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Beatriz S. DâAmbrosio William J. Boone Shelly Sheats Harkness |
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Patricia S. Moyer M. Gail Jones |
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Controlling Choice: Teachers, Students, and Manipulatives in Mathematics Classrooms
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Laura Jacobsen Spielman Gwendolyn M. Lloyd |
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Regular Features |
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Norman G. Lederman Lawrence B. Flick |
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Publishing in School Science and Mathematics |
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Book Reviews: Rockets; The Age of Reptiles; Geography Fun: Cool Activities and Projects for Young Explorers |
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Ted Eisenberg |
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Problems: 4803-4808 Solutions to 4771-4777 |
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Guidelines |
Inside Back Cover |
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Beatriz
S. DâAmbrosio,
William
J.
Shelly
Sheats Harkness,
This
paper describes
the mechanism
used to
gain insights
into the
state of
the art
of mathematics
instruction in
a large
urban district
in order
to design
meaningful professional
development for
the teachers
in the
district. Surveys
of close
to 2,000
elementary, middle
school, and
high school
students were
collected in
order to
assess the
instructional practices
used in
mathematics classes
across the
district. Students
were questioned
about the
frequency of
use of
various instructional
practices that
support the
meaningful learning
of mathematics.
These included
practices such
as problem
solving, use
of calculators
and computers,
group work,
homework, discussions,
and projects,
among others.
Responses were
analyzed and
comparisons were
drawn between
elementary and
middle school
studentsâ responses
and between
middle school
and high
school responses.
Finally, fifth-grade
student responses
were compared
to those
of their
teachers. Student
responses indicated
that they
had fewer
inquiry-based experiences,
fewer student-to-student
interactions, and
fewer opportunities
to defend
their answers
and justify
their thinking
as they
moved from
elementary to
middle school
to high
school. In
the elementary
grades students
reported an
overemphasis on
the use
of memorization
of facts
and procedures
and sparse
use of
calculators. Results
were interpreted
and specific
directions for
professional development,
as reported
in this
paper, were
drawn from
these data.
The paper
illustrates how
student surveys
can inform
the design
of professional
development experiences
for the
teachers in
a district.
Controlling
Choice: Teachers, Students, and Manipulatives in Mathematics Classrooms
Patricia
S. Moyer ,
M.
This research study examines the instructional practices of 10 middle
grades teachers related to their use of manipulatives in teaching mathematics
and their control of mathematics tools during instruction. Through 40
observations of teaching, 30 interviews, and an examination of 67 written
documents (including teachersâ plans and records), profiles were developed
that describe how teachers used and controlled manipulatives during instruction.
Results showed that teachers used a variety of manipulatives and other
mathematics tools over the course of the year-long study. Teachers reported
using a mathematics tool (manipulative, calculator, or measuring device) in 70%
of their lessons, and this self-report was verified by observations in which
teachers used mathematics tools in 68% of their lessons. During a 3- to 4-month
period of ãfree access,ä in which students had some measure of control in
their selection and use of the mathematics tools, the students used
manipulatives spontaneously and selectively. During free access, teachers
exhibited various behaviors, including posting lists of items on containers,
assigning group leaders to manage tools, and negotiating the control of the
mathematics tools during instruction.
Laura Jacobsen Spielman and Gwendolyn M. Lloyd
Virginia
Polytechnic Institute and
This paper communicates the impact of prospective teachersâ learning of mathematics using novel curriculum materials in an innovative classroom setting. Two sections of a mathematics content course for prospective elementary teachers used different text materials and instructional approaches. The primary mathematical authorities were the instructor and text in the textbook section and the prospective teachers in the curriculum materials section. After one semester, teachers in the curriculum materials section (n = 34) placed significantly more importance on classroom group work and discussions, less on instructor lecture and explanation, and less on textbooks having practice problems, examples, and explanations. They valued student exploration over practice. In the textbook section (n = 19), there was little change in the teachersâ beliefs, in which practice was valued over exploration. These results highlight the positive impact of experiences with innovative curriculum materials on prospective elementary teachersâ beliefs about mathematics instruction.