Analysis of Concatenations and Order of Operations
in Written Mathematics
Mary A. Lee, Minnesota State University
Shelley J. Messner, Mankato Morris Area High School
Concatenations in written mathematics are the positioning of symbols next
to each other to imply an operation without a symbol for the operation.
Concatenations have been identified in previous research as an obstacle
to understanding, or a cognitive difficulty, in the learning of algebra.
The additive inverse symbol with concatenations poses questions not addressed
by the usual conventions for order of operations. In this study, texts
of grades 6 through 9 were surveyed, and quantitative and qualitative analyses
were made of the instructional emphasis on selected concatenations. Results
indicated much curricular emphasis on unsigned (without negative signs)
numeral forms and integer, as compared to minimal curricular emphasis on
signed (with negative signs) fraction, mixed number, decimal, and exponent
numeral forms. A recommendation is to increase curricular emphasis on signed
numeral forms and to include the additive inverse unary operation in the
conventional order of operations.
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Achieving the Reforms Vision: The Effectiveness
of a Specialists-Led Elementary Science Program
Renée S. Schwartz, Oregon State University
Fouad Abd-El-Khalick, American University of Beirut
Norman G. Lederman, Oregon State University
This report describes an evaluation project that aimed to assess the potential
of two elementary science specialists, as compared to elementary classroom
teachers, to realize the reforms vision for science instruction in elementary
classrooms. Participant science specialist background, views of elementary
science teaching, and planning and assessment practices were compared to
those of regular elementary classroom teachers in the specialist district,
as well as in a comparable district not employing specialists. Specialistsâ
views and practices were better aligned with those envisioned by current
national reform documents in science education. Despite the constraints
imposed by the nature of a program evaluation, the present report provides
evidence to suggest that students taught by the science specialists (a)
were engaged in open-ended, inquiry-oriented, science-based activities
of the kind often advocated, but mostly absent, in elementary school, and
(b) demonstrated problem solving and higher order and critical thinking
skills. This report is the first to provide empirical support for the advocated
ãeffectivenessä of elementary science specialists in achieving the visions
espoused by current reform efforts.
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Establishing Factorial Validity of the
Mathematics Teaching Efficacy Beliefs Instrument
Larry G. Enochs, Oregon State University
Phillip L. Smith and DeAnn Huinker, University of Wisconsin-Milwaukee
The Mathematics Teaching Efficacy Belief Instrument (MTEBI) for preservice
teachers resulted from the modification of the Science Teaching Efficacy
Belief Instrument STEBI-B. The MTEBI consists of 21 items, 13 items on
the Personal Mathematics Teaching Efficacy (PMTE) subscale and eight items
on the Mathematics Teaching Outcome Expectancy (MTOE) subscale. Possible
scores on the PMTE scale range from 13 to 65; MTOE scores may range from
8 to 40. The first version of the MTEBI had 23 items like the STEBI-B;
however, subsequent analysis in this validation required two items be dropped.
Reliability analysis produced an alpha coefficient of 0.88 for the PMTE
scale and an alpha coefficient of 0.75 for the MTOE scale (n = 324).
Confirmatory factor analysis indicates that the two scales (PMTE and MTOE)
are independent, adding to the construct validity of the MTEBI.
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The Effectiveness of Schoolyards
as Sites for Elementary Science Instruction
Linda L. Cronin-Jones
University of Florida
This study compared the impacts of traditional classroom and outdoor schoolyard
instruction on the environmental science content knowledge and attitudes
of 285 third- and fourth-grade students. A modified Solomon Four
Group design, including control, classroom treatment, and schoolyard treatment
groups, was used. Both the indoor classroom and outdoor schoolyard treatments
consisted of corresponding 10-day units focusing on plant and animal ecology.
Valid and reliable content knowledge and attitude assessments were administered
before and after instruction. Analyses of variance and post hoc analyses
of posttest scores and gain scores indicated that elementary students learned
significantly more about selected environmental science topics through
outdoor schoolyard experiences than through traditional indoor classroom
experiences. Both classroom and schoolyard treatment groups developed more
positive environmental attitudes as a result of instruction, but the attitude
posttest and gain scores of these two groups were not significantly different
from each other.
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