Abstract:
Research in cognitive psychology suggests that cognitive factors such as spatial
abilities and verbal reasoning are important in developing geometric knowledge of
students in elementary school. However, these cognitive abilities are less explored in
teacher education. The study adopted cross-sectional survey design to investigate
relationships among knowledge types in geometry, and how spatial ability and verbal
reasoning relate to and account for knowledge in basic shape and space among pre service teachers. A sample of 757 pre-service teachers from 12 public colleges of
education in Ghana participated in the study. Cognitive tests on spatial ability, verbal
reasoning and basic Geometry content knowledge were validated for the main data
collection. The instrument was found to be reliable and achieved measurement
invariant across gender and programmes offered by pre-service teachers. Descriptive
statistics and structural equation modeling were employed to analyze and estimate
model parameters to answer the research questions and hypotheses. Bootstrapping
was conducted to determine significance of effect sizes in the relationship paths
connecting spatial ability, verbal reasoning and basic Geometry content knowledge.
The study found that pre-service teachers performed better in procedural and
declarative tasks than in conditional tasks. Pre-service teachers also did better in 2-D
tasks than in 3-D tasks. The declarative, conditional and procedural knowledge were
found to be significantly interrelated in a way that defines pre-service teachers‟
content knowledge. From the structural equations, pre-service teachers‟ spatial ability
significantly affected their basic Geometry content knowledge. Verbal reasoning was
also found to intermediate the effect of spatial ability on basic Geometry content
knowledge. Finally, the results of multigroup structural equation modeling show that
the relationship among spatial ability, verbal reasoning and basic Geometry content
knowledge was structurally invariant across programme of study but moderated by
gender of pre-service teachers. Implications for the design of curriculum, teaching,
learning and assessment tasks in basic geometry at colleges of education were
discussed.
Description:
A thesis in the Department of Mathematics Education,
Faculty of Science Education, Submitted to the School of
Graduate Studies in partial fulfilment
of the requirements for the award of the degree of
Doctor of Philosophy
(Mathematics Education)
in the University of Education, Winneba
FEBRUARY 2019