Abstract:
This investigation was designed to determine the extent to which
students who are completing planned curricula in mathematics education
are proficient in spatial visualization abilities and possess mathematical
understandings. The effects of mathematics curricula upon
the development of these abilities and understandings and the relationships
between these abilities and understandings were examined by
comparing group mean test scores of prospective elementary and
secondary mathematics teachers with those of (a) prospective social
science teachers, (b) prospective English teachers, (c) prospective
science teachers, (d) prospective art/industrial arts teachers, (e)
freshman mathematics students, (f) experienced elementary mathematics
teachers, and (g) experienced secondary mathematics teachers.
Criterion tests were the Differential Aptitude Test of Space Relations,
Form A, (DATSR), the Revised Minnesota Paper Form Board
Test, Series MB, (MPFB), and the Sequential Test of Educational Progress-Mathematics, Form 1B, (STEPM). The study being of a
post-test-only design, the criterion instruments were administered
to the freshman students at the beginning of Fall Term 1964. Prospective
teachers completed the tests during the term in which they
were enrolled in their respective special teaching methods courses.
Single classification of analysis of covariance using DATSR,
MPFB, and STEPM group means was employed to statistically test
the null hypotheses. Means of combined verbal and mathematical sub-test scores on the Washington Pre-College Tests were applied as covariance
controls of scholastic aptitude, and group mean cumulative
grade-point-averages were similarly used to control group differences
in academic ability. F ratios were computed and evaluated to determine
whether differences in group means on the criterion instruments
were significant. The data were further analyzed to determine correlations
between the variables and other curricula data. Reliability
coefficients for the criterion instruments were computed for each
group involved in the study.
FINDINGS: The following conclusions relative to students at Central Washington
State College were drawn from the data obtained and analyzed in
this investigation: 1. The spatial visualization abilities of prospective elementary
mathematics teachers are significantly different from similar
abilities of experienced elementary mathematics teachers,
while the spatial visualization abilities of prospective secondary
mathematics teachers do not differ significantly.
2. Spatial visualization abilities of prospective secondary mathematics
teachers and experienced elementary mathematics
teachers are significantly different, as are the similar abilities
of prospective elementary mathematics teachers and experienced
secondary mathematics teachers.
3. The spatial visualization abilities of prospective elementary
mathematics teachers are not significantly different from
similar abilities of prospective teachers in other academic
fields of endeavor involved in the study, except in the field
of science.
4. Spatial visualization abilities of prospective secondary mathematics
teachers are significantly different from similar abilities
of prospective teachers of social sciences and prospective
teachers of English, but are not significantly different
from spatial visualization abilities of prospective teachers of
art/industrial arts or prospective teachers of science.
5. Prospective secondary mathematics teachers have a significantly
different degree of development of spatial visualization
abilities than do prospective elementary mathematics
teachers. It would appear, based on the means of the collected
data, that the former group has a higher degree of
development.
6. The spatial visualization abilities of first-quarter freshman
mathematics students are significantly different from similar
abilities of prospective elementary mathematics teachers
but are no different from these same abilities of prospective
secondary mathematics teachers.
7. Mathematics achievement can be used, at significant levels
of confidence, as a valid index of spatial visualization abilities
of prospective teachers in several academic fields,
freshman mathematics students, and experienced elementary
and secondary mathematics teachers.
8. There is no significant dependence of a teacher's spatial
visualization abilities on his scholastic ability. This is also
true for the first-quarter freshman mathematics students.