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 Volume 6 , Number 1, May 2021  

ISSN : 2579-8383 (Print) ISSN : 2579-8405 (Online) 
70 

  

  

The Effect of Cooperative Learning on Reasoning Ability 
and Mastery of Mathematical Concepts  

 
Agus Suyanto 

STKIP Kusuma Negara, Jakarta 
agussuyantompd68@gmail.com 

 

Accepted: 
Jan 3th   2021 

Reviewed: 
March 5th 2021 

Published: 
May 30th 2021 

 

Abstract : The purpose of this study was to determine the effect of learning methods on students' 
reasoning abilities and mastery of mathematical concepts. In this study, the authors used 
experimental research methods. Inferential analysis was performed using the Manova statistic 
(Multavariate Analysis of Arians). The results of the study concluded: (1) There was a significant 
effect of cooperative learning methods on reasoning abilities and mastery of mathematical 
concepts. This is evidenced by the value of Fo = 18, 154 and Sig = 0.000 <0.05. In this case, the 
reasoning ability and mastery of mathematical concepts in the experimental group was higher than 
the control group. (2) There is a significant effect of cooperative learning methods on 

mathematical reasoning abilities.˗value for the category of mathematical reasoning ability of 0.000 
<0.05. Thus the null hypothesis is rejected or there is a significant difference between the 
mathematical reasoning ability of the group of students who were given the STAD type 
cooperative learning method and the mathematical reasoning ability of the group of students who 
were given the Jigsaw cooperative learning method. (3) There is a significant effect of the 
cooperative learning method. mastery of mathematical concepts. This is evidenced by the test 

results contained in the Test of Between table˗ Subject Effects in the statistical test above, it is 

known that the value of F = 29.894, p . value˗the value for the category of mastery of mathematical 
concepts is 0.000 < 0.05. Thus the null hypothesis is rejected or there is a significant difference 
between the mastery of mathematical concepts in the group of students who were given the STAD 
cooperative learning method and the mastery of mathematical concepts in the group of students 
who were given the Jigsaw cooperative learning method. 
  
Keywords: Cooperative Learning Methods, Reasoning Ability, Mastery of Mathematical 
Concepts 

 

INTRODUCTION 

The world of education today faces a challenge to produce quality human resources, 

namely human resources who are able to live in the world of globalization. Education as a printer 

of human resources should receive continuous attention to improve its quality. Improving the 

quality of education also means improving the quality of human resources. 

In order to educate the nation's life, improving the quality of education is very important 

for sustainable development in all aspects of human life. The national education system must 

always be developed in accordance with the needs and developments that occur at the local, 

national and global levels1. 

 
1Mulyasa, E. 2006. Education Unit Level Curriculum. Bandung: PT Teen Rosdakarya.p.4 

mailto:agussuyantompd68@gmail.com


 
 
 

 
 EDUCATIO : Journal Of Education  
 Volume 6 , Number 1, May 2021  

ISSN : 2579-8383 (Print) ISSN : 2579-8405 (Online) 
71 

  

  

The development of science and technology must be responded positively by the world 

of education. One form of positive response from the world of education is to make curriculum 

changes dynamically in accordance with the fast-moving development of science and technology. 

This can be realized in the form of a school business as an educational institution by providing 

the best service for all its students. 

Schools as educational institutions must strive to continuously make improvements in 

various fields, both facilities and infrastructure, administrative and information services, as well as 

the quality of learning as a whole. Efforts to improve the quality of education in schools do not 

only depend on teacher factors, but also depend on other factors that are interrelated as a system 

to produce quality educational outputs. But in essence the teacher is still the main element that 

determines the most influencing educational outcomes. 

Mathematics apart from being a field of science in the world of education is also a very 

important field of study, both for students and for the development of other sciences. The 

position of mathematics in the world of education is very beneficial because mathematics is a tool 

in the education of intellectual development and intelligence. 

Mathematical material is arranged in a logical order (hierarchical) in the sense that a 

mathematical topic will be a prerequisite for the next topic. Therefore, to learn a new mathematical 

topic, past learning experiences from someone will affect the occurrence of the mathematics 

learning process. Because of the hierarchy of mathematics, discontinuous learning of mathematics 

will interfere with the learning process. This means that learning mathematics will occur smoothly 

if the learning itself is carried out continuously. 

Mathematics in general is very difficult for students to understand, because mathematics 

has abstract objects and requires high enough reasoning to understand every hierarchical 

mathematical concept, so it is necessary to apply better and more appropriate teaching models to 

help students mastery as early as possible. at the school level on mathematics. But we need to 

underline also that a good teaching is not enough to get optimal student learning outcomes, 

because one of the problems faced by teachers in conducting mathematics teaching is how to 

grow and stimulate reasoning (logic) abilities and mastery of concepts correctly by students. . 

The main characteristic of reasoning in mathematics is deductive, or in other words 

mathematics is deductive, namely the truth of a concept or statement is obtained as a logical result 

of previous truths so that the relationship between mathematical concepts or statements is 

consistent. Rochmadi also said that in principle, in learning mathematics, both inductive and 

deductive thinking patterns can be used to learn mathematical concepts.2. 

Slavin in Solihatin states that "cooperative learning model is a learning model in which 

students work in small groups to help each other in learning the subject matter"3. 

Johnson & Johnson in Isjoni stated that "the understanding of the cooperative learning 

model is to group students in the class into small groups so that students can work together with 

the maximum ability they have and learn from each other in the group"4. 

 
2Rochmadi. 2008. The Use of Inductive-Deductive Mindset in Constructivism Toxic Mathematics Learning. Paper at the 

National Seminar on Mathematics Education: Teacher Certification, at the Postgraduate Campus of UNNES Semarang, January 
16, 2008 

3Solihatin, E. 2007. Cooperative Learning: Analysis of Social Studies Learning Model. Jakarta: Earth Literacy. 
4Isjoni. 2007. Cooperative Learning. Bandung: Alphabeta p. 14 



 
 
 

 
 EDUCATIO : Journal Of Education  
 Volume 6 , Number 1, May 2021  

ISSN : 2579-8383 (Print) ISSN : 2579-8405 (Online) 
72 

  

  

Sanjaya stated that "cooperative learning is more than just group learning or group work 

because in cooperative learning there is a cooperative structure of encouragement or tasks that 

allow open interactions and effective interdependent relationships among group members"5. 

From some of the definitions above, it can be concluded that cooperative learning is one 

of the effective learning methods by forming small groups to work together, interact, and exchange 

ideas in the learning process. In cooperative learning, learning is said to be incomplete if one of 

the friends in the group has not mastered the lesson material. 

The philosophy underlying cooperative learning in education is homo homini socius which 

emphasizes that humans are social creatures. The cooperative learning model is very different 

from direct teaching. In addition to cooperative learning models developed to achieve academic 

learning outcomes, cooperative learning models are also effective for developing students' social 

skills. 

Elements and Characteristics of Cooperative Learning Elements of Cooperative Learning. 

Positive Interdependence. Positive interdependence requires promotive interactions that allow 

fellow students to motivate each other to achieve optimal learning outcomes. Each student 

depends on other members because each student gets different material or different assignments, 

therefore students need each other because if there are students who cannot do the task, the group 

assignments cannot be completed. 

From the description above, the authors are interested in conducting research that wants 

to know: "The Effect of Cooperative Learning Methods on Reasoning Ability and Mastery of 

Mathematical Concepts. 

 

METHODS 

The research was conducted in class VII of SMP Negeri 1 Cikulu, Lebak Regency and 

SMP Negeri 2 Cileles. The research method used is the experimental method, this method was 

chosen because it is a research method whose purpose is to find the causal factors and effects, to 

control events in the interaction of variables, and to predict the results at a certain level of 

accuracy.6. 

The research sample was students of class VII B and VII C of SMP Negeri 1 Cikulur with 

20 students as the experimental class using the STAD method, and 20 students from class VII B 

and VII C, as the control class using the Jigsaw method. This data collection is to determine the 

reasoning ability and mastery of high and low mathematical concepts. Data Analysis Prerequisite 

Test, Data Normality Test. The data normality test was conducted to determine whether the data 

from each group was normally distributed or not. The normality test of the data will be tested with 

the Liliefors test. According to Nana Sudjana, the normality test of the data was carried out using 

the Liliefors (Lo) test with the following steps. It begins with determining the significance level, 

which is at a significance level of 5% (0.05). Then the Homogeneity Test of 4 Variants and the 

Homogeneity Test of the Covariance Variance Matrix 

 

 

 
5Sanjaya, Vienna. 2009. Educational Process Standard Oriented Learning Strategy. Jakarta: Kencana Prenada Media group. 
6Suharsimi Arikunto. 2008. Basics of Educational Evaluation. Jakarta: Earth Literacy Publisher. 



 
 
 

 
 EDUCATIO : Journal Of Education  
 Volume 6 , Number 1, May 2021  

ISSN : 2579-8383 (Print) ISSN : 2579-8405 (Online) 
73 

  

  

RESULT AND DISCUSSION 

The normality test of the data was carried out using the Kolmogorov-Smirnov test with a 

significance level of = 0.05. The summary of the results of the normality test is presented in the 

following table. 

 

Table 1. Calculation Results of Data Normality Test 

 One-Sample Kolmogorov-Smirnov Test 

  Y1A1 Y1A2 Y2A1 Y2A2 

N  

 

Normal Parameters 

 

 

mean 

40 

 

35.82 

40 

 

32.68 

40 

 

15.82 

40 

 

13.90 

Std. Deviation 2,086 2.505 1,430 1,614 

Most Extreme Absolute .158 .227 .149 .150 

Differences Positive  .112 .132 .118 .125 

negative  -158 -.227 -149 -.150 

Kolmogorov-Smirnov 

Z 

 
1.002 1.433 

.940 
.947 

asymp. Sig. (2-tailed)  .268 .033 .339 .331 

 

Test distribution is Normal 

The table above shows that all data groups tested for normality with the one-sample 

Kolmogorov-Smirnov test with SPSS obtained that the data group gave a significant value in the 

Asym row. Sig (2-tailed) were 0.268, 0.033, 0.339, and 0.331, respectively. 

From the value of sig. These all produce a sig value. > 0.05. Thus it was concluded that the 

four data groups in this study came from a normally distributed population. This shows that one 

of the prerequisites for the F test in the study has been fulfilled. 

1. Homogeneity Test of Covariance Variant Matrix 

a. Covariance Variance Matrix . Homogeneity 

Tests were carried out using Box's test of equality of covariate matrices. The test results are as 

follows. 

Table 2 

Box's Test of Equality of Covariance Matrices 

Box's 

F 

df1 

df2 

Sig. 

2.171 

.704 

3 

1.095E6 

.550 

 



 
 
 

 
 EDUCATIO : Journal Of Education  
 Volume 6 , Number 1, May 2021  

ISSN : 2579-8383 (Print) ISSN : 2579-8405 (Online) 
74 

  

  

 

To fulfill the manova assumption, we try to accept the null hypothesis if the p-value of Box's 

M test > 0.05. The test results obtained the value ofp-Value sig is 0.550 > 0.05. Then the null 

hypothesis is accepted, which means that the variance-covariance matrix between the learning 

method groups is homogeneous. 

b. Homogeneity of Variance 

Testing the homogeneity of variance using Levene's test as follows. 

 

 

Table 3 Levene's Test Equality of Error Variances 

 F df1 df2 Sig. 

Reasoning 

Ability 
3.006 1 78 .087 

Concept 

Mastery 
.001 1 78 .977 

a. Design:Intercept + MB 

The requirement that the data homogeneity of arithmetical significance value > significant 

value (0.05), then the null hypothesis (H0) is accepted according to the requirements. The results 

of the homogeneity test of 2 groups of learning mathematics for mathematical reasoning abilities 

obtained the value of sig. = 0.087 which means the value of sig. > 0.05. So it can be concluded 

that the variance of the mathematical reasoning data between the STAD and Jigsaw type learning 

method groups is homogeneous. 

Furthermore, the results of the homogeneity test of 2 groups of learning mathematics for 

mastery of mathematical concepts obtained the value of sig. = 0.977 which means the value of sig. 

> 0.05. So it can be concluded that the variance of the data for mastery of mathematical concepts 

between the STAD and Jigsaw learning method groups is homogeneous. 

2. Hypothesis test 

Table 4 

Multivariate Test 

Effect Value F 
Hypothesis 

df 

df 

error 
Sig. 

Party 

Eta 

Squared 

Intercept Pillai's Trace 

Wilk's 

Lambda 

Hotelling 

Trace 

Ray's Largest 

Root 

.996 

.004 

268,026 

268,026 

1.032E4a 

1.032E4a 

1.032E4a 

1.032E4a 

2,000 

2,000 

2,000 

2,000 

77,000 

77,000 

77,000 

77,000 

.000 

.000 

.000 

.000 

.996 

.996 

.996 

.996 

MB Pillai's Trace .320 

.680 

18.154a 

18.154a 

2,000 

2,000 

77,000 

77,000 

.000 

.000 

.320 

.320 



  
 

Yuli Choirul Ummah 
Dismantling Paradigm Book Ta'limul Muta'allim 

 
 

  

 
 EDUCATIO : Journal Of Education  
 Volume 6 , Number 1, May 2021  

ISSN : 2579-8383 (Print) ISSN : 2579-8405 (Online) 
75 

 
 

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Wilk's 

Lambda 

Hotelling 

Trace 

Ray's Largest 

Root 

.472 

.472 

18.154a 

18.154a 

2,000 

2,000 

77,000 

77,000 

.000 

.000 

.320 

.320 

a. Exact statistics 

b. Design:Intercept+MB 

 

Table 5 

Test of Between-Subjects Effect 

Source 
Dependent 

Variable 

Type III 

Sum of 

Squares 

df 
Mean 

Square 
F Sig. 

Party 

Eta 

Squared 

Corrected 

Model 

Reasoning 

Ability 

Concept Mastery 

204,800a 

74.113b 

1 

1 

204,800 

74.113 

36,710 

29,894 

.000 

.000 

.320 

.277 

Intercept  Reasoning 

Ability 

Concept Mastery 

93982.050 

17671,513 

1 

1 

93982.050 

17671,513 

1.685E4 

7.128E3 

.000 

.000 

.995 

.989 

MB Reasoning 

Ability 

Concept Mastery 

204,800 

74.113 

1 

1 

204,800 

74.113 

36,710 

29,894 

.000 

.000 

.320 

.277 

Error Reasoning 

Ability 

Concept Mastery 

435150 

193.375 

78 

78 

5.579 

2.479 

   

Total Reasoning 

Ability 

Concept Mastery 

94622,000 

17939,000 

80 

80 

    

Corrected 

Total 

Reasoning 

Ability 

Concept Mastery 

639,950 

267,488 

79 

79 

    

a. R Squared = .320 (AdjustedR Squared = .311) 

b. R Squared = .277 (AdjustedR Squared = .268) 

 

 

The Multivariate Test table explains the average comparison of students' reasoning abilities 

and mastery of mathematical concepts between the two cooperative learning methods. There are 

four statistical tests, namely Pillai's Trace, Wilk's Lambda, Hotelling's Trace, and Ray's largers 



  
 

Yuli Choirul Ummah 
Dismantling Paradigm Book Ta'limul Muta'allim 

 
 

  

 
 EDUCATIO : Journal Of Education  
 Volume 6 , Number 1, May 2021  

ISSN : 2579-8383 (Print) ISSN : 2579-8405 (Online) 
76 

 
 

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Root. These four tests are based on the eigenvalues where the formula for each statistical test is 

as follows. 

From the table above in the intercept label section, the value of Pillai's Trace is positive, which 

is 0.996. Increasing this value has a significant effect on cooperative learning methods or 

significant average differences between groups of data. The value of Wilk's Lambda ranges from 

0 to 1, if the value of Wilk's Lambda is close to 0 it means that there is a significant effect on the 

cooperative learning method or a mean difference between the data groups. On the other hand, 

the value of Wilk's Lambda is close to 1, which means that there is no significant effect on the 

cooperative learning method or there is no significant difference in average between groups of 

data. From the table above Wilk's Lambda value is 0.004 close to zero, 

The Hotelling's Trace value shows a positive value, which is 268, 026. The increasing 

Hotelling's Trace value is always greater than the Pillai' trace value, the Hotelling's Trace value 

above shows a significant influence on the learning method, but in some cases if the eign value is 

small then Hotelling's Trace and Pillai' tarce values will be close together. This shows an indication 

that there is no significant effect on the learning method. 

The value of Roy's Largest is positive, namely 268.026, the value of Roy's Largest is always 

less than or equal to the value of Hotelling's trace. This value indicates a significant influence on 

the cooperative learning method. 

In the learning method line, the significance figures were tested using Pillai's Trace, Will's 

Lambda, Hotelling's Trace, and Ray's largest Root procedures. The first four procedures show a 

significance number below 0.05 (ie 0.000, 0.000, 0.000, 0.000) then H0 is rejected, so it is 

concluded that there is an effect of cooperative learning methods on students' reasoning abilities 

and mastery of mathematical concepts. 

Levenu's test was used to test the homogeneity of variance univariately. The results of the 

homogeneity test of the two groups of cooperative learning methods for reasoning abilities 

obtained the value of sig. = 0.087 which means the value of sig. > 0.05. It can be concluded that 

the variance of the mathematical reasoning ability data between the STAD and Jigsaw cooperative 

method groups is homogeneous. Furthermore, the results of the homogeneity test of the two 

groups of cooperative learning methods for mastery of mathematical concepts obtained the value 

of sig. = 0.977 > 0.05. So it can be concluded that the variance of the data for mastery of 

mathematical concepts between the STAD and Jigsaw cooperative method groups is 

homogeneous. 

The Test of Between-Subject Effect table describes the univariate model testing. It can be 

seen that the p-value for the cooperative learning method category for the response to 

mathematical reasoning ability is 0.000 < 0.05, as well as the response to mastery of mathematical 

concepts is 0.000 < 0.05, which means that there is a significant difference between the average 

reasoning ability and mastery of concepts. mathematics between the two cooperative learning 

methods. 

 



  
 

Yuli Choirul Ummah 
Dismantling Paradigm Book Ta'limul Muta'allim 

 
 

  

 
 EDUCATIO : Journal Of Education  
 Volume 6 , Number 1, May 2021  

ISSN : 2579-8383 (Print) ISSN : 2579-8405 (Online) 
77 

 
 

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Discussion 

 The test results prove that in cooperative learning there is a positive interdependence 

between students. In cooperative learning students feel that they are working together to achieve 

one goal and are bound to one another. A student will not be successful unless all members of his 

group are also successful. Students will feel that they are part of a group that also contributes to 

the success of the group. then the increasing interaction between students. Cooperative learning 

increases the interaction between students. This, occurs in the event that one student will help 

other students to succeed as a member of the group. This mutual assistance will take place naturally 

because a person's failure in a group affects the group's success. To solve this problem, Students 

who need help will get it from their group of friends. The interaction that occurs in cooperative 

learning is in terms of exchanging ideas about the problem being studied together. 

 

CONCLUSION 

There is a significant effect of cooperative learning methods on reasoning abilities and mastery of 

mathematical concepts. This is evidenced by the value of Fo = 18,154 and Sig. = 0.000 < 0.05. In 

this case, the reasoning ability and mastery of mathematical concepts in the experimental group 

was higher than the control group. 

There is a significant effect of cooperative learning methods on mathematical reasoning 

abilities. This is evidenced by the test results contained in the Test of Between –Subject Effects 

table in the statistical test above, it is known that the value of F = 36,710, the p-value for the 

category of mathematical reasoning ability is 0.000 <0.05. Thus the null hypothesis is rejected or 

there is a significant difference between the mathematical reasoning ability of the group of students 

who were given the STAD type cooperative learning method and the mathematical reasoning 

ability of the group of students who were given the Jigsaw cooperative learning method. 

There is a significant effect of cooperative learning methods on the mastery of 

mathematical concepts. This is evidenced by the test results contained in the Test of Between –

Subject Effects table in the statistical test above, it is known that the F value = 29.894, the p-value 

for the category of mastery of mathematical concepts is 0.000 <0.05. Thus the null hypothesis is 

rejected or there is a significant difference between the mastery of mathematical concepts in the 

group of students who were given the STAD cooperative learning method and the mastery of 

mathematical concepts in the group of students who were given the Jigsaw cooperative learning 

method. 

 

REFERENCES 

Arikunto, Suharsimi. Educational Evaluation Basics. Jakarta: Earth Literacy Publisher. 2008. 

Isjoni. Cooperative Learning. Bandung: Alphabeta 2007 

Mulyasa, E. 2006. Education Unit Level Curriculum. Bandung: PT Pemuda Rosdakarya. 



  
 

Yuli Choirul Ummah 
Dismantling Paradigm Book Ta'limul Muta'allim 

 
 

  

 
 EDUCATIO : Journal Of Education  
 Volume 6 , Number 1, May 2021  

ISSN : 2579-8383 (Print) ISSN : 2579-8405 (Online) 
78 

 
 

zzzzzz  

  

Rochmadi. 2008. The Use of Inductive-Deductive Mindset in Constructivism Toxic Mathematics 

Learning. Paper at the National Seminar on Mathematics Education: Teacher 

Certification, at the Postgraduate Campus of UNNES Semarang, January 16, 2008 

Solihatin, E. 2007. Cooperative Learning: Analysis of Social Studies Learning Model. Jakarta: Earth 

Literacy. 

Sanjaya, Vienna. 2009. Educational Process Standard Oriented Learning Strategy. Jakarta: 

Kencana Prenada Media group. 

Sharan, Shlomo. 2012. The Handbook of Cooperative Learning. Yogyakarta: Family. 

Soedjadi, R. 2000. Tips for Mathematics Education in Indonesia. Jakarta: Director General of 

Education, Ministry of National Education. 

Suriasumantri, Jujun S. 2007. Philosophy of Science: A Popular Introduction. Jakarta: Sinar 

Harapan Library. 


