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Developing Estimation Strategies by Making Connections among Number, Geometry,
Measurement, and Data Concepts: Discussing Strategies
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Discussing Strategies
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Estimation activities
encourage students to make connections among the mathematics concepts they
are learning and the skills they are developing. In this multipart video
example, the class discussions and the decisions the teacher makes contribute
to students' opportunities to connect their understandings of number, measurement,
geometry, and data in order to make estimates. Purposeful activities together
with skillful questioning by the teacher can help students understand relationships
among mathematical ideas, as described in the Connections Standard. In the
first part, Estimating Scoops, the teacher presents an estimation task (estimate
the number of scoops of cranberries in a jar) to the second-grade students
and talks about the teaching decisions she is making. In this second part,
Discussing Strategies, the students work in groups to share their ideas
and reach a reasoned consensus about their estimates. In the third part,
Estimating Cranberries, the students estimate the number of cranberries
rather than the number of scoops.
Video
Segment
In a section
of the lesson preceding this video clip, the following occurs: the teacher
has one student place three scoops of cranberries in the glass jar while
another student tallies the number of scoops. Many in the class, on seeing
the benchmark of three scoops, want to change their estimate of the total
number of scoops to fill the jar. The teacher gives each group an identical
jar already containing three scoops. She directs the groups to come up
with a single estimate and an explanation of how they thought about the
situation.
In this
second video segment, a group of students is working to analyze the situation,
revise their initial ideas, and decide on their group's estimate. Observe
the teacher's discussion of the strategies used by the students. What
mathematical ideas are emerging?
QuickTime
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Video
Transcript
(Click and drag the text below
to scroll)
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Discussion
For students to
function effectively in groups, the teacher must take care to be very
clear about his or her expectations for how students will work together.
Reaching a consensus requires that all students have an opportunity
to tell their ideas and then negotiate with the others to arrive at
a group answer that the group members can all justify. In the video,
the teacher asks different students in the same group questions to
guide them in clarifying and adjusting their estimates and in considering
alternatives.
Following the small-group
work, the class comes back together with their revised estimates.
The estimates range from nine and one-half to thirteen and one-half
scoops. The teacher points out that the range has narrowed significantly
from the original estimates, which ranged from five to twenty-two
scoops. Each group fills its jar and records the number of scoops.
The range for the actual number of scoops is from ten and one-half
to thirteen and one-half. The teacher facilitates a discussion comparing
the sets of data and notes how the use of the benchmark has made the
group's estimates much closer to the actual counts.
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Take
Time to Reflect
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- In what
ways does the teacher help her students build new ideas
on what they already know?
- How
does the teacher's strategy of moving from the whole group
to small groups facilitate participation by all students?
- Also
consider this video segment
in which the teacher discusses the participation of a student
with Down's Syndrome.
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Video
Credit
Roche, Robert .
"Cranberry Estimation." In Estimating produced by WGBH Boston.
Teaching Math, A Video Library, K–4. Funded and distributed by
the Annenberg/CPB Math and Science Project, P.O. Box 2345, S. Burlington,
VT 05407-2345, 1-800-LEARNER.
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Discussing Strategies
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