess I think that a good vignette would be so
exemplary of the standard that it wouldn't require additional
searching on my part. The Learning Environment vignette did, in my
opinion, illustrate what the standard is all about. I still had a
hard time looking at it from a read-the-vignette-first-then-try-to-
guess-what-standard-it-is point of view. I do think that an essay
would encapsulate the needed background and contextual information for
a vignette to be more of an all-inclusive obvious illustration of a
particular standard, but then it would be an essay or paper and not a
vignette... I guess my desire will never be realized because we each
come to the table with our own experiences, goals, and aspirations.
As such, our perspectives are definitely different, so when we look at
a vignette, our individual lens will let us see what we want to see,
which may be different from the person sitting next to you. Hurray
for many people with many experiences to lend such a broadened view of
education!?
Perhaps I am being critical but I didn't think that the vignette for
standard 2 (Teachers as participants in observation, supervision, and
improvement process) was adequate. The elaborated description spent a
good chunk of space describing how administrators should work with the
teachers by doing 4 things. Since I've never taught other than my
student teaching, I don't know what a supervisor is... My first
instinct is a mentor teacher or department chair or something. In
either case, neither (in my understanding) fall under the title of
"administrator." As such, that makes sense why none of those four
things seem to occur. Also, collaboration/ teamwork seems better
suited for groups larger than 2? At the same time, however, i
recognize that working with even one other person does in fact
constitute collaboration. But still, the standard made me think it
meant something more along the lines of the Monday schedule in the
Alpine school district where the students are dismissed an hour early
and then each department meets together to plan/ collaborate/ improve,
etc...
Teacher Knowledge and Implementation - didn't love it. This seemed
like it would've gone a lot better in the teachers as participants in
observation, supervision and improvement procces. I didn't exactly
feel like the teacher demonstrated all that he is supposed to
demonstrate. After collaborating with his supervisor, the lesson
seemed to illustrate that the teacher knew what he was talking about,
but I didn't feel that this vignette fulfilled its potential.
Disappointing. (Can you tell I'm typing these as I read? I feel that
either I'm getting tired of reading and thus apathetic, or these are
getting less and less-exemplary).
Did anyone else think that some of the standards were so very very
related that maybe they didn't need to have so many/ separate them as
much as they did?
Nothing about the last vignette indicated that it was a teacher
education/ development course for future teachers except the closing
thoughts. This was only an ok vignette for me - not amazing but not
horrible either. I felt like the vignette did not provide enough
information for me to peg it as this standard using cues from the
elaboration of the standard.
The Reflection on Student Learning Standard, when elaborated, seems to
place a heavy emphasis on the teacher's reflection to use the insights
to guide students to a better understanding of his/ her personal
learning style and their instructional decisions. The elaboration
also says that "teachers need information gathered in a variety of
ways and using a range of sources" (p 56). First of all, I did not
feel that the vignette did a satisfactory job of describing the
above. Secondly, I want to know what teachers can do to gather
information in a variety of ways and using a range of sources. I know
they can observe, administer tests/ quizes/ homework, projects,
etc..., but does that satisfy a "variety of ways"? Basically you're
either observing students as they work with one another, or you're
observing what they've produced using paper and pencil. What else can
you do? I am having a hard time thinking outside the box and so this
is a question I hope some of you will respond to.
Is it so terribly difficult to write vignettes that correspond to a
particular problem? Maybe I am being far too critical, but I felt
that most of these standards required more information than what was
given in order to be adequate examples of the standards. For
questions, please see the paragraph immediately above this one.
In particular, I felt that the "Knowledge of Mathematics and General
Pedagogy" vignette did a fairly good job of illustrating the
standard. It seemed evident to me that this teacher certainly did
have a sound understanding of the mathematics her students were
working with, and she seemed able to handle her students' problems
(Are there more multiples of 8 or of 3), which indicates forethought
of potential student strategies. She handled her students question
appropriately by turning it around and giving it back to the rest of
the class. The tasks was obviously motivating enough to encourage her
students to explore further. When I first read it though, I did not
think it was a very good example of the first standard; it was only
when I went back through the detailed explanation line by line,
seeking for evidence of the standard in the vignette was I able to see
the connection. I guess I think that a good vignette would be so
exemplary of the standard that it wouldn't require additional
searching on my part. The Learning Environment vignette did, in my
opinion, illustrate what the standard is all about. I still had a
hard time looking at it from a read-the-vignette-first-then-try-to-
guess-what-standard-it-is point of view. I do think that an essay
would encapsulate the needed background and contextual information for
a vignette to be more of an all-inclusive obvious illustration of a
particular standard, but then it would be an essay or paper and not a
vignette... I guess my desire will never be realized because we each
come to the table with our own experiences, goals, and aspirations.
As such, our perspectives are definitely different, so when we look at
a vignette, our individual lens will let us see what we want to see,
which may be different from the person sitting next to you. Hurray
for many people with many experiences to lend such a broadened view of
education!?
Perhaps I am being critical but I didn't think that the vignette for
standard 2 (Teachers as participants in observation, supervision, and
improvement process) was adequate. The elaborated description spent a
good chunk of space describing how administrators should work with the
teachers by doing 4 things. Since I've never taught other than my
student teaching, I don't know what a supervisor is... My first
instinct is a mentor teacher or department chair or something. In
either case, neither (in my understanding) fall under the title of
"administrator." As such, that makes sense why none of those four
things seem to occur. Also, collaboration/ teamwork seems better
suited for groups larger than 2? At the same time, however, i
recognize that working with even one other person does in fact
constitute collaboration. But still, the standard made me think it
meant something more along the lines of the Monday schedule in the
Alpine school district where the students are dismissed an hour early
and then each department meets together to plan/ collaborate/ improve,
etc...
Teacher Knowledge and Implementation - didn't love it. This seemed
like it would've gone a lot better in the teachers as participants in
observation, supervision and improvement procces. I didn't exactly
feel like the teacher demonstrated all that he is supposed to
demonstrate. After collaborating with his supervisor, the lesson
seemed to illustrate that the teacher knew what he was talking about,
but I didn't feel that this vignette fulfilled its potential.
Disappointing. (Can you tell I'm typing these as I read? I feel that
either I'm getting tired of reading and thus apathetic, or these are
getting less and less-exemplary).
Did anyone else think that some of the standards were so very very
related that maybe they didn't need to have so many/ separate them as
much as they did?
Nothing about the last vignette indicated that it was a teacher
education/ development course for future teachers except the closing
thoughts. This was only an ok vignette for me - not amazing but not
horrible either. I felt like the vignette did not provide enough
information for me to peg it as this standard using cues from the
elaboration of the standard.
The Reflection on Student Learning Standard, when elaborated, seems to
place a heavy emphasis on the teacher's reflection to use the insights
to guide students to a better understanding of his/ her personal
learning style and their instructional decisions. The elaboration
also says that "teachers need information gathered in a variety of
ways and using a range of sources" (p 56). First of all, I did not
feel that the vignette did a satisfactory job of describing the
above. Secondly, I want to know what teachers can do to gather
information in a variety of ways and using a range of sources. I know
they can observe, administer tests/ quizes/ homework, projects,
etc..., but does that satisfy a "variety of ways"? Basically you're
either observing students as they work with one another, or you're
observing what they've produced using paper and pencil. What else can
you do? I am having a hard time thinking outside the box and so this
is a question I hope some of you will respond to.
Is it so terribly difficult to write vignettes that correspond to a
particular problem? Maybe I am being far too critical, but I felt
that most of these standards required more information than what was
given in order to be adequate examples of the standards. For
questions, please see the paragraph immediately above this one.
Rachelle
Feb 13, 2008, 9:02:37 PM2/13/08
to MthEd608Winter2008
When I initially read through the vignettes, I was distracted from
focusing on Keith's question because overall I was simply impressed
with the good teaching that was described. I always enjoy reading the
vignettes that accompany the Standards because they are great examples
of what standards-based mathematics really looks like (which is
something I feel like I have rarely seen).
So after being impressed with the vignettes, I went back for a closer
look at how well each vignette supported the specific Standard it was
supposed to exemplify. In taking a good look, I decided that although
the vignettes do not embody every single aspect discussed in
elaborating the Standard, they certainly make clear what each Standard
is getting at. I think that if the Standards were left on their own
without vignettes to support them, many teachers might read the words
and think they are teaching as the Standards intend without actually
doing so. For example, If a teacher were to read under Standard 1 of
Teaching and Learning Mathematics (Knowledge of Mathematics and
General Pedagogy) that "teachers of mathematics should have a deep
knowledge of sound and significant mathematics" (page 19), he might
think "Well, I've taken math past Calculus, I must have a deep
knowledge of significant mathematics," even though he never understood
that fourth graders could discuss ideas about orders of infinity. I
think that these vignettes support the Standards well because even
though they don't illustrate every point of the Standards, they embody
the overall feeling of what the Standards are trying to articulate.
focusing on Keith's question because overall I was simply impressed
with the good teaching that was described. I always enjoy reading the
vignettes that accompany the Standards because they are great examples
of what standards-based mathematics really looks like (which is
something I feel like I have rarely seen).
So after being impressed with the vignettes, I went back for a closer
look at how well each vignette supported the specific Standard it was
supposed to exemplify. In taking a good look, I decided that although
the vignettes do not embody every single aspect discussed in
elaborating the Standard, they certainly make clear what each Standard
is getting at. I think that if the Standards were left on their own
without vignettes to support them, many teachers might read the words
and think they are teaching as the Standards intend without actually
doing so. For example, If a teacher were to read under Standard 1 of
Teaching and Learning Mathematics (Knowledge of Mathematics and
General Pedagogy) that "teachers of mathematics should have a deep
knowledge of sound and significant mathematics" (page 19), he might
think "Well, I've taken math past Calculus, I must have a deep
knowledge of significant mathematics," even though he never understood
that fourth graders could discuss ideas about orders of infinity. I
think that these vignettes support the Standards well because even
though they don't illustrate every point of the Standards, they embody
the overall feeling of what the Standards are trying to articulate.
Rachelle
Feb 13, 2008, 9:22:05 PM2/13/08
to MthEd608Winter2008
I just replied to this, it said it was successful, but now it won't
show up. I'm a little irritated and I apologize if there end up being
two really similar posts from me. Here goes round two.
Janelle, I'm not sure I can really answer your question about what
"Implementation" means, but I've noticed something that gave me
insight into the topic. "Teacher Knowledge and Implementation of
Important Mathematics" is under the "Standards for the Observation,
Supervision, and Improvement of Mathematics Teaching" while "Knowledge
of Mathematics and General Pedagogy" is under the "Standards for
Teaching and Learning Mathematics." In fact, the "Teacher Knowledge
and Implementation of Important Mathematics" Standard discusses what
supervisors should focus on when assessing a teachers teaching. I
think the fact that the two Standards are so similar is because on is
focusing on how we should teach mathematics while the other is about
what should be focused on when we assess others' teaching. I think the
fact that they are so similar is actually a good sign that NCTM is
being consistent when they talk about what the important features are
of teaching mathematics.
> > they were being used to exemplify?- Hide quoted text -
>
> - Show quoted text -
show up. I'm a little irritated and I apologize if there end up being
two really similar posts from me. Here goes round two.
Janelle, I'm not sure I can really answer your question about what
"Implementation" means, but I've noticed something that gave me
insight into the topic. "Teacher Knowledge and Implementation of
Important Mathematics" is under the "Standards for the Observation,
Supervision, and Improvement of Mathematics Teaching" while "Knowledge
of Mathematics and General Pedagogy" is under the "Standards for
Teaching and Learning Mathematics." In fact, the "Teacher Knowledge
and Implementation of Important Mathematics" Standard discusses what
supervisors should focus on when assessing a teachers teaching. I
think the fact that the two Standards are so similar is because on is
focusing on how we should teach mathematics while the other is about
what should be focused on when we assess others' teaching. I think the
fact that they are so similar is actually a good sign that NCTM is
being consistent when they talk about what the important features are
of teaching mathematics.
>
> - Show quoted text -
CJ
Feb 14, 2008, 1:36:20 AM2/14/08
to MthEd608Winter2008
To my count, there were six vignettes, and to reduce the strain on the
short term memory, I am going to refer to them as the multiple
vignette, the absolute value vignette, the polynomial vignette, the
average vignette, the elbow vignette, and the pendulum vignette.
I liked the multiple vignette, because I could pick out specific
examples of the teacher using her knowledge of mathematics and
pedagogy to structure the students' discussion. For example, she
helped the students to pursue their own questions, but also skillfully
tweaked those questions to make them a little more interesting. She
used the calculators to transform what could have been an exercise in
multiplication to an investigation in number theory, and grounded her
actions in student thinking. My only suggestion might be to highlight
these details more specifically throughout the vignette, but maybe
that wasn't the purpose of the vignettes.
I have issues with the absolute value vignette, mostly because it was
unclear to me exactly how the students were using the calculators. It
said that they were setting up tables of values and using the tables
to make graphs. With a graphing calculator, these tasks seem kind of
trivial to me, so I don't know what the students were doing every time
the vignette mentioned that they were working on something. How long
does it take to type a function into the calculator? And if they
weren't using the calculators to make the graphs, what were they using
them for? To evaluate the absolute value of negative two? If someone
can help me to understand what the students were doing, please do.
Thanks. I also felt that it would be much more interesting to discuss
why the absolute value graph is shaped the way it is, which may set a
stage for a more enlightened sense-making discussion of the
transformations. I felt like the teacher had gone to great lengths to
get technology into her classroom, but I wasn't really impressed by
what she was doing with it. The atmosphere and student support for
each other, however, was amazing. Ms. Chavez, take a sweeping bow.
The polynomial vignette gave nice examples of teacher-student
interactions, and the teacher did make a mental note to include
technology in his lesson plan, but the exchanges all seemed kind of
brief and the teacher seemed to make essentially the same suggestions
to each pair of students rather than get into their ways of thinking.
(By the way, I'm not saying I could do any better, but maybe a better
vignette might help people like me.)
The average vignette seemed kind of average, it was your basic sharing
of ideas between teachers but I didn't see how those ideas were
carried out. I would have liked to here WHY Pete thinks that the
suggested problems are different from the problems he usually used, or
a little more in-depth analysis of his own teaching. Likewise, Mr.
Johnson in the elbow vignette seemed to recognize a difference when he
tried a suggested lesson, but doesn't really elaborate on what was
different from his point of view. So I don't know if he really caught
the big ideas of the standard or saw his lesson as simply a change of
pace.
Finally, I was tempted to name the pendulum vignette the sine vignette
but on a second and third reading I can't find a place where sinusoids
are ever mentioned. Did this connection really never come up? If so,
why not? I really believe strongly in each of the bullets used to
describe this standard, but I kind of wish that they were spelled out
a little more in the vignette.
Overall, I like how the vignettes give life to the standards, but they
bring so much to mind for someone who has been in the classroom that
it easy to forget what the vignettes are trying to demonstrate. I
suggest that NCTM use their wide margins to re-iterate the bullets for
the standard at appropriate places throughout the vignettes.
short term memory, I am going to refer to them as the multiple
vignette, the absolute value vignette, the polynomial vignette, the
average vignette, the elbow vignette, and the pendulum vignette.
I liked the multiple vignette, because I could pick out specific
examples of the teacher using her knowledge of mathematics and
pedagogy to structure the students' discussion. For example, she
helped the students to pursue their own questions, but also skillfully
tweaked those questions to make them a little more interesting. She
used the calculators to transform what could have been an exercise in
multiplication to an investigation in number theory, and grounded her
actions in student thinking. My only suggestion might be to highlight
these details more specifically throughout the vignette, but maybe
that wasn't the purpose of the vignettes.
I have issues with the absolute value vignette, mostly because it was
unclear to me exactly how the students were using the calculators. It
said that they were setting up tables of values and using the tables
to make graphs. With a graphing calculator, these tasks seem kind of
trivial to me, so I don't know what the students were doing every time
the vignette mentioned that they were working on something. How long
does it take to type a function into the calculator? And if they
weren't using the calculators to make the graphs, what were they using
them for? To evaluate the absolute value of negative two? If someone
can help me to understand what the students were doing, please do.
Thanks. I also felt that it would be much more interesting to discuss
why the absolute value graph is shaped the way it is, which may set a
stage for a more enlightened sense-making discussion of the
transformations. I felt like the teacher had gone to great lengths to
get technology into her classroom, but I wasn't really impressed by
what she was doing with it. The atmosphere and student support for
each other, however, was amazing. Ms. Chavez, take a sweeping bow.
The polynomial vignette gave nice examples of teacher-student
interactions, and the teacher did make a mental note to include
technology in his lesson plan, but the exchanges all seemed kind of
brief and the teacher seemed to make essentially the same suggestions
to each pair of students rather than get into their ways of thinking.
(By the way, I'm not saying I could do any better, but maybe a better
vignette might help people like me.)
The average vignette seemed kind of average, it was your basic sharing
of ideas between teachers but I didn't see how those ideas were
carried out. I would have liked to here WHY Pete thinks that the
suggested problems are different from the problems he usually used, or
a little more in-depth analysis of his own teaching. Likewise, Mr.
Johnson in the elbow vignette seemed to recognize a difference when he
tried a suggested lesson, but doesn't really elaborate on what was
different from his point of view. So I don't know if he really caught
the big ideas of the standard or saw his lesson as simply a change of
pace.
Finally, I was tempted to name the pendulum vignette the sine vignette
but on a second and third reading I can't find a place where sinusoids
are ever mentioned. Did this connection really never come up? If so,
why not? I really believe strongly in each of the bullets used to
describe this standard, but I kind of wish that they were spelled out
a little more in the vignette.
Overall, I like how the vignettes give life to the standards, but they
bring so much to mind for someone who has been in the classroom that
it easy to forget what the vignettes are trying to demonstrate. I
suggest that NCTM use their wide margins to re-iterate the bullets for
the standard at appropriate places throughout the vignettes.
erin...@byu.edu
Feb 14, 2008, 1:38:51 PM2/14/08
to MthEd608Winter2008
At this point I feel like there's not a lot of controversy to which I
can respond. So I'll just say the following:
Chris. To you I say touche. I thoroughly enjoyed reading your
commentary and wish I had the ability for your sarcasm and wit. You,
my friend, should take a sweeping bow. I agree with you and think you
put things well when you said that you "like how the vignettes give
life to the standards, but they bring so much to mind... that it is
impass: can the vignettes truly demonstrate the standards when they
are a- missing some points of the standards, or b- demonstrating too
much. If both of these things are happening, can it be a "good"
vignette? What constitutes a good vignette? Maybe somebody will
respond to this :)
can respond. So I'll just say the following:
Chris. To you I say touche. I thoroughly enjoyed reading your
commentary and wish I had the ability for your sarcasm and wit. You,
my friend, should take a sweeping bow. I agree with you and think you
put things well when you said that you "like how the vignettes give
life to the standards, but they bring so much to mind... that it is
easy to forget what the vignettes are trying to demonstrate."
Earlier, however, Rachelle said "I think that these vignettes support
the Standards well because even though they don't illustrate every
point of the Standards, they embody the overall feeling of what the
Standards are trying to articulate." I feel that we are thus at an
point of the Standards, they embody the overall feeling of what the
impass: can the vignettes truly demonstrate the standards when they
are a- missing some points of the standards, or b- demonstrating too
much. If both of these things are happening, can it be a "good"
vignette? What constitutes a good vignette? Maybe somebody will
respond to this :)
Janellie
Feb 14, 2008, 2:24:18 PM2/14/08
to MthEd608Winter2008
Erin, you are going crazy with the questions!! But, they are all
really good questions. I have decided to respond to the question
about what makes a good vignette. Like you, I enjoyed what both
Rachelle and Chris said on the issue. Without the vignettes, a
individual may think he or she is doing a good job with the standard.
However, I am not so sure that a teacher would change their way of
teaching based solely on the vignettes. They may agree with the
vignette, but think their way is fine too. Or, they may disagree with
the vignette and think their classroom better exemplifies the
Standard. Much more is needed for change (obviously things such as
professional development). I appreciated the discussion that was had
before the vignettes about the Standard, but maybe it would be helpful
as well to discuss in more detail how the specific vignette relates to
the Standard. That said, I would say a good vignette could be used
for multiple standards, but it should be very clear that it is
specifically addressing the one it was intended to address. Since a
vignette could not possibly cover every aspect of the Standard every
time, I feel that it may be more beneficial for a vignette to delve
deeply into a segment of the Standard to make it extremely clear what
is expected. In response to another question, I would say, yes, it is
difficult to write a vignette (as least it would be for
me).
really good questions. I have decided to respond to the question
about what makes a good vignette. Like you, I enjoyed what both
Rachelle and Chris said on the issue. Without the vignettes, a
individual may think he or she is doing a good job with the standard.
However, I am not so sure that a teacher would change their way of
teaching based solely on the vignettes. They may agree with the
vignette, but think their way is fine too. Or, they may disagree with
the vignette and think their classroom better exemplifies the
Standard. Much more is needed for change (obviously things such as
professional development). I appreciated the discussion that was had
before the vignettes about the Standard, but maybe it would be helpful
as well to discuss in more detail how the specific vignette relates to
the Standard. That said, I would say a good vignette could be used
for multiple standards, but it should be very clear that it is
specifically addressing the one it was intended to address. Since a
vignette could not possibly cover every aspect of the Standard every
time, I feel that it may be more beneficial for a vignette to delve
deeply into a segment of the Standard to make it extremely clear what
is expected. In response to another question, I would say, yes, it is
difficult to write a vignette (as least it would be for
me).
Tenille
Feb 14, 2008, 2:33:49 PM2/14/08
to MthEd608Winter2008
Janelle, I am going to take a stab at discussing what NCTM meant by
"implementation". A lot of what I have to say is similar to what
Rachelle already pointed out about the categorization of the different
standards. I think it might be helpful to a list of all the standards
for each section (although I can't be sure since I have not seen such
a list. In general, implementation refers to how the mathematics
develops in the class. I like to think of mathematics teaching as
having two phases: planning phase and implementation phase. While
ideally we would like the planning and implementation of the
mathematics to be similar, but unfortunately it is not (see papers by
Mary Kay Stein for more information). In fact, the implementation of
worthwhile mathematical tasks is very tricky and while rich
mathematical tasks are necessary for implementing rich mathematics, it
is not sufficient. Hence the presence of this standard. The teacher
must have a rich and connected knowledge of mathematics in order to
implement a task well. After rereading the vignette, while Mr. Cooper
with Mrs. Johnson's help did connect the mathematics to the students'
lives and different aspects of mathematics. However, in their
discussion at the end of class, I didn't feel that it was focused on
mathematical knowledge. In fact, I was bothered by the use of the
word "activity" and Mrs. Johnson indication that improvement will
result from experience and support omitting the need for a strong
mathematical knowledge (as the standard would imply).
"implementation". A lot of what I have to say is similar to what
Rachelle already pointed out about the categorization of the different
standards. I think it might be helpful to a list of all the standards
for each section (although I can't be sure since I have not seen such
a list. In general, implementation refers to how the mathematics
develops in the class. I like to think of mathematics teaching as
having two phases: planning phase and implementation phase. While
ideally we would like the planning and implementation of the
mathematics to be similar, but unfortunately it is not (see papers by
Mary Kay Stein for more information). In fact, the implementation of
worthwhile mathematical tasks is very tricky and while rich
mathematical tasks are necessary for implementing rich mathematics, it
is not sufficient. Hence the presence of this standard. The teacher
must have a rich and connected knowledge of mathematics in order to
implement a task well. After rereading the vignette, while Mr. Cooper
with Mrs. Johnson's help did connect the mathematics to the students'
lives and different aspects of mathematics. However, in their
discussion at the end of class, I didn't feel that it was focused on
mathematical knowledge. In fact, I was bothered by the use of the
word "activity" and Mrs. Johnson indication that improvement will
result from experience and support omitting the need for a strong
mathematical knowledge (as the standard would imply).
Shawn
Feb 14, 2008, 2:45:42 PM2/14/08
to MthEd608Winter2008
I think that the vignettes did support the description of the standard
as much as perhaps they were designed to do. Here is what I mean by
that. I think that the Mathematics Teaching Today is trying to change
this huge paradigm of mathematics teaching. Researchers know that
teaching mathematics traditionally doesn't yield the best results.
However, convincing the population at large and even practicing
teachers is turning out to be a long process. Many either don't want
to change or are unsure of how to change. If they read research they
might not know what the types of activities the researcher describes
look like. Vignettes certainly help with that and help paint a
picture of what researchers mean for those who still need convincing.
I don't think that there is a perfect vignette for any standard. When
someone tries to implement an idea there is always room for
improvement. I think that it is a good idea to critique these
vignettes to help us be more effective teachers and implement the new
ideas from the critiques. One of the goals of the research of Dr.
Corey is to study the knowledge it takes to make a great lesson
better. I think this type of knowledge is needed here to critique
these vignettes.
With that said, I'm not sure that I have the knowledge yet to do this
well, but here are some things I noticed. I think that the vignettes
that we read were good and supported the ideas behind the standards.
Each standard started with a set of bullet points which served as an
outline for a following elaboration. The vignettes showed how a
teacher conducted a lesson which hit most of the bullet points. An
example of what I think how the typical vignette covered the bullets
was the one from Standard 6: Reflection on Student Thinking. This
was the one where Mr. Santos went around and observed his students
finding the solutions to the polynomial raised to the polynomial. He
was supposed to ensure that every student is learning sound math
(which he did by going around to all the groups), challenge and extend
their ideas (which he did by suggesting the students try investigating
the base of 1 in the last group), adapting or changing activities
(which he mentally changed the lesson plan for the next day based on
what happened that day), commenting on student's learning to parents
and administrators (which it didn't say he did), and provide regular
feedback to the students (which it didn't say he did or was going to
do).
as much as perhaps they were designed to do. Here is what I mean by
that. I think that the Mathematics Teaching Today is trying to change
this huge paradigm of mathematics teaching. Researchers know that
teaching mathematics traditionally doesn't yield the best results.
However, convincing the population at large and even practicing
teachers is turning out to be a long process. Many either don't want
to change or are unsure of how to change. If they read research they
might not know what the types of activities the researcher describes
look like. Vignettes certainly help with that and help paint a
picture of what researchers mean for those who still need convincing.
I don't think that there is a perfect vignette for any standard. When
someone tries to implement an idea there is always room for
improvement. I think that it is a good idea to critique these
vignettes to help us be more effective teachers and implement the new
ideas from the critiques. One of the goals of the research of Dr.
Corey is to study the knowledge it takes to make a great lesson
better. I think this type of knowledge is needed here to critique
these vignettes.
With that said, I'm not sure that I have the knowledge yet to do this
well, but here are some things I noticed. I think that the vignettes
that we read were good and supported the ideas behind the standards.
Each standard started with a set of bullet points which served as an
outline for a following elaboration. The vignettes showed how a
teacher conducted a lesson which hit most of the bullet points. An
example of what I think how the typical vignette covered the bullets
was the one from Standard 6: Reflection on Student Thinking. This
was the one where Mr. Santos went around and observed his students
finding the solutions to the polynomial raised to the polynomial. He
was supposed to ensure that every student is learning sound math
(which he did by going around to all the groups), challenge and extend
their ideas (which he did by suggesting the students try investigating
the base of 1 in the last group), adapting or changing activities
(which he mentally changed the lesson plan for the next day based on
what happened that day), commenting on student's learning to parents
and administrators (which it didn't say he did), and provide regular
feedback to the students (which it didn't say he did or was going to
do).
Shawn
Feb 14, 2008, 2:54:45 PM2/14/08
to MthEd608Winter2008
In your post, Erin, you mentioned that you felt you were being too
critical in some areas. I think that this is not a bad thing. If we
weren't critical about these vignettes, I don't think that we would be
able to find better ones for the next edition of the Standards, or
even have better standards.
Your post also had me think about an article by Jacobs and Morita
(they recorded Japanese and American teachers watching and commenting
on Japanese and American math lessons). When they started their
Discussion Section, they posed the question about whether or not
Americans are comfortable with any type of math instruction. I think
that this is true for most American teachers. I'm hoping that with
more critical eyes in the field of math education we can bring up to
standard our teaching overall here in the United States.
critical in some areas. I think that this is not a bad thing. If we
weren't critical about these vignettes, I don't think that we would be
able to find better ones for the next edition of the Standards, or
even have better standards.
Your post also had me think about an article by Jacobs and Morita
(they recorded Japanese and American teachers watching and commenting
on Japanese and American math lessons). When they started their
Discussion Section, they posed the question about whether or not
Americans are comfortable with any type of math instruction. I think
that this is true for most American teachers. I'm hoping that with
more critical eyes in the field of math education we can bring up to
standard our teaching overall here in the United States.
CJ
Feb 14, 2008, 5:50:44 PM2/14/08
to MthEd608Winter2008
I think the absolute value vignette was also in the discourse article.
How could I forget that sweeping bow?
How could I forget that sweeping bow?
CJ
Feb 14, 2008, 5:58:52 PM2/14/08
to MthEd608Winter2008
Shawn, I agree that there probably is not perfect vignette for a
standard, because the ideal implementation of each standard will
always depend on the students involved. I'm not sure, but I seem to
remember Dr. Leatham mentioning that he only had us read the vignettes
involving technology. That means that there were more vignettes. What
I don't know is whether there is more than one vignette per standard.
If so, then perhaps there is a vignette that demonstrates how Mr.
Santos reports progress to parents and gives feedback. If not, maybe
that's okay. It would be strange, however, to have a vignette in which
Mr. Santos does all the things described in the polynomial vignette
and then flashes forward to parent teacher conferences to show him
talking with parents. I think a vignette that hit all the bullet
points might risk losing its authentic flavor. It would be interesting
to know the reason why the vignettes were included. I think that we
can make a lot of pretty good guesses about their purpose, but I
wonder how the authors and editors would characterize their reasons
for including them.
standard, because the ideal implementation of each standard will
always depend on the students involved. I'm not sure, but I seem to
remember Dr. Leatham mentioning that he only had us read the vignettes
involving technology. That means that there were more vignettes. What
I don't know is whether there is more than one vignette per standard.
If so, then perhaps there is a vignette that demonstrates how Mr.
Santos reports progress to parents and gives feedback. If not, maybe
that's okay. It would be strange, however, to have a vignette in which
Mr. Santos does all the things described in the polynomial vignette
and then flashes forward to parent teacher conferences to show him
talking with parents. I think a vignette that hit all the bullet
points might risk losing its authentic flavor. It would be interesting
to know the reason why the vignettes were included. I think that we
can make a lot of pretty good guesses about their purpose, but I
wonder how the authors and editors would characterize their reasons
for including them.
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