731
Chintya Novelia, Ali Asmar
META-ANALYSIS OF THE EFFECT OF THE APPLICATION OF THE
PROBLEM-BASED LEARNING MODEL ON THE MATHEMATICAL
PROBLEMSOLVING ABILITY OF STUDENTS IN MATHEMATICS
LEARNING
Chintya Novelia, Ali Asmar, Edwin Musdi, Armiati
Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Padang, Indonesia
Email: chintyanovelia2511@gmail.com
Abstract
Students' problemsolving abilities can be improved in one way, namely by choosing the right mathematics
learning model. One learning model that can be used is the problembased learning model. The aim of this
research is to re-analyze the influence of the problembased learning model on students' mathematical
problemsolving abilities by reviewing, summarizing data and analyzing several research results that have
been published on Google Scholar as many as 14 articles using statistical methods. The type of research
in this article is meta-analysis research. The research steps include data collection, coding, calculating
the increase in problem solving abilities and effect size, and drawing conclusions. Based on the research
results, the average effect size is 2.02 in the very large category. Based on the average effect size, it can
be concluded that the problembased learning model influences students' mathematical problemsolving
abilities.
Keywords: problem solving ability; meta analysis; problem based learning
INTRODUCTION
Mathematics is one branch of science that has an important role in the development of science
and technology. Mathematics is a compulsory subject for students from elementary school to university.
Success in mathematics will help learners take good decisions and prepare them to compete in
economics and technology (Siregar et al., 2020). The five basic standards of learning mathematics
include mathematical communication, mathematical reasoning, mathematical problem solving,
mathematical connections, and a positive attitude towards mathematics (Aini & Mukhlis, 2020).
Problem-solving skills are an important part of learning maths (Umrana et al., 2019). Even problem-
solving skills are considered important in math learning (Argarini, 2018).
The ability to solve problems is a step to find solutions to problems that arise in everyday life.
According to (Umrana et al., 2019). Problem solving is the process followed by students to solve a
problem they face until it is no longer a problem. According to Polya in Rusmana, (2020) states that
there are four stages of problemsolving steps, namely understanding the problem, planning the solution,
solving the problem and re-examining the resolution. One way to improve students' problem-solving
skills is to choose the appropriate mathematical learning model. One of the learning models that can be
used is the problem-based learning model.
Problem-based learning is an innovative learning model that teaches many important strategies
to meet the skills needs of the 21st century (Surur & Tartilla, 2019). Problem-based learning is a
problem-based learning model that can help students understand learning material, which in turn can
develop their thinking skills (Kodariyati & Astuti, 2016). Problem-based learning can train and develop
the ability of students to solve problems related to real problems in everyday life (Oktaviani et al.,
2018). The syntax of the problem-based learning model according to Arends in Oktaviani et al., (2018)
that is (1) Provide problem orientation to students, (2) organizing learners to research, (3) assist in
investigating both independently and in groups, (4) develop and subsequently present the work of
students, (5) analyze and evaluate the process in solving existing problems (Dutertre, 2015).
This study aims to quantitatively analyze the influence of problem-based learning models on the
ability to solve students' mathematical problems in mathematics learning.
Jurnal Sosial dan Teknologi (SOSTECH)
Volume 3, Number 9, September 2023
p-ISSN 2774-5147 ; e-ISSN 2774-5155
732
Chintya Novelia, Ali Asmar
Meta-Analysis of the Effect of the Application of the Problem-
Based Learning Model on the Mathematical Problemsolving
Ability of Students in Mathematics Learning
e-ISSN 2774-5155
p-ISSN
2774-5147
RESEARCH METHOD
This research is a type of quantitative research that uses data analysis techniques, especially meta-
analysis. Meta-analysis is a technique used to summarize the results of two or more studies with the
aim of combining, reviewing, and summarizing previous studies. In addition, using meta-analyses,
many different questions can be investigated based on data from previously published research findings.
According to Card in Utami, (2017) states that the meta-analysis is a synthesis of several studies that
focus on the results obtained in the study. According Saputri & Wardani, (2021) states that meta-
analysis is research conducted by reviewing, summarizing data, and analyzing many existing research
results using statistics. While according to Soetjipto, (1995) Meta-analysis is an attempt to summarize
various research findings quantitatively. One of the conditions needed to conduct a meta-analysis is the
examination of the results of similar studies. The population used in this study is 14 articles which are
educational journal articles and thesis research and dissertations in national journals published within
the last 10 years about the influence of problem-based learning models on students' problem-solving
abilities in mathematics learning. The research steps used in this article include:
Data collection
The first step in this research is to collect articles found on Google Scholar. Criteria used to
collect articles according to Saputri & Wardani, (2021) as follows:
1. The selected article is a published article
2. The selected articles are articles published in the last 10 years.
3. The selected article uses a problem-based learning model as an independent variable.
4. The selected article uses mathematical problem-solving capabilities as a dependent variable.
a. The samples used in the article range from elementary to tertiary level.
Based on these criteria, 14 relevant articles were selected to be analyzed.
Coding
Coding is an important requirement to facilitate data collection and analysis. Therefore, the meta-
analysis tool is carried out using coding tables (Boisandi & Darmawan, 2017). The variables used to
encode and produce the necessary information are the name of the researcher, year of study, title of
study, level of education, and research data. Each article is coded from A1 to A14 according to
predefined variables. The following examples of meta-analysis coding results are presented in Table 1:
Table 2. Meta-Analysis Coding Examples
No
Kode
Heading
Research
Name
Researchers
Year
Ladder
Education
Average
Pretes
Postest
1
A1
The effectiveness of the
Problem Based
Learning Model is seen
from the Mathematical
Problem Solving Ability
Nurma
Angkotasan
2014
SMA
70,28
82,95
2
A2
Improving Students'
Mathematical Problem
Solving Ability through
Problem-Based
Learning
Tina Sri
Sumartini
2016
SMK
44,03
71,81
3
A3
The Effect of Problem-
Based Learning on the
Mathematical Problem
Solving Ability of High
School Students
Ibnu Imam
Al Ayubi,
Erwanudin,
Martin
Bernard
2018
SMA
69,42
89,62
Calculation of the increase in problem-solving ability (N-gain) and effect size of each article
To determine the increase in problem-solving ability in this study, the N-gain test was used.
Meanwhile, to find the effect size of each item, Cohen's formula is used in (Ambarika & Wardani, 2021;
733
Chintya Novelia, Ali Asmar
Meta-Analysis of the Effect of the Application of the Problem-
Based Learning Model on the Mathematical Problemsolving
Ability of Students in Mathematics Learning
e-ISSN 2774-5155
p-ISSN
2774-5147
Saputri & Wardani, 2021) as follows.
𝐸𝑓𝑓𝑒𝑐𝑡 𝑠𝑖𝑧𝑒 =
𝑃𝑜𝑠𝑡𝑡𝑒𝑠𝑡 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑐𝑜𝑟𝑒 − 𝑃𝑟𝑒𝑡𝑒𝑠𝑡 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑐𝑜𝑟𝑒
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑡 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
Tabel 2. Kriteria Penilaian Effect size
Effect size
Interpretasi
0 < d < 0,2
Kecil
0,21 < d 0,50
Sedang
0,51 < d 1,00
Besar
d > 1,00
Sangat Besar
RESULT AND DISCUSSION
Based on the data collection steps carried out by searching for articles on Google Scholar, 14
articles will be analyzed. The following are the results of grouping articles based on education level,
independent variables and dependent variables.
Table 3. Grouping of Article Analysis Results Data
Types of analysis
Hasil analisis
Jumlah analisis
Education Level
SD/MI
SMP
SMA/SMK
Perguruan Tinggi
6
2
5
1
Variabel Terikat
Kemampuan pemecahan masalah matematis
14
Variabel Bebas
Model Problem Based Learning
14
Based on Table 3, it is known that there are 6 articles with research subjects at the elementary
level, 2 articles at the junior high school level, 5 articles at the high school / vocational level and 1
article at the university level. The bound variable included in each item is mathematical problem-
solving ability. While the free variable is the problem-based learning model.
Calculation of the increase in problem-solving ability (N-gain) and effect size of each article
Table 4. Analysis Results of Improved Problem Solving Ability Based on Gain Test
No
Kode Artikel
Rata-rata pretest
Rata-rata postest
Gain
Keterangan
1
A1
67,32
74,75
0.23
Low
2
A2
70,28
82,95
0.43
Intermediate
3
A3
69,43
81,50
0.39
Keep
4
A4
60,25
68,61
0.21
Low
5
A5
44,03
71,81
0.50
Intermediate
6
A6
69,42
89,62
0.66
Intermediate
7
A7
41,33
61,77
0.35
Intermediate
8
A8
9,24
42,91
0.37
Intermediate
9
A9
32,34
76,71
0.66
Intermediate
10
A10
49,78
75,66
0.52
Intermediate
11
A11
60,83
84,17
0.60
Intermediate
12
A12
44,04
74,67
0.55
Intermediate
13
A13
71,19
95,61
0.85
Higt
14
A14
11,01
84,12
0.82
Higt
Based on Table 4, it is known that there are 10 items of problem solving skill improvement
with medium category, 2 items with low category, and 2 items with high category.
734
Chintya Novelia, Ali Asmar
Meta-Analysis of the Effect of the Application of the Problem-
Based Learning Model on the Mathematical Problemsolving
Ability of Students in Mathematics Learning
e-ISSN 2774-5155
p-ISSN
2774-5147
Table 5. Effect Size Article
No
Kode Artikel
Effect Size
Keterangan
1
A1
0.58
Big
2
A2
0.98
Big
3
A3
0.94
Big
4
A4
0.65
Big
5
A5
2.16
Very big
6
A6
1.57
Very big
7
A7
1.59
Very big
8
A8
2.62
Very big
9
A9
3.45
Very big
10
A10
2.01
Very big
11
A11
1.81
Very big
12
A12
2.38
Very big
13
A13
1.90
Very big
14
A14
5.68
Very big
Rata-rata Effect Size
2,02
Very big
Based on Table 5, it is known that there are 4 articles with large category effect sizes and 10
articles with very large category effect sizes.
Tabel 6. Effect size Artkel Berdasarkan Jenjang Pendidikan
No
Jenjang Pendidikan
Jumlah artikel
Rata-rata Effect size
Keterangan
1
SD/MI
6
1.97
Sangat Besar
2
SMP
2
1.83
Sangat Besar
3
SMA/SMK
5
3.80
Sangat Besar
4
Perguruan Tinggi
1
1.90
Sangat Besar
From Table 6, it can be seen that the level of influence of the application of problem-based
learning models on problem-solving abilities at each level of education is in a very broad category. The
effect size for the elementary / MI level is 1.97, the junior high school level is 1.83, the high school /
vocational level is 3.80, and the higher education level is 1.90.
The results of the meta-analysis of the effect of problem-based learning on the ability to solve
mathematical problems in mathematics learning were seen in the improvement before and after the test,
most of which were in the moderate category. There are 10 items in the medium category, 2 items in
the low category, and 2 items in the high category. Problem solving skills increase because the learning
process follows a problem-based learning model, students understand the problem given faster because
right at the beginning of the learning activity, the teacher has provided the delivery material (Susilowati,
2020).
CONCUSSION
The problem-based learning model affects the ability of students to solve mathematical
problems, this is shown from the results of the effect size test. Based on effect size, there was
an increase in problem solving before and after treatment with the problem-based learning
model, with an average effect size of 2.02 at a very large level. Recommendations for future
research include the use of more articles and a more careful selection of articles used in meta-
analysis studies.
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Meta-Analysis of the Effect of the Application of the Problem-
Based Learning Model on the Mathematical Problemsolving
Ability of Students in Mathematics Learning
e-ISSN 2774-5155
p-ISSN
2774-5147
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