




































GEOMETRY LEARNING BASED ON COGNITIVE CONFLICT  
IN THE DEPARTMENT OF MATHEMATICS 

 UNIVERSITAS NEGERI MEDAN 
Hasratuddin1, KMS. M. Amin Fauzi 2, Nurhasanah Siregar 3 

1,2,3 Lecturer at the Department of Mathematics, FMIPA UNIMED Medan 
Email1: siregarhasratuddin@yahoo.com  

Email2: amin_fauzi29@yahoo.com 
Email3: nurhasanahsiregar@yahoo.com  

 
 

ABSTRACT. Geometry is one of the compulsory courses for students majoring in 
mathematics at the State University of Medan. Geometry has a deductive axiomatic 
character, which is a science whose truth leads to previous truths. Conflict is an 
action from the existence of a gap that arises and is felt from an information or 
incident. Cognitive conflict occurs when students become aware of a mismatch 
between what is on their mind and information from outside. The concept of 
learning geometry occurs as a result of the information or system received by a 
person that causes action, interaction and reflection. Thus for action to occur, it is 
necessary to have contextual problems that challenge as a source of conflict. With 
cognitive conflict, which results in an awareness of incongruity with prior 
knowledge, this can spur emotions or motivate students to seek the real truth. This 
motivation can encourage the integration of efforts to find the real truth as a result 
of one's rational thinking ability and will be arranged in a cognitive structure and 
occupy long-term memory. The purpose research is to improvement of students' 
mathematical reasoning abilities and creative thinking in learning geometry 
through cognitive conflict approaches in the Mathematics. This type of research is a 
semi-experimental study with a two-class control and pretest-posttest experimental 
design. The location of this research is the Department of Mathematics, Universitas 
Negeri Medan. While the subjects in this research were 35 students in the 2019 F 
PSPM and 32 PSPM 2019 A classes. The object in this study is a learning geometry 
based on a cognitive conflict approach.  The research result that the role of 
cognitive conflict in learning geometry will be able to improve students' rational 
thinking and emotional intelligence.  

Keywords: cognitive conflict, learning, geometry, rational thinking, emotional. 

PRELIMINARY 

A new paradigm of learning geometry is connecting learning and thinking and developing 
personality attitudes. Hasratuddin (2018) said that teaching geometry now is the time to 
focus on thinking skills and learning reflection, interaction and development of specific 
thinking concepts, and developing interactive social attitudes and behavior. This becomes 
the basis for and consideration of changes in the geometric learning process, no longer only 
emphasizing the development of the cognitive realm alone, but need to involve attitudes or 
emotional intelligence. 

Naturally, students have a tendency to understand the world around them. Students 
construct their concepts as a result of their observations and investigations of the world 

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mailto:siregarhasratuddin@yahoo.com
mailto:amin_fauzi29@yahoo.com
mailto:nurhasanahsiregar@yahoo.com


around them (Bayer, 2016). Therefore, studying geometry is a concept construction process 
based on observing a conflict or real world context. 
 The existence of a conflict with someone will lead to dissatisfaction. Learning through 
conflict is learning that raises dissatisfaction in students, because students realize that what 
they have is not in accordance with the real truth. Naturally, students tend to nullify 
dissatisfaction. The desire to minimize conflict is a very strong human motivation (Kang et 
al., 2015). This characteristic states that learning is a construction activity, where students 
discover their own concepts, principles or procedures for themselves. According to this 
principle, studying geometry is a construction activity. Learners construct internally, mental 
representations that can concrete images, schemata, procedures, work methods at the level 
of abstract symbols, intuitions, contexts, schemata settlement, or through experiments. The 
characteristic of this construction, among others, is that students find themselves solving 
procedures of a contextual problem.  

In the framework of learning geometry, conflicts can occur if students realize that 
their understanding or perception of mathematical objects is incompatible with the nature 
of the true geeometric object.Students will consciously try to eliminate this conflict by 
accepting the truth they should. This realization made him not repeat the mistakes he had 
made again. The process of eliminating conflict will strengthen the true understanding of a 
concept. Therefore, learning through the process of eliminating conflict can lead to strong 
and holistic understanding for students. 

One alternative learning that can spur the mastery of student conceptions is to use 

cognitive conflict strategies, which is the application of constructivism. Osborne (1993) 

suggests that cognitive conflict strategies have a general pattern, namely: exposing 

alternative frameworks, creating conceptual cognitive, encouraging cognitive 

accommodation. Lee and Kwon (2003) state that there are three phases in the cognitive 

conflict learning process, namely the preliminary stage, the conflict stage and the resolution 

stage. In the preliminary stage, the lecturer can explore the initial conceptions of students 

and create anomalous situations. that is, a situation that is contrary to the student's prior 

knowledge. In the conflict stage, the lecturer observed the student's response to the 

anomalous situation given. Recognition of anomalous situations can be in the form of 

attraction or anxiety. The resolution phase, with lecturer conditioning, students will 

attempted resolve conflicts in cognitive structures to gain knowledge in accordance with 

scientific concepts. The stages of cognitive conflict-based geometry learning carried out in 

this study are as follows: 

1. Cognitive conflict orientation. In this case, the lecturer provides a conflict context 
that contains conceptual barriers to students. Students understand and discuss in 
groups. 

2. Lecturers facilitate classical discussions. Students present alternative solutions as a 
comparison. 

3. Lecturers provide opportunities for students to reflect on conflict resolution.  
4. Students find complete and applicable knowledge. 

From the cognitive conflict-based learning stage above, the problem of cognitive 
conflict context is the starting point of the learning process, and will end by eliminating the 
conflict that is presented. Learning through conflict elimination will not occur if there is no 
conflict to condition it. So that learning through cognitive conflict can facilitate students to 
gain a strong understanding.Therefore, to build conflict, the lecturer should create events 

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that are not in accordance with the student's final conception. The event in question is a 
symptom or situation that cannot be explained by the conception captured by the student, 
but can be explained by the actual concept. For example, students would know about 
Original numbers, A = {1,2,3,4, ...} and whole numbers, C = {0,1,2,3, ...}. Then, if students are 
asked "which has more natural numbers with whole numbers? What is their answer? Also 
they certainly know about rectangles. Then, do they know about the rectangle? 

Learning mathematics through cognitive conflict is cognitive conflict conditioning 
during the mathematical process. Conflict conditioning can occur when introducing concepts 
(as a preventive measure) or it can also occur to straighten misconceptions that occur to 
students. The delivery of procedural information or the provision of "drill" alone cannot 
achieve optimal cognitive conflict learning. A learning approach that demands a sense of 
dissatisfaction is more appropriate for learning through cognitive conflict. This feeling of 
dissatisfaction will lead to long duration retention. 

The emotional intelligence referred to in this research is a series of non-cognitive 
abilities and skills that affect a person's ability to successfully cope with environmental 
demands and pressures such as the ability to recognize feelings of oneself and others and 
interpret them, reach and generate feelings to help critical thinking and emotional 
development. . Emotional intelligence includes interpersonal and intrapersonal intelligence. 
The application of cognitive conflict as a preventive action can be started by predicting 
student conceptions of the given topic. Predictions about student conceptions can be made 
based on previous student experiences or the lecturers' personal experiences with the 
subject matter. 

Research methods 

1. This type of research is a semi-experimental study with a two-class control and pretest-
posttest experimental design.  

2. The location of this research is the Department of Mathematics, FMIPA UNIMED Medan, 
Jl. Willem Iskandar Psr. V Medan Estate. 

3. While the subjects in this research were 35 students in the 2019 F Mathematics 
Education Study Program (PSPM) and 32 PSPM 2019 A classes.  

4. The object in this study is a learning geometry based on a cognitive conflict approach.  
5. Implementation of learning 

The learning action stage with the cognitive conflict approach to be carried out in this 
study are; 

a. Conflict situation. At this stage, the lecturer presents problems in the form of 
challenges or conflicts to be resolved by students either individually or in groups. 

b. Organizing learning. At this stage the lecturer organizes assignments related to 
problem conflicts. 

c. Investigation guidance. At this stage the lecturer encourages students to collect 
information in carrying out experiments to get explanations and problem solving. 
Presentation and sharing. At this stage the lecturer gives the opportunity to convey 

student ideas or solutions to the conflicts given. Students report their own or group 
problem solving or activity results or discuss their answers to conflict solutions. Process 
analysis and evaluation as a reflection stage. At this stage the lecturer fosters student 
analysis and evaluation as a reflection of thinking, so that students find concepts or 
knowledge. 

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Research Results and Discussion 
A. Online Learning Process. 
1. Meeting 1.  

Learning begins with providing "Online Lecture Rules", namely; 1)Prepare equipment 
and special rooms for your meeting, 2) Straighten your intention to learn, 3) Dress 
politely and neatly, 4) Login on time, 5) Leave 10 minutes before the class meeting 
starts, 6) Turn off the Mic (mute) when not talking , 7) Raise your hand when you 
want to talk, 8) Focus and not leave the meeting, 8) Do not share the meeting link 
with others. This thickest system recognition aims to form students who are orderly, 
civilized and have good emotional intelligence. In discipline 2) straighten the 
intention, this is harmonious in studying. This means that it is not enough for them to 
just study online or join online courses. If you learn, it's true, it can be done 
anywhere and anytime. Thus, it is not wrong that Ngadim Makarim, Minister of 
Education and Culture in 2020 said the term "independent learning". Obviously, 
learning does not form morals or good behavior, because learning while squatting, 
smoking in the bathroom can also be done. However, if you are studying, it is clear 
that there must be a teacher, it cannot be done anywhere, you can ask questions if 
you don't know, and there are ethics as manners that must be maintained. This is 
something that must be done by teachers so that a culture of good character for 
students is formed. After that, the teacher / lecturer can provide useful knowledge 
for students. Al'adaabul fauqol 'ilmu =: adab is more than science. 
 
Student Response. 

S1: About the intention. Initially when asked about their answer to "learning" Of 
course, the intention to learn this must be changed to learning, because we will 
provide knowledge when they have morals. This is called the partial formation of 
emotional intelligence. 

2. Second online learning. 

The lecturer gives a problem in the form of a conflict in mathematics study 
program students "what is mathematics". The purpose of giving this conflict problem 
is so that students have a consistent attitude towards the application and practice of 
mathematical values in the form of consistent, rational, honest, obedient, critical and 
creative thinking. (Hasratuddin, 2018). As for the student response to the conflict 
"what is mathematics?", The researchers grouped them into 4 parts, namely; 
a. S1: Mathematics is a branch of knowledge that deals with numbers. 
b. S2: Mathematics is an exact science. 
c. S3: Mathematics is solving life's problems. 
d. S4: Mathematics is the mother of all knowledge.  
From the 4 student responses, at S1 a mathematical principle and value were found 
that mathematics is not a knowledge, but is a science that is not the result of 
experiments but is found (Wittgenstein, 1974b). This is what makes mathematics 
equalized with philosophy. In this session the lecturer gave a challenge in the form of 
a conflict to students, namely to investigate whether the following statements were 
the same or different? 1) Arrogant people are not smart, and 2) smart people are not 
arrogant. Apparently, to give answers with reasonable reasons is mathematical logic. 

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Obviously the problem does not involve numbers or numbers but it can only be 
solved by mathematical means. The conclusion that can be found is that 
mathematics does not only solve problems related to numbers. 
 From the S2 response, it was found that in terms of mathematical 
measurements it is not always certain, thus mathematics is not an exact science. But 
mathematics must be in rules or systematics. Soejadi (1997) in the book 
Mathematical Tips "The supreme judge of mathematics is systematic, while the 
highest judge of science is reality, the iron is burned expands". 
 From S3's response, it was found that mathematics is a tool and means of 
solving all problems in general, which is the closest to being true and based on 
rational human reason. As such, all disciplines use mathematical principles. From S4's 
response, it was found that mathematics is the mother of all sciences. This is based 
on all fields of science that require mathematics. Freuthental (1991) states that 
mathematics is a human activity. The point is that mathematics is used by all humans 
who have activities. The logical consequence is that any human being who is active 
must use mathematics. Furthermore, people who don't use math are those who 
have no activity. In conclusion, people who shy away from math are better off to stay 
inactive. 
 From this learning activity, the lecturer directs students to understand and 
live out the objectives of learning mathematics, among others; 1) Math teaches you 
to admit when you're wrong. Mathematics makes humans aware of their limitations 
or admits that they are often wrong. 2) To choose exact and correct words. Math 
teaches you to choose the right and correct words. 3) To think several steps ahead. 
Mathematics teaches you to think ahead (move on). 4) Not like everyone else but in 
your own way. Mathematics teaches you to think your way, (reasonable skepticism). 
5) And never give up. Mathematics teaches you to never give up. 

 For this purpose, students are expected to understand that they are often 
wrong, have weaknesses and are limited in everything (above the sky there is still a 
sky). This will form students who do not have to be arrogant, arrogant and like to 
ridicule or slander others. And, it is hoped that students will have the principle of 
understanding means forgiving everything as a part of good emotional intelligence. 
Then from the attitude value in goal 1, it is hoped that students will have an attitude 
towards goal 3, namely as a wise, wise and lucky person, they must always have the 
principle "today must be better than yesterday, and tomorrow the day after 
tomorrow must be better than today in things can choose the right and the right, 
according to the second goal. Furthermore, in that it will always be better day by day, 
students will arrive at the 5th goal, 

3. The third online learning is by providing conflict with the material. 

At the third meeting, the conflict given was "if there is a rectangle having a 
circumference of 24 cm, then determine the size of the rectangle that has the largest 
area". Various responses were given by students on this problem. There are students 
who say that the size of a rectangle with a circumference of 24 m is 5 x 7 with an area 
of 35 m2. There were students who gave the answer 6 x 6, but because it was already 
a square, the answer was changed to 5.5 m, x 6.5. This happened because the concept 
of rectangles and squares was not fully understood for them. 

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So, this moment will be a strengthening of the square concept that lecturers 
must do, so that they will find a strengthening of their reasoning ability about the 
square concept. And immediately, students will accept this if it is given based on logic 
or reasoning. Of course, this acceptance is part of the realm of emotional intelligence. 
Therefore, it is not excessive if it is found that cognitive conflict-based learning will be 
able to improve students' reasoning abilities and emotional intelligence. 

So that in order to strengthen the understanding of the concept of the 
rectangle, the lecturer asks students to define a rectangle. There are students who 
define a rectangle as a rectangle that has 2 pairs of equal sides. There are also students 
who define a rectangle as a rectangle that has length and width, and so on. From this 
answer, the lecturer began to describe 4 flat buildings, as follows. 

 

 Then, ask students to indicate which of the flat shapes is a rectangle. 
Student response; 
S1: A quadrilateral is a polygon with four sides and four corners.  

S2:  

 

S3:  

 

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From the answers to the three respondents above, it can be concluded that 
students still have doubts about the meaning of rectangles. Thus the conflict will be used 
for discussion until it finds answers rationally.Bayer, M (2016), said that learning with 
cognitive conflicts will be able to improve students' mathematical reasoning abilities. 
And, this is what is called a process of improving students' reasoning abilities. 

B. Formative test results 1 

After 3 online meetings, the researcher gave 1 formative test of 1 question, 
namely "If there are any triangles, right angles, equilateral and isosceles having the same 
circumference, then determine which triangle has the largest area! ” 
Following are the results of the reasoning skills test obtained by 47 students of the 
Mathematics Department of FMIPA UNIMED Medan, with a range of scores of 0-100. 

Table 1. Descriptive Statistics Data of Final Learning Test 

Statistics 
Reasoning ability 

Low Moderate High 

Number of 12 23 12 

Mean 39.44 65.33 78.67 

Stdev 9.91 14.36 12.39 

Min scor 21 57 71 

Max scor 57 71 100 
 

Based onIn the table 1. above, it can be seen that the low level student groups 
have not achieved optimal performance. Their achievement range is 21-57, which is still 
below the average class achievement. Whereas for the medium level group, it reached a 
score of 57-71, and the high-level group reached 71-100. Statistically, the descriptive 
statistical table of the achievement scores for the student's reasoning ability shows that 
the average level of achievement of the moderate level group has reached the minimum 
completeness, which is above a score of 60. above there are 32 out of 47 people (68%) 
who achieved completion. This shows that cognitive conflict learning is effective in 
improving students' mathematical reasoning abilities. Against student emotional 
intelligence in cognitive conflict learning can be seen in the following discussion. 

 
 
 
 

ELEMENT 
STUDENT'S EMOTIONAL INTELLIGENCE SCORE 

Level / 

Class 

Below  

(0 - 19) 

Low 

(20 - 39) 

Normal 

(40 - 59) 

Super  

(60 - 79) 

Perfect (80 - 

100) 

Condition  Early End Early End Early End Early End Early End 

Average  32.5 45.2 32.5 45.2 32.5 45.2 32.5 45.2 32.5 45.2 

Std. Dev 19.2 16.4 19.2 16.4 19.2 16.4 19.2 16.4 19.2 16.4 

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Table 2.  Student Emotional Intelligence Achievement Scores. 

 
From the table of emotional intelligence achievements above, it can be seen that for each 
level as follows; 
a. Below; before learning 6 people (13%) changed after learning to 2 people or 4%. 
b. Low: before learning 13 people (28%) changed after learning to 12 people or 27%.  
c. Normal; before learning 19 people (40%) changed after learning to 20 people or 42%. 
d. Super; before learning 9 people (19%) changed after learning to 10 people or 21%. 
e. Perfect; before learning 6 people (13%) changed after learning to 2 people or 4%. 

In general, it can be said that students who have below normal emotional 
intelligence before learning are 17 or 36%, after learning they turn into 14 people or 
30%. So there are 3 people whose emotional intelligence has changed to normal. So, it 
can be said that the emotional intelligence of students majoring in mathematics at the 
State University of Medan can be improved through learning with a cognitive conflict 
approach. In addition, based on students' responses to learning with a cognitive conflict 
approach, it can make students happy and eager to always get this learning for the next 
course. 

CONCLUSION 
Based on the research results, it can be concluted that: 

1. Learning geometry based on the cognitive conflict approach in the Mathematics 

department of the State University of Medan can improve reasoning skills.  

2. Learning geometry based on the cognitive conflict approach in the Mathematics 

Department of State University of Medan can improve emotional intelligence which 

includes self-understanding, understanding of others, empathy, motivation and self-

control. 

3. Through learning geometry with a cognitive conflict approach, students gain a 

strong understanding of the fundamental concepts of geometry rationally. So that, 

students will have a long memory or long term retention for any geometric 

concepts. 

4. Learning conflict-based cognitive geometry can help students correct 

misconceptions or misconceptions. 

 

REFERENCES 

Bayer, M. 2016. Fostering Conceptual Change by Cognitive Conflict based Instruction on 
Student Understanding of Heat and Temperature. Eurasia Journal of Mathematics, 
Science and Technology Education, Volume2, Number 2, July 2016.www.ejmste.com. 
accessed on 23 February 2019. 

Freudenthal H. (1991). Revisiting Mathematics Education. Dordrecht: Reidel Publishing. 

Given, BK (2007). Teaching to the Brain's Natural Learning Systems. Alexanderia: ASCD. 

Hasratuddin. 2018. Why You Should Study Mathematics. Ed. 2. Perc. Edira: Medan. 

Lots 6 2 13 12 19 20 9 10 0 3 

Percentage 13 4 28 27 40 42 19 21 0 6 

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http://www.ejmste.com/


Kang, S., Koh, H., Noh, T., & Scharman, LC 2015. The Influence of Students Cognitive and 
Motivational variables in Respect of Cognitive Conflict and Conceptual Change. 
International Journal of Science Education, (Online), Vol. 27, No. 9, 2015. 

Lee, G. & Kwon, J. (2003). What Do We Know About Student's Cognitive Conflict in Science 
Classroom: A Theoretical Model a Cognitive Conflict Process. [on line] available: 
www.eric.ed.gov/ERICWebportal (01 May 2016). 

Mc Gregor, D. (2007). Developing Thinking; Developing Learning. New York: Open University 

Press. 

R Soedjadi. (2000). Mathematics Education Tips in Indonesia.Directorate General of Higher 

Education, Ministry of National Education 

Wittgenstein, L. (1974b). Philosophical Investigations. Oxford: Blackwell. [Paper reference 
1]understanding Mathematics Teaching, 77, 20–26. 

 
 

 

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http://www.eric.ed.gov/ERICWebportal

	1. This type of research is a semi-experimental study with a two-class control and pretest-posttest experimental design.  
	2. The location of this research is the Department of Mathematics, FMIPA UNIMED Medan, Jl. Willem Iskandar Psr. V Medan Estate. 
	3. While the subjects in this research were 35 students in the 2019 F Mathematics Education Study Program (PSPM) and 32 PSPM 2019 A classes.  
	4. The object in this study is a learning geometry based on a cognitive conflict approach.  
	5. Implementation of learning 
	CONCLUSION 



