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Methods course documentation
Analyzing classroom vignettes from an inquiry perspective (D5.2)
Facilitator's plan (by Raffaella Borasi) -- Notes on articulating
and announcing the task for the midterm paper
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Notes in preparation to articulating the task for the midterm paper:
- provide participants with a detailed written description of
the task for this paper, so that they can refer back to it as they begin
to work on the paper
- in writing these directions, keep in mind my goals for this assignment:
- I want the students to have an opportunity to synthesize and apply
what they have learned about the recommendations for school mathematics
reform, and about an inquiry approach more specifically (but I do not want
to reduce it to an inquiry approach only, given that this is a methods
course, and not a course on teaching math through inquiry only); more specifically,
this means:
- an appreciation of how the goals of instruction need to change, and
how their worthiness can be evaluated;
- an appreciation of how teaching practices need to change, and how one
can evaluate whether they are appropriate and effective
- I want students to really do an in-depth analysis of a specific
instructional episode (or it would not accomplish the previous goal); this
means that:
- they have to choose an episode that is "rich" enough (i.e.,
represent an attempt to respond to school math reform), is "complete"
enough (i.e., has a beginning and an end to it), and also is not too long
(or it would take them forever to do the in-depth analysis I want them
to do)
- they need specific directions about the kind of analysis I am expecting
from them (i.e., what to look for and comment upon), and perhaps also a
"model" to get a more concrete sense of what this may involve
- I do not want to specify the length of the paper, since it would depend
a lot on the complexity of the episode chosen -- so I am not going to say
anything about it in the written assignment, but I will try to respond
to this question if raised.
Text of the assignment prepared as a result:
Midterm take-home exam: Choose
a specific instructional episode from one of the classroom stories you read
so far in the course, and then discuss in writing to what extent this episode
meets (or does not meet) the recommendations made in the NCTM Standards
and the principles of an inquiry approach to teaching mathematics. More
specifically, your paper will need at least to:
- briefly identify the specific episode you have chosen
(for ex: "the first 3 days in the Area story, where the students work
on the problem of finding the area of the rocket");
- identify the main instructional goals informing this
experience (note that in most cases these goals will not have been explicitly
stated and you will have to "derive" them from other information
provided in the story) & discuss their "worthwhileness" in
light of the guidelines offered by relevant NCTM Standards and the principles
of an inquiry approach;
- identify key activities/instructional strategies used
by the teacher & for each of these activities/strategies discuss (a)
how (and why/why not) it responds to the recommendations contained in the
NCTM Teaching Standards, and (b) to what extent it seems informed by an
inquiry approach (and why/why not);
- identify and discuss the effects of these activities/strategies
and what students learned as a result of the experience
(Major assignment worth 10 points and to be graded)
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Notes in preparation to announcing the midterm paper:
- make sure the midterm paper deadline is announced at least 2 weeks
in advance of the due date (so that people can set time aside for it);
also, describe the nature of the task at the time the "stories of
inquiry-based math classes" are assigned, so that students can start
looking for potential vignettes as they do this reading assignment
- when describing the task:
- remind that this task was already mentioned in the Course Description
as one of the "major assignments" that would be graded
- describe the nature of this task and goals (see my notes in previous
section):
- I want the students to have an opportunity to synthesize
and apply what they have learned about the recommendations for school mathematics
reform, and about an inquiry approach more specifically (but I do not want
to reduce it to an inquiry approach only, given that this is a methods
course, and not a course on teaching math through inquiry only); more specifically,
this means:
- an appreciation of how the goals of instruction need
to change, and how their worthiness can be evaluated;
- an appreciation of how teaching practices need to change,
and how one can evaluate whether they are appropriate and effective
- discuss how they should choose an appropriate episode:
- elegible sources: shorter episodes within the books they already read
(i.e., Learning mathematics through inquiry; Living and learning mathematics)
OR other instructional episodes that represent an effort towards school
mathematics reform -- make clear that if they choose this option, they
need to show me the episode in advance and get my approval;
- show other potential sources for these episodes: MaryAnn Rossboch's
unpublished report of an inquiry unit on the Olympics in her 3rd grade
class; other unpublished report of innovative units from some of my previous
students; some teacher narratives from Deborah Schifter's forthcoming book
-- I can loan a copy of these materials upon request
- criteria to consider when chosing the vignette:
- "rich" enough -- i.e., represent an attempt
to respond to school math reform)
- "complete" enough (i.e., has a beginning and
an end to it)
- not too long (or it would take them forever to do the
in-depth analysis I want them to do)
- go over the other points of the text of the written assignment articulating
the kind of analysis I want from them, and answer questions about them
- if someone ask about the length of the paper (and I expect this will
happen!), say that it would depend on the complexity of the episode chosen
and the writing style, but I want an in-depth analysis -- so I doubt
that they could achieve that in less than 5-8 pages double spaced
- announce that I have a couple of papers students wrote in previous
years they could look at as "models" -- they will have to ask
me for one, though, so that I can give them one that does NOT address the
same episode they have chosen
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