Abstract:
Nowadays, Calculus has got tremendous applications in Physics, Chemistry, Economics,
Accounting and Engineering. However, learning Calculus concepts in high schools and higher
institutions is found to be a challenging problem. Students have low motivation, poor conceptual
understanding and reasoning in learning calculus concepts such as limit, continuity, derivative
and definite integrals. Because of this, the overarching aim of the present study was to investigate
students’ conceptual understanding, reasoning and motivation by applying GeoGebra software in
multi-teaching approaches coupled with a genetic decomposition model grounded in APOS
(Action, Process, Object & Schema) theory. The study involved an intervention mixed research
design encompassing both the quantitative and qualitative approaches. A quasi- experimental
design was employed for the quantitative approach and case study design was used for the
qualitative method. Two universities were randomly selected out of Amhara Regional state
universities. A pretest was administered to collect baseline information regarding the concept of
calculus. Thereafter, first year physics students at U1 University were assigned as experimental
group and first year physics students at U2 University were assigned as the comparison group
using random sampling technique. Next, Calculus concepts were delivered using GeoGebra
integrated with multi-teaching approaches coupled with a genetic decomposition model grounded
in APOS theory, whereas the comparison group learned the same content using the traditional
method for twelve weeks. Diagnostic Tests (Pretest, Mid-term Test & Posttest) and Motivation
scales based on the ARCS (attention, relevance, confidence and satisfaction) model were employed
to collect quantitative data, and semi structured questions and open-ended questions were used to
collect qualitative data using students’ interview and reflections respectively. Descriptive
Statistics, t-test, ANCOVA, Correlations and Multiple Regression were employed to analyze the
quantitative data. However, thematic analysis and descriptive analysis were used for analyzing
the qualitative data. The results from the analyses of quantitative data revealed that the treatment
group got significantly higher mean scores on conceptual understanding, reasoning and
motivation than the comparison group. Hence, the findings emerged out of this study indicated
that the implementation of GeoGebra software together with multi-teaching approaches coupled
with genetic decomposition model grounded in APOS theory improves students’ calculus learning
better than the traditional approach. On the other hand, results from the qualitative data
uncovered that GeoGebra integrated with multi-teaching approaches improves students’ interest,
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motivation, visualization and understanding of calculus concepts. Moreover, students elicited
manifestation of constructions of mental structures in a coherent and logical manner while
learning calculus activities designed based on a genetic decomposition model grounded in APOS
theory. In sum, the finding showed that GeoGebra integrated with multi-teaching approaches
guided with APOS theory is effective to enhance students’ motivation, conceptual understanding
and reasoning in learning calculus concepts. The finding opens a greater opportunity to
recommend technology integrated mathematics curriculum in Ethiopian higher education.
Key Words: GeoGebra Software, Multi-teaching, Conceptual Understanding, APOS theory,
Motivation