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Methods course documentation
Learning about resources to support instructional innovation (D7.3)
Facilitator's plan for a session based on an Investigation from the "Connected
Mathematics Project" (by Raffaella Borasi)
Note: What follows is the outline for a 1 to 1 1/2 hour session
based on Investigation 1 of the first unit on rational numbers (entitled
"Bits and Pieces I") within the "Connected Mathematics"
curriculum series. This investigation aims at developing a deeper understanding
of fractions based on the construction of "fraction strips" and
their use in a variety of thought-provoking activities. We invite readers
to look at the Logistics and scheduling information for more information
about the choice of this activity and its rationale.
Plan for the session
- Have the participants read excerpts from the "overview" of
"Bits & Pieces I" to give them a sense of the whole unit
and, thus, the overall context for the specific activities they will experience.
- In pairs, have the participants "read & do" (i.e., read
the text and do the suggested activities/exrcises as if they were the students)
"Investigation 1" -- where the meaning of fractions is sought
after through an activity involving the creation and use of fraction strips.
(Note: If some of the participants have already done this activity, put
them in a group and ask them to look instead to the following "Investigation
2" -- where students are asked to use benchmarks to help them better
evaluate the magnitude of given fractions). To make sure that the participants
truly work in pair, give only 1 copy of the text to each pair. (materials
needed: 1 copy per pair of the text of the investigation, with solutions
covered -- encourage participants to write on that copy as they need; several
strips of papers of the right length to make fraction strips)
- Have the pairs discuss what surprised them the most in this experience,
and what they learned about fractions, and compare it with their own experience
with fractions as students in elementary and middle school. (The group
who did investigation 2 could also report on their experience after Investigation
1 has been discussed) The main goal of this discussion is to make explicit
important characteristics of this lesson, including:
- the focus on "making sense"/understanding fractions vs. operating
with them
- the value (and limitations) of fraction strips as a manipulative
- the importance of keeping in mind what the "whole" is in
each situation
- the value of hands-on activities to gain such an understanding
- (if Investigation 2 is discussed) the value of "benchmarks"
and estimations
- the importance of actually engaging in the activities designed for
the students in order to get a sense of theur pedagogical value
- Have the participants in the large group discuss both how they read
these materials and what uses they could make of materials of this
kind to support their teaching. The goal here is to lead participants to
recognize the value of these instructional materials, and also realize
that such a value may not become apparent until they themselves engage
with the materials "as learners", doing all the exercises as
students would.
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about resources to support instructional innovation"
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