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Methods course documentation
Exploring implications for assessment (D5.3)
Facilitator's plan (by Raffaella Borasi) (For Implementation
D)
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Preliminary reading assigment
In preparation for this session, assign
the following readings on assessment:
- Introduction to the 1995 NCTM Assessment
Standards
-- to give students a sense of the reasons
given for the need for new assessment
-- to show how changing assessment is an integral
part of the school mathematics reform agenda (and thus further make connection
between what we are doing in the course and nationwide movements/give more
legitimation to what we are doing)
-- to introduce students to the less known of the NCTM Standards
- Clarke, D.J., Clarke, D.M. & Lovitt,
C.J. (1990). Changes in mathematics teaching: Call for assessment alternatives.
In 1990 NCTM Yearbook
-- to give students a lot of concrete
ideas about how the directives for new assessment can be put into practice
in the classroom
To make these readings more meaningful,
also ask the participants to begin to think about how a learning experience
like the inquiry on Area they just engaged in could be reasonably assessed.
Rationale: I think that these preliminary
readings can sensitize the students to issues about assessment, and thus
make them better appreciate the experience with taking an item from the
new New York State test in the next class; also, these readings are intended
to complement the theoretical readings about an inquiry approach they are
doing essentially at the same time. Asking the participants to think about
how assessment could take place for an inquiry experience they just engaged
in is intended to make the issue of assessment more personal and real.
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Experience of solving an item from an innovative State-wide
test (about 45-50 minutes)
Rationale for this activity:
- In the spirit of continuing to have
the participants "experience as learners" new pedagogical practices
and then reflect on these experiences, in the case of assessment I want
them to engage first as learners in taking some of the most unusual items
in a new assessment tool, share their results, noticing by doing so that
how different these results can be, and from here begin to approach issues
about scoring and evaluation.
- As New York State is now piloting new
state-wide tests that are informed by the NCTM Standards, it may be especially
effective to introduce these tests to the participants -- so that they
know how the State is moving, and what may directly affect their practice
in future years, and also make further connection with what we are doing
in tyeh course and concurrent school mathematics reform.
- Since the state has now published training
materials that include full copies of pilot tests at different grade levels,
complete with rubrics for their scoring and samples of students work, I
want to take advantage of these resources, and make participants aware
that they exist.
- Although less important compared with
the previous points, I also wanted to be able to engage the participants
in a more "active", and thus pleasurable, activity, in the midst
of heavy-duty discussions about theoretical aspects of an inquiry approach
and its implications for instruction.
Test item selected for this activity:
(From one of the Grade 8 New York State
pilot tests)
The local sports complex charges
different prices for their tickets to different sporting events. The table
below shows their current prices. [Anyone under 16 years of age would pruchase
a child's ticket.]
Ticket Prices
|
Child |
Adult |
| Hockey |
$4.50 |
$7.00 |
| Basketball |
$5.00 |
$9.00 |
| Football |
$6.25 |
$11.50 |
Ken's Scout Troop earned money in
order to go to Saturday's football game. His father bought 8 tickets for
the scouts and one ticket for himself as the Scoutmaster.
When Ken's father pays for the tickets,
how much change will he receive from a $100 bill?
Note: reproduce
this item on a separate sheet of paper, with no "box" for the
answer, so that participants may be more inclined to give answers other
than simply a numerical one.
Rationale for the choice of this item:
Although at first I was looking for an
item that dealt with area -- to make connections with the participants'
own inquiry and the discussions about the goals of teaching this topic developed
in class -- I ended up going for the "safer" choice of this item,
since I knew that it had been successful in previous implementations (see
In-service Program).
Plan for the session:
- (10-15 min., of what seems necessary)
Divide the participants in groups
of 3, pass the hand-out with the test item (without telling them
where it is coming from!), and ask them to solve this problem and
write down their solutions just as if they were doing it for the test.
- (15-20 min.) Have
each group share their response with the rest of the class; encourage questioning
and challenging; make sure that in the discussion the following points
come up:
- diversity in the strategies and tools
participants have used to solve the problem (i.e., graphs, tables, algebraic
expressions, etc.) -- make sure to show some of the examples that other
groups of participants have generated (see In-service program Participants'
work), in case this group does not show sufficient variety;
- diversity in how people interpreted and
framed the problem, the assumptions they made etc. (again, show other examples
if necessary);
- diversity in what people thought it was
necessary to include in their response
- challenge of scoring responses to open-ended
items of this kind.
- (5 min)
Now reveal that the item came from one of the new state-wide tests New
York State is piloting. Introduce these tests and their significance in
terms of effect for teaching practices and curriculum across the state.
Also give some information about the grade levels they should be given
and some approximate timetable for their expected implementation. Also
read aloud some of the directions to take the test -- pointing out the
regulation about meeting the needs of students with learning differences.
- (10-15 min.) Show
(both on overhead and by distributing copies of relevant pages to each
participant -- so that they have a record of the material that is available
in the state booklet) the rubrics created by the State for this item and
the samples of student work provided. Make sure that in the discussion
the following points come up:
- students often produce the same kind of
variety as adult group;
- support that the rubrics created by the
State can provide to a teacher in scoring this kind of exam -- and indentify
ways these rubrics could be used;
- limitations in the rubrics themselves,
as sometimes they do not expect or value the most creative thinking and
interpretations that students educated through an inquiry approach may
produce.
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Discussion of readings on assessment
Informed by the previous activity, I want
then to go back to the readings on assessment the students did for homework,
and invite comments about them.
Make sure that in this discussion the following
points are addressed:
- why new assessment is needed if we try
to teach according to NCTM Standards and/or an inquiry approach
- what are some characteristics of the assessment
that is needed to truly measure the math learning achieved as a result
of inquiry experiences
- concretely identify some of these characteristics
(or the lack thereof) in the items of the New York State examined (make
sure that their "extended task" component is mentioned), and
perhaps also brainstorm some other assessment activities that could complement
them.
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