How Grades 1-7 Teachers Assess Mathematics and
How They Use the Assessment Data
Elizabeth Warren, Australian Catholic University
Steven Nisbet, Griffith University
The purpose of this study was to explore mathematics assessment methods
employed by teachers and ways teachers used assessment data. The sample
for the study consisted of 398 mathematics teachers in Grades 1 to 7 in
a state in Australia. The teachers completed a Likert-scale survey. Using
Scheffe pair-wise comparisons and correlation coefficients to examine the
relationships between grade level, use of assessment data, and use of assessment
techniques, the researchers found several significant differences in teaching
and assessment cultures across Grades 1 to 7.
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The Measurement of Volume: Why Do Young Children
Measure Inaccurately?
Charlotte Strange Reece, Jacksonville State University
Constance Kamii, University of Alabama at Birmingham
A total of 257 children in grades 2-5 were individually interviewed
to find the grade level at which they demonstrated transitive reasoning
and unit iteration in the measurement of volume. In the transitivity task,
the children were asked if a larger, empty container could be used to compare
the quantity of popcorn kernels (about 350 cc) in two containers that looked
very different. The unit-iteration task was similar except that children
were asked if a small cup could be used to compare similar quantities of
rice in two containers. It was found that a majority of children (51%)
demonstrated transitive reasoning by third grade and that a majority (56%)
demonstrated unit iteration by fourth grade. A conclusion reached is that
the standard of the National Council of Teachers of Mathematics (2000)
expecting children to understand units of measurement by grade 2 is unrealistic.
Better principles of teaching are also suggested to encourage children
to think logically.
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The Tabular Mode: Not Just Another Way
to Represent a Function
Ellen Hines, Northern Illinois University
David B. Klanderman, Trinity Christian College
Helen Khoury, Northern Illinois University
Understanding mathematical functions as systematic processes involving
the covariation of related variables is foundational in learning mathematics.
In this article, findings are reported from two investigations examining
studentsā thinking processes with functions. The first study focused on
seven middle school studentsā explorations with a dynamic physical model.
Students were videotaped during the 20- to 45-minute sessions occurring
two or three times per week over a period of 2 months, and studentsā written
work was collected. The second investigation included 19 preservice elementary
and middle school teachers enrolled in a course focusing on a combination
of mathematical content and pedagogy. Participantsā written problem-solving
work and reflective writing were collected, and participants were individually
interviewed in 50-minute videotaped sessions. Results from both investigations
indicated that students often relied on a table, or some variation of a
table, as a cognitive link advancing the development of their reasoning
about underlying function relationships.
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Task Dynamics in a College Biology Course for
Prospective Elementary Teachers
Hedy Moscovici, California State University ö Dominguez Hills
This paper explores the dynamic profile of a task as interpreted by
a group of six prospective elementary teachers enrolled in a college biology
course. Because of various constraints, such as lack of planning time,
provision of materials and equipment, and lack of previous knowledge, the
assigned task shifted from the planned or intended task (as defined by
the instructor before implementation and presented to the students during
the field trip) to a transitional or technical task (influenced by the
list of materials available and on-site conditions) and, finally, to an
enacted task (tasks actually performed by the different students).
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