![](bg5.png)
Subject 3 did not include attributes attached to the
operation. In addition, Subject 3 was also less
thorough in conducting the operation.
This research wanted to survey whether the
students learnt the group axioms in this question. The
researcher observed that most of the students
memorized the group axioms (closure, associativity,
neutral element, inverse element) but they could not
analyze them. We categorized the mistakes into two
groups on this question. In the 1st Category, students
listed the group axioms but they accepted them
“Correct” without sufficiently analysing it. In short,
they accepted that associativity was proved without
analysing. In the 2nd Category, the result we found is
that the students could not comprehend the required
associativity.
It could be said that the students preferred to copy
rather than to think abstractly when we consider that
they attended to the university as a result of test exam,
i.e. the central exam system (Soylu, 2008). It sounds
believable that they could have just memorized the
rules of theory without internalizing the descriptions.
Trying to proving the group axioms without thinking
on descriptions is a sign of rote learning based
education system. Whether a cognitive teaching has
been done on the algebraic structures or not has not
been known. Unless we internalize the meanings of
the concepts covered with the different learning
methods, mastering on a subject by rote will come
into the question. Using computer programmes, e.g.
computer algebra system CBS), will provide
convenience but, are there any academic members
applying to the computer programmes or how are
their perspectives to these embodying processes?
Doing a scientific research by academic members
about this matter, their opinions and their approaches
could be significantly useful (Tatar and Zengin,
2016). The questions, which measure whether
definitions and features of algebraic structures are
learnt, are generally measure proving, reasoning, and
discernment ability. Individuals experience many
problems in their daily life and they think
mathematically to solve their problems. Actions like
explaining a proposition, saying why it is right or
wrong and choosing and using different logical
thinking ways and proving types, present individual’s
ability on mathematical thinking. In this sense, the
students of the mathematics department are supposed
to use their ability of mathematical thinking and to let
the operations they do make sense. Mistakes made by
students, who participated in the study, came up as a
result of either misunderstanding the conditions of
group theory or examining these conditions wrong
(Arikan, et.all., 2015). Some challenges could be
experienced during the learning process but the
matter is to identify them correctly and to enhance
various methods to deal with them. Having
difficulties at the learning abstract concepts is the
most important one. Students can apply to rote
learning in order to overcome this difficulty, but they
can have difficulty in practice at this time. For
example, student lists the axioms (closure,
associativity, inverse element, neutral element) while
controlling the set whether it is group or not, but he
or she makes the operation supposing that the set is
closed (Arikan, et.all., 2015). In other words, student
cannot practice what he or she memorized or could
not know what to do in other cases. We have been
thinking the fact that this problem traces to the gaps
of education which was received in both high school
and university years. Students’ infrastructure they set
up with math training, which they had during their
education life up to attending university, has
inadequate mathematics they meet at the university.
They assume that the success at this lesson to be able
to perform the operations without using calculator
and dealing with just practical solutions in the math
exams. However, they meet theoretical mathematics
after the graduation from a high school before the
college and as a natural result, they are afraid of
another learning difficulty, which we thought it arises
from the same reasons, is the one which is dealing
with proving the theories (Ocal, 2017). While it is
rehearsing as if definitions and proofs have no
significance at secondary education, the theoretical
side of the mathematics is at the forefront at the
university, especially at the Algebra Math-1 Class.
Students even do not know how to study for this
lesson and they are having enormous learning
difficulties. Our suggestion to minimize this wavers
during this gradation process is to lecture the abstract
mathematics, such as logic, proving methods before
Linear Algebra and Mathematics Analysis I class, in
which the main subjects of the theoretical
mathematics have been taken into account.
Conceptual learning has much higher degree of
importance in the mathematics education for the
students who study at the mathematics department.
Unless the students can successfully comprehend
algebraic definitions, concepts and structures, they
will try to memorize these phenomenon’s(Soylu,
2008).
4 CONCLUSIONS
Based on the results of data analysis, it can be
concluded that the conceptual understanding of
ICMIs 2018 - International Conference on Mathematics and Islam
442