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Arguments in Critical Thinking Ability
1stNonik Indrawatiningsih
STKIP PGRI Pasuruan
Pasuruan, Indonesia
nonik_pinkgirl@yahoo.com
Abstract—The ability to think critically is an essential skill
and becomes one of the primary goals in college. A person who
can think critically will be able to use appropriate criteria to
evaluate an argument. There must be clear evidence and
accompanied by a plausible explanation. This study aims to
investigate students' critical thinking skills in determining an
argument. The subject is the students of mathematics education
program at one private university in Pasuruan, i.e., 31 students.
Then, some students who have unique answers are selected to be
interviewed further about their critical thinking ability to an
argument. This research is a descriptive qualitative research.
Based on the results of a written test of 31 students, there is one
student who has a unique answer. The answer is different from
other students, so from the results of these tests, the student is
selected for the further interview. The findings of this study
highlighted that the student can mention arguments with the
accurate reasons and has a potential to have the ability to think
critically.
Keywords— argument, Critical Thinking Ability
I. INTRODUCTION
Critical thinking is an essential skill that every student in
Higher Education should develop. This skill is vital to assess
any information, explain the reasons and be able to solve
problems that have not known the solution. In addition,
Douglas also said that critical thinking skills are generally
recognized as essential skills and become one of the primary
goals in college [1]. Critical thinking skills are preferred over
algorithmic cognitive abilities. It is also expressed by Amit
and Azikovitsh that the current reformation in mathematics
education throughout the world includes the transition from
algorithmic cognitive abilities towards higher cognitive
abilities, i.e., critical thinking skills [2].
According to Ennis, critical thinking is a reflective
thought which is plausible and focuses on what decisions to
believe or what to do [3]. Ennis defines the ability to think
critically related to decision making whether someone should
believe or not in an argument [4]. One indicator of people
who have the ability to think critically is he/she can evaluate
the accuracy of various arguments. In the same way, Cottrell
also conveys that evaluation is an essential part of critical
thinking, involving a series of cognitive processes aimed
identifying a problem, choosing a solution plan, and
evaluating. Assuming this, people who have the ability to
think critically can use appropriate criteria to evaluate an
argument [5].
In a study conducted by Norris and Phillips shows that
there are still many students who have difficulty in
determining a claim/argument and provide a proof of the
claim/argument that has been given to him [6]. Therefore,
students’ critical thinking skill – in this case is the skill in
analyzing an argument- needs to be provoked. Furthermore,
providing a proof is a crucial aspect of explaining a reason
for the claim/argument [9].
Students who can examine and evaluate
arguments/claims are supporting evidence that the student
has critical thinking skills [10]. The ability to think critically
can encourage students to think independently and solve
problems in the context of everyday life [11]. As'ari states
that a person who has the ability to think critically is the one
who can determine whether a statement or an issue has been
given arguments/claims or not [12]. A person who has the
ability to think critically should be able to evaluate
information from various sources of information.
Arguments are a core component of critical thinking,
which includes the ability to construct its own argument,
agree or disagree with claims to the information/news that has
been heard [14;15;16]. Accordingly, someone who has the
ability to think critically should be able to criticize news or
reports from various sources of information. It involves
critical thinking and argumentation skills to determine
whether the claim/argument has been given right or wrong
[13]. Students must justify their arguments supported by the
evidence to argue that arguments must be accompanied by
contradictory examples or facts that do not support
As was discussed above, students' ability in determining
argument becomes an important indicator for students who
have critical thinking ability. For this reason, this research has
been participated by the mathematics students who have the
answers which is unique or different from the others in order
to find out if students who have unique answers or have the
potential to have critical thinking skills. Is argument an
important indicator used to track one's critical thinking
ability.
II. METHODS
This research has been administered using a qualitative
descriptive research. The subject of the research was the
students of Mathematics Education Study Program at one of
the private universities in Pasuruan force year 2015 amounted
to 31 students. There were 31 students tested and then some
of them, who have unique answers, have been selected and
interviewed further. A semi-structured interview was
conducted to investigate the results of tests that have been
done in depth. The instrument used is the critical thinking
ability of the material of triangular congruence which is made
in the form of proof which refers to the indicator of critical
thinking ability, namely argument identification. The
instrument that is examined to the students as a following Fig.
1. Interviews were carried out with the questions that
focused on how they explained the answers already done to
know whether there was a potential for critical thinking skills
or not. Interviews are conducted for 20-30 minutes. The
First International Conference on Science, Mathematics, and Education, (ICoMSE 2017)
Copyright © 2018, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Advances in Social Science, Education and Humanities Research, volume 218
12
interviews were recorded and then transcribed and finally
coded.
Fig. 1. Test Instrument
III. RESULTS
The arguments referred to in this study is a collection of
statements that have a causal relationship or a sentence
consisting of several statements and conclusions. This study
aims to investigate students who potentially have the ability to
think critically using with identifying their unique answers
and examine them whether they can explain the argument or
not. This suggests that the argument is a fundamental indicator
that must be possessed by people who have the ability to think
critically. Likewise, O'Rourke also conveys that students who
are able to examine and evaluate arguments/claims are
supporting evidence that the student has critical thinking skills
[8]. A person who knows that the sentence/information that
has been given to him or she is an argument or not is an
indicator of a person who has critical thinking skills [10]. The
following will explain the results and discussion of the
research.
The test revealed that there was only one from 31 students
who has a unique answer. The answer is different from other
students so that researchers conduct further interviews with
the student. Interviews here aim to identify if students who
have this unique answer have the potential to have critical
thinking skills and how the student explains the arguments that
the researcher has given while pointing out that the argument
is a fundamental indicator to track whether a person has
critical thinking skills or not. Here are the results of student
tests that have different answers with other students.
Fig. 2 the test result student about the argument
Pay attention to the picture below!
Prove that ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴!
Solution
• 𝐴𝐵 // 𝐷𝐶 as a consequence 𝐴𝐵
̅
̅
̅
̅
=𝐶𝐷
̅
̅
̅
̅
𝐴𝐷// 𝐵𝐶 as a consequence 𝐴𝐷
̅
̅
̅
̅
=𝐵𝐶
̅
̅
̅
̅
𝐴𝐶
̅
̅
̅
̅
on ∆𝐴𝐵𝐶 = 𝐴𝐶
̅
̅
̅
̅
on ∆𝐴𝐵𝐶 (coinciding)
Based on triangle congruent theorem is side, side, side, so ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
• ∠𝐵𝐴𝐶 = ∠𝐷𝐶𝐴 (in the opposite, because of 𝐴𝐵 // 𝐷𝐶)
𝐴𝐶
̅
̅
̅
̅
on ∆𝐴𝐵𝐶 = 𝐴𝐶
̅
̅
̅
̅
on ∆𝐶𝐷𝐴 (coinciding)
Based on triangle congruent theorem was corner, side, corner, so∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
Which of the following is classified to argument and non-argument? Give the reason!
1. If 𝐴𝐵
̅
̅
̅
̅
=𝐶𝐷
̅
̅
̅
̅
, 𝐴𝐷
̅
̅
̅
̅
=𝐵𝐶
̅
̅
̅
̅
, 𝐴𝐶
̅
̅
̅
̅
=𝐴𝐶
̅
̅
̅
̅
so∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
𝐴𝐵
̅
̅
̅
̅
̅
=𝐶𝐷
̅
̅
̅
̅
,𝐴𝐷
̅
̅
̅
̅
=𝐵𝐶
̅
̅
̅
̅
,𝐴𝐶
̅
̅
̅
̅
=𝐴𝐶
̅
̅
̅
̅
So ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
2. ∠𝐵𝐴𝐶 = ∠𝐷𝐶𝐴
𝐴𝐶
̅
̅
̅
̅
=𝐴𝐶
̅
̅
̅
̅
∠𝐴𝐶𝐵 = ∠𝐶𝐴𝐷
So ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
3. If 𝐴𝐵 // 𝐷𝐶 as a consequence 𝐴𝐵
̅
̅
̅
̅
=𝐶𝐷
̅
̅
̅
̅
If 𝐴𝐷// 𝐵𝐶 as a consequence 𝐴𝐷
̅
̅
̅
̅
=𝐵𝐶
̅
̅
̅
̅
𝐴𝐶
̅
̅
̅
̅
=𝐴𝐶
̅
̅
̅
̅
So ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
4. If ∠𝐵𝐴𝐶 = ∠𝐷𝐶𝐴, 𝐴𝐶
̅
̅
̅
̅
=𝐴𝐶
̅
̅
̅
̅
and ∠𝐴𝐶𝐵 = ∠𝐶𝐴𝐷 So ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
5. If 𝐴𝐵
̅
̅
̅
̅
̅
=𝐶𝐷
̅
̅
̅
̅
,𝐴𝐷
̅
̅
̅
̅
=𝐵𝐶
̅
̅
̅
̅
, and 𝐴𝐶
̅
̅
̅
̅
=𝐴𝐶
̅
̅
̅
̅
so ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
Advances in Social Science, Education and Humanities Research, volume 218
13
The following was the interview result of the
subject about the argument
R : for number 1 you answered an argument. Why?
S : the argument loaded conclusion, in here there
was statement 1 and statement 2 and both
statements could be concluded.
R : which one was the statements?
S : if AB
̅
̅
̅
̅
=CD
̅
̅
̅
̅
, AD
̅
̅
̅
̅
=BC
̅
̅
̅
̅
, AC
̅
̅
̅
̅
=AC
̅
̅
̅
̅
so ∆ABC ≅
∆CDA these were statement 1AB
̅
̅
̅
̅
=CD
̅
̅
̅
̅
, AD
̅
̅
̅
̅
=BC
̅
̅
̅
̅
,
AC
̅
̅
̅
̅
=AC
̅
̅
̅
̅
these were statement 2, so ∆ABC ≅
∆CDA was the conclusion
R : did the argument have to load statement and
conclusion?
S : yes ma'am, for example, there was no conclusion
it meant that it was no argument.
R : was the statement same with the premise? And
then the conclusion?
S : in my opinion they were same
R : could you be explained what premise/statement
was?
S : premise was …. (while thinking). I did not define
it ma'am, but the example was like number 1 if
AB
̅
̅
̅
̅
=CD
̅
̅
̅
̅
, AD
̅
̅
̅
̅
=BC
̅
̅
̅
̅
, AC
̅
̅
̅
̅
=AC
̅
̅
̅
̅
so ∆ABC ≅ ∆CDA
R : how about the conclusion?
S : based on the conclusion was taken from some
premises/statements then gave the conclusion
From the conversation above the subject can
already understand that the argument must contain a set
of premises and conclusions. If there is no conclusion
by subject, it is not an argument. Subjects are also able
to name their respective premises and conclusions. The
above conversation indicates that the subject of
potential possesses critical thinking skills, this is
evident when in-depth interviews are conducted on
arguments. The subject can determine whether it is an
argument or not and clarify that the characteristics of
the argument must contain the premise and conclusion
while not the argument only contains the premise
without conclusion. However, the subject has not
connected a valid and invalid argument. He has only
limited to explaining arguments and arguments, not yet
getting into more in-depth content about valid and
invalid arguments.
IV. DISCUSSION
Based on the information received by the
researcher, the subject is classified as a student who
has the moderate academic achievement. At the time
of the learning process took place in the subject is also
not very active in learning. The value of his
achievements was also standard. However, it turned
out that based on the test results and continued with
the above interview. There are findings that the subject
is able to analyze the information and can mention that
the information has been given an argument or not and
he can give reasons/clarification why it is called
arguments.
A person who cannot distinguish whether the
information that has been given to him is an argument
or not means the person cannot think critically. As
Asari says that if one cannot determine whether an
information that has been given to it is a
claim/argument or not, or the person cannot
distinguish which is the premise and what is the
conclusion in an argument, the person is far from being
said to have the ability to think critically [10]. Such
people tend not to have critical thinking skills.
O'Rourke argues that students who can examine
and evaluate an argument/claim, identify and evaluate
an argument, and can provide supporting evidence,
then the student performs an essential part of critical
thinking [8]. It also occurs on this subject, he can
check and assess whether the information that has
been given is an argument or not, otherwise he can also
give a reason why it is called an argument or not so
that this subject can already be concluded that he was
involved in critical thinking and have the ability to
think critically.
The results show that the most crucial primary
indicator in critical thinking ability is that students can
define arguments or not against information that has
been given to them. Evaluating arguments against
existing information is an essential tool for assessing
students' critical thinking skills especially knowledge
of arguments. It is vital that students be able to filter
the information well and not get stuck from the
arguments/claims that have been said by someone.
The ability to think critically is necessary for students
to succeed in the future. Therefore, critical thinking
skills must be applied and developed in the core
curriculum and teaching and learning process to
produce students who have the quality of thinking of
future leaders. Therefore, it is essential to develop
students' critical thinking skills in all subject lessons,
especially mathematics. Mathematics learning not
only teaches mathematical content.
V. CONCLUSION
Based on the results and discussion above, the
conclusions can be drawn is as follows.
1. Based on the test results from 31 students, there is
only one student who has a unique answer which
subsequently conducted interviews related to the
answer.
2. After interviewing the answer, it turns out this
student has the potential for critical thinking skills
whereas this student belongs to students who have
Advances in Social Science, Education and Humanities Research, volume 218
14
3. moderate academic achievement and time of
learning process in this student class is not active.
4. Arguments are the necessary and essential tool for
knowing whether a person has the potential to have
critical thinking skills.
ACKNOWLEDGMENT
The paper is supported by The Indonesian
Endowment Fund for Education (LPDP).
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