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NEW DOCTORAL DEGREES Teaching and learning outcomes in undergraduate calculus courses for students of technical and science studies in Croatia and Denmark
Ljerka Jukić
; Department of Mathematics, University of Osijek, Osijek, Croatia
Abstract
The issue of retention of
knowledge is an important area of research that has the potential
to improve teaching practices and achieve curricular goals. This
issue is a matter of great concern since many educators and
mathematics lecturers noticed a low level of students’ retention
of definitions, concepts and theorems after mathematics course
instruction and examination. Only small number of studies
investigated retention of university students' knowledge,
especially in calculus, therefore this study provides valuable
insights into the retained knowledge in calculus, focusing on the
non-mathematics students. We investigated retained calculus
concepts for students coming from two universities that differ in
various aspects, one in Croatia and one in Denmark.
In the first chapter we give motivation for this study. Also we
provide historical overview of the most important mathematicians
who gave their contribution to the first notions and findings in
integral and differential calculus. The chapter ends with the core
topics of differential and integral calculus introduced to the
first year university students.
We compared the calculus teaching at a Croatian and Danish
university in terms of students' retention of core calculus
concepts in integrals and derivatives two months after
instructions. We focused on the procedural and conceptual
knowledge. The results showed that for both universities, a large
portion of taught subject matter was forgotten. Investigating
students grades and scores on the questionnaire, we found that the
passing grades of Calculus 1 course did not predict the results in
the test two months later. Students with the lowest passing grades
had better results two month later, or there was no difference.
Next we investigated the retention of core procedural and
conceptual concepts in integral calculus among Croatian students
in physics, electrical engineering, and civil engineering study
programs. The students were surveyed three times in several time
periods: two, six and ten months after instructions in integral
calculus, combining that with the beginning and the end of
Calculus 3. The result showed that the students improved their
answers to the conceptual questions. In the second investigation
that took place six months after examination and at the beginning
of Calculus 3, students answers showed deterioration in most of
the procedural questions. In the third investigation that took
place ten months after instructions in integrals and at the end of
Calculus 3, procedural knowledge improved.
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This strongly indicated
that students' procedural knowledge was very fragile, and that
students might forget procedural knowledge quickly when this
knowledge is not used any more. We discovered that students
generalize every integral of the form $\displaystyle \int
\frac{\mathrm{d}x}{f(x)}$ to $\ln{(f(x))}+C$.
We investigated students' knowledge 14 months after instructions,
we found effect of mental structures called met-befores and
met-afters that affected students' knowledge in differential
calculus. When we investigated students' concept image and concept
definition of definite integral two months after instructions and
examination, we discovered that students retained highly
incoherent knowledge of definite integral as an area. Here we also
added to Tall-Vinner discussion claiming that it differs from
student to student if concept definition is part of the concept
image. Also, we found that improper use of technology leads to
retention of superficial conceptual
knowledge and deterioration of procedural knowledge.\\
Keywords
Hrčak ID:
74907
URI
Publication date:
21.12.2011.
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