Exploring Polygon Rings
Lyle R. Smith, Augusta State University
Some topics in mathematics
are unique because they can be explored by learners from the early grades
through the advanced grades. One such topic is polygon rings.
As suggested in the Curriculum and Evaluation Standards for School Mathematics
(National Council of Teachers of Mathematics, 1989), students can learn
mathematics by actively engaging in the activities outlined in this article.
The activities integrate problem solving, reasoning, and communication,
and they offer a fascinating look at the beauty of the structure of mathematics.
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The Effects on Studentsí Cognitive
Achievement When Using the Cooperative Learning Method in
Earth Science Classrooms
Chun-Yen Chang and Song-Ling Mao, National Taiwan Normal University
This study investigated
the effects of cooperative learning instruction versus traditional teaching
methods on studentsí earth science achievement in secondary schools.
A total of 770 ninth-grade students enrolled in 20 sections of a required
earth science course participated in this nonequivalent control group quasi-experiment.
The control groups (n = 10) received a traditional approach, while the
experimental groups (n = 10) used cooperative strategies. Study results
include (a) no significant differences were found between the experimental
groups and the control groups when overall achievement (F = 0.13, p > .05),
knowledge-level (F = 0.12, p > .05), and comprehension-level (F = 0.34,
p > .05) test items were considered; and (b) students who worked cooperatively
performed significantly better than students who worked alone on the application-level
test items (F = 4.63, p < .05). These findings suggest that cooperative-learning
strategies favor studentsí earth science performance at higher but
not lower levels of cognitive domains in the secondary schools.
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The Border Crossings of a Multicultural
Science Education Enthusiast
Julie A. Luft, University of Arizona
Jill was a preservice science
education student who wanted to make science more accessible to all students.
This study is an examination of the "borders" she encountered as she completed
her student teaching in a cultural setting that was different from her
own. Her student teaching experience was documented through interviews,
participant observations, field notes, lesson plans, and a journal. An
inductive analysis of the documents and a context chart of the coded data
revealed that Jill encountered the (a) cultural border of her students,
(b) cultural border of science instruction, and (c) cultural border of
the school. While some borders were crossed, others were not. This study
suggests that during field experiences, preservice teachers may encounter
multiple cultural borders, some consistent and some inconsistent with their
instructional philosophy. As student teachers work with diverse populations,
supervisors and cooperating teachers need to recognize the borders student
teachers will encounter and encourage student teachers to examine their
beliefs about practice as a means to acknowledge and understand the encountered
borders.
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Subtraction From a Historical Perspective
Susan C. Ross and Mary Pratt-Cotter, University of Southern Mississippi
The algorithms used for
subtraction vary. In the United States, three different algorithms were
used almost equally until the 1940s: the equal additions, the decomposition,
and the Austrian method. After William Brownell modified the decomposition
algorithm, the use of other algorithms was practically eliminated in mathematics
textbooks. Today, some texts introduce the equal additions algorithm, but
the decomposition is still the predominant algorithm. This article reviews
the historical use of each of the three algorithms in the United States,
discusses the modification to the decomposition algorithm, and gives a
brief overview of the current status of subtraction algorithms.
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The State of Readiness of Initial Level Preservice
Middle Grades Science and Mathematics Teachers and Its Implications on
Teacher Education Programs
Paul J. Bischoff, Douglas D. Hatch, and Lettie J. Watford, Georgia
Southwestern State University
The purpose of this study
was to document through interview and videotaped data the current state
of readiness of 10 preservice middle grade teachers, regarding their ability
to plan, implement, and reflect on an integrated mathematics and science
lesson. The results showed that only one student was successful in implementing
a lesson that compared favorably to national standards. This studentís
lesson plan contained minimal pedagogical considerations and consisted
primarily of notes emphasizing fine detail of distinction about the content
of the lesson using her own examples. The lesson plan and post-lesson-plan
interview data of the remaining students indicated an adherence to algorithmic
learning, rote memorization, and procedural knowledge. There were numerous
content errors in the plans, and these students orally described a lack
of self-confidence in their ability to teach this lesson successfully.
The most successful student demonstrated her competence in meeting standards
of pedagogical content knowledge and was most successful in analyzing her
own teaching. The results showed that most subjects of this study needed
extensive training in content and pedagogy and in synthesizing these in
a way consistent with modern learning theory.
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