This study examined the effect of Problem-based Learning (PBL) on students' creative mathematical thinking in Indonesia during the last eight years using meta-analysis. Data were obtained from primary studies published in national journals, conference proceedings, and master thesis from 2012 to 2020. This study analyzed 19 effect sizes from 19 primary studies that fulfill the inclusion criteria. The effect size index used the Hedges'

Mathematical creative thinking is an essential prerequisite for academic achievement and success in the workplace (Bochniak,

Mathematics instructions can be improved by implementing more appropriate models (Freeman-Green et al.,

Over the years, there appears to be an increase in the implementation of PBL in education (Ceker & Ozdamli,

To meet this need, it is necessary to integrate convincing quantitative findings to provide useful information for education policy (Higgins & Katsipataki,

Preceding meta-analyses have evaluated the effectiveness of PBL in general (e.g., Mustaffa et al.,

This study examined the overall effect of PBL and attempted to analyze the causes of variation in outcomes by examining the relationship between study characteristics. These characteristics contribute to revealing important information about how PBL will be implemented in the future. The questions addressed in the study were: (1) does the use of the PBL produce a more significant effect size on students' creative mathematical thinking than conventional approaches? And (2) does the effect size of students' creative mathematical thinking on the implementation of PBL between study groups vary in terms of the study year, education level, research class, sample size, treatment duration, and publication source?

This study applied a meta-analysis. It is a set of quantitative techniques for combining evidence from several related studies (Cumming,

Firstly, empirical data is obtained from online databases, including ERIC (Education Resources Information Center), SAGE, and Springer. The three databases capture journal articles related to the research objectives. Furthermore, Semantic Scholar and Google Scholar databases are used to identifying journal articles, productions, and theses related to the research problems. The keywords used were "problem-based learning" and "creative thinking skills" to reach English articles. The keywords "

Secondly, determining inclusion criteria, namely the feasibility of the standards used in selecting primary studies. At this stage, we have considered suggestions by Rothstein and Hopewell (

1. The articles were published from 2012 to 2020

2. The research design used experimental and quasi-experimental with the control class as a comparison

3. The duration of the treatment is at least three weeks

4. The treatment group used PBL

5. The independent variable measured is creative thinking

6. It contains statistical information for calculating effect sizes, i.e., mean, standard deviation, and sample size.

Based on the criteria, nineteen articles were obtained. Information regarding the studies is presented in

The meta-analysis instrument was in the form of coding sheets (Tamur et al.,

No | Study Characteristics | Group | Frequency |
---|---|---|---|

1 | Study year | 2012-2013 | 2 |

2013-2014 | 1 | ||

2014-2015 | 4 | ||

2015-2016 | 2 | ||

2016-2017 | 2 | ||

2017-2018 | 4 | ||

2019-2020 | 4 | ||

2 | Education level | Primary Schools | 3 |

Secondary Schools | 9 | ||

High Schools | 3 | ||

Higher Education | 4 | ||

3 | Sample size | ≤30 | 5 |

≥31 | 14 | ||

4 | Treatment duration | 3-4 meetings | 3 |

>4 meetings | 16 | ||

5 | Publication source | Theses | 3 |

Proceeding | 2 | ||

Journal | 14 |

Bias risk was evaluated based on random sequence generation, disclosure, blinding, blinding the interveners, the blinding of results evaluators, incomplete data results, selective data reporting, and other factors (Schuch et al.,

No | Bias Conditions | Score |
---|---|---|

1 | Number of observed studies | 19.00000 |

2 | Number of missing studies that would bring p-value to > alpha | 971.00000 |

Based on

the degrees of freedom used in estimating _{within}_{g}=J^{2}xV_{d}_{d}^{2}

· it is weak if between 0 and 0.20;

· it is small if between 0.21 and 0.50;

· it is moderate if between 0.51 and 1.00; and

· it is large if higher than 1

If a statistical test at a predetermined level of probability (p <0.05) is reached, the null hypothesis is rejected, and the alternative hypothesis is accepted (Dunst & Hamby, _{b}

The calculation results regarding the overall effect size in each study with the help of CMA software are shown in

No | Author | Effect Size | Standard Error | Lower Limit | Upper Limit |
---|---|---|---|---|---|

1 | Khoiri ( |
1.75 | 0.28 | 1.20 | 2.31 |

2 | Nugroho, et al. ( |
0.94 | 0.25 | 0.46 | 1.43 |

3 | Azmi, et al. ( |
0.95 | 0.26 | 0.45 | 1.45 |

4 | Anwar ( |
0.75 | 0.26 | 0.25 | 1.26 |

5 | Katminingsih and Widodo ( |
0.95 | 0.22 | 0.53 | 1.37 |

6 | Kurniawati ( |
0.00 | 0.22 | -0.43 | 0.43 |

7 | Nurqolbiah ( |
0.24 | 0.23 | -0.21 | 0.68 |

8 | Rochani ( |
0.71 | 0.25 | 0.22 | 1.20 |

9 | Arhasy and Mulyani ( |
1.01 | 0.24 | 0.55 | 1.48 |

10 | Fahrudin ( |
0.71 | 0.29 | 0.15 | 1.27 |

11 | Septian and Rizkiandi ( |
1.75 | 0.27 | 1.21 | 2.28 |

12 | Astuti, et al. ( |
3.22 | 0.49 | 2.27 | 4.18 |

13 | Risnawati, et al. ( |
1.11 | 0.14 | 0.82 | 1.39 |

14 | Ahmad and Gunawan ( |
0.08 | 0.28 | -0.47 | 0.62 |

15 | Alifiani, at al. ( |
0.49 | 0.25 | 0.02 | 0.99 |

16 | Indriani, et al. ( |
0.24 | 0.26 | -0.27 | 0.75 |

17 | Masitoh and Prasetyawan ( |
0.19 | 0.23 | -0.25 | 0.63 |

18 | Masitoh ( |
0.92 | 0.29 | 0.36 | 1.49 |

19 | Sefrinal ( |
0.50 | 0.25 | 0.02 | 0.99 |

The information presented in

No | Model | n | Z | P |
_{b} |
Effect size | Standard error | 95% Confidence Interval | ||
---|---|---|---|---|---|---|---|---|---|---|

Lower limit | Upper limit | |||||||||

1 | Fixed effect | 19 | 14.001 | 0.000 | 95.617 | 81.175 | 0.777 | 0.056 | 0.669 | 0.886 |

2 | Random effects | 19 | 6.295 | 0.000 | 0.821 | 0.130 | 0.566 | 1.077 |

This finding is in line with the results of Susanti, Juandi, and Tamur (

Of the 19 studies, each had an average effect size. The characteristics of the studies were carried out including; year of study, education level, sample size, duration of the experiment and research publication. A summary of the analysis results based on the research characteristics is presented in

Firstly, the analysis of research characteristics in _{b}_{tabel}

Study Characteristics | Group | Number Studies | Hedge’s g | Test of null (2 Tail) | Heterogeneity | |||
---|---|---|---|---|---|---|---|---|

Z-value | P | Between Classes Effect (Qb) | Df(Q) | P | ||||

Study Year | 2012-2013 | 2 | 1.294 | 6.943 | 0.000 | 55.683 | 6 | 0.000 |

2013-2014 | 1 | 0.949 | 3.722 | 0.000 | ||||

2014-2015 | 4 | 0.871 | 7.280 | 0.000 | ||||

2015-2016 | 2 | 0.115 | 0.723 | 0.470 | ||||

2016-2017 | 2 | 1.255 | 6.333 | 0.000 | ||||

2017-2018 | 4 | 1.064 | 9.574 | 0.000 | ||||

2019-2020 | 4 | 0.261 | 2.090 | 0.037 | ||||

Education Level | Primary Schools | 3 | 0.929 | 5.919 | 0.000 | 6.806 | 3 | 0.078 |

Secondary Schools | 9 | 0.851 | 11.367 | 0.000 | ||||

High Schools | 3 | 0.475 | 3.384 | 0.001 | ||||

Higher Education | 4 | 0.705 | 5.234 | 0.000 | ||||

Sample Size | ≤30 | 5 | 0.675 | 5.076 | 0.000 | 0.711 | 1 | 0.399 |

≥31 | 14 | 0.799 | 13.086 | 0.000 | ||||

Treatment Duration | 3-4 meetings | 3 | 1.116 | 7.293 | 0.000 | 5.644 | 1 | 0.018 |

>4 meetings | 16 | 0.726 | 12.186 | 0.000 | ||||

Publication Sources | Thesis | 3 | 1.218 | 5.782 | 0.000 | 13.812 | 3 | 0.037 |

Proceedings | 2 | 0.889 | 6.949 | 0.000 | ||||

Journal | 14 | 0.765 | 11.224 | 0.000 |

Secondly, based on the level of education, it consists of four groups: higher education, high schools, secondary schools, and primary schools, each of which has an effect size of 0.705; 0.475; 0.851; 0.929 (moderate), respectively. The result of _{b}_{tabel}

Thirdly, based on the sample size, it consisted of two groups, ≤ 30 and ≥31, with effect sizes of 0.675 and 0.799 (moderate), respectively. Based on the results, _{b}_{tabel}

Fourthly, based on the duration of the treatment consisted of two groups, the treatment duration of 3-4 meetings had an effect size of 1,116 (large), and more than four meetings had an effect size of 0.726 (moderate). From the result, _{b}_{tabel}

Fifthly, based on the publication sources, this study concluded that the results found in the thesis document (effect size = 1,218) were greater than those in the proceeding articles (effect size = 0.889) and the journal articles (effect size = 0.765). This variable is analyzed to check whether selective reporting factors give rise to the effect of publication bias. The heterogeneity test results showed that the combined effect sizes of the three study groups were different. However, they showed no signs of bias. The reasons why the combined effect size of the thesis is much larger than that of proceedings or journals are still unclear.

The current research shows that PBL has a positive impact on students' creative thinking in mathematics. This study's effect size is consistent with previous studies' findings (e.g., Susanti et al.,

This meta-analysis aimed to analyze the effectiveness of using PBL on students’ creative thinking in mathematics. The overall effect size was 0.821, with a standard error of 0.130 and 95% degrees of freedom. This shows that PBL has a moderate effect on students' creative mathematical thinking. The results of the studies’ analysis show that the application of PBL to the students' creative thinking relates to the study year, research class, treatment duration, and publication sources. It was found that the PBL is more effective in conditions of treatment duration of fewer than four meetings. There is a tendency that the implementation of PBL for the first time has a significant impact on students' creative thinking. Besides, the results of the analysis also show variations in the effect sizes according to the published sources. Although this does not indicate a publication bias, the hypothesis that the results of a significant study are likely to be published needs to be tested again. For this reason, more studies need to be carried out in this area to provide a complete picture to mathematics educators about the effectiveness of PBL in mathematics classrooms.

The authors thank M. Borenstein and the CMA team from Englewood, the USA, for all their technical assistance and contributions to the research project.

^{st}century learning.

^{st}International Education Postgraduate Seminar, Johor Bahru-Malaysia. Retrieved from http://eprints.utm.my/id/eprint/60893/