The Effect of Realistic Mathematics Education in Enhancing Indonesian Students' Mathematical Reasoning Ability: A Meta-Analysis

ABSTRACT

The next similar research is the research conducted by Juandi dkk. (2022) who examined a meta-analysis of the last two decades of realistic mathematics education approaches. This study examined 54 effect sizes from 38 individual studies conducted in the last two decades with the databases ERIC, Sage Publications, Springer Publications, Semantic Scholars, and Google scholars. The results of this study are the overall effect size of 0.97 using the estimated random effects model. This shows that the application of RME has a significant positive effect on students' mathematical abilities. The moderator variables analyzed in this study were sample size, treatment duration, learning mix, and education level. The difference between this research and the study that the author conducted is that this study is devoted to discussing mathematical abilities in terms of reasoning and solving mathematical problems of students, the range of years of study increases, there is an increase in the number of articles, in previous studies there was no moderator variable for technological assistance status, so the authors added a variable moderator in the form of technological assistance status.
This research will give detailed information on the impact of RME on student MRA in Indonesia. This research attempts to estimate and examine the effect of RME implementation in enhancing the MRA of Indonesian students, as well as to explore the moderating factors that influence students' heterogeneous MRA. As a result, it might be considered for educators to carry out the most effective learning approach to teach and strengthen students' ability to think.

B. METHODS
The research methods used in this study was meta-analysis. This study used a metaanalysis to synthesize several relevant primary studies utilizing quantitative methods. There were various advantages to doing a meta-analysis. More openness, identifying and eliminating bias, better-estimating population characteristics, analyzing results in a variety of fields, presenting clear proof of substantial rejection, and offering a methodical approach throughout the synthesis procedure are among the benefits (Litte et al., 2008;Shelby & Vaske, 2008). The population in this study were studies in the form of national and international journal proceedings and journal articles regarding the use of the RME approach to students' mathematical reasoning and problem solving abilities from 2010-2022. The sample taken is a study of the RME approach to reasoning and problem solving abilities with inclusion criteria. The instrument in this study used a coding data sheet which had been validated by two metaanalyst experts to obtain the final schematic on the coding sheet. Bernard et al. (2014); Borenstein (2009);Cooper (2017) indicated in their research that the There were several steps to the meta-analysis investigation, as seen in the flowchart in Figure 1. As a result, these steps were employed in this investigation. In this section, the researchers discuss several phases, considering eligibility criteria and strategies for searching the literature, extraction of data, selection of study, and analysis of statistic. The formulation of the problem in this study is whether the use of the Realistic Mathematics Education Approach has a positive effect on the submission of students' mathematical reasoning abilities and problem solving abilities in terms of the studies analyzed and whether there are differences in the effect size of the application of the Realistic Mathematics Education Approach to marketing reasoning abilities and solving abilities students' mathematical problems in terms of educational level, sample size and based on technology or nontechnology. For the interpretation and repotting stages can be seen in the results and discussion section

Inclusion Criteria
Preliminary research on the influence of RME adoption on improving MRA was still broad and universal. To narrow the scope of this meta-analysis, the inclusion criteria were defined using the PICOS technique (Population, Interventions, Comparator, Outcomes, and Study Design) (Liberati, et al., 2009), specifically: a. The primary study's population consisted of students in Indonesia. b. The preliminary study's intervention was the application of RME. c. In the primary research, the intervention's comparator applied traditional learning. d. MRA was the prior study's result. e. The main research used a quasi-experimental study design using a causal-comparative approach. f. The preliminary study presented statistical data in the intervention and comparison groups, class capacity, t-value, p-value, mean, standard deviation are some examples. g. The preliminary study was national and international publications between 2010 and 2022.
The primary studies that did not meet the inclusion criteria in the study selection approach were deleted.

Extracting Data
Authors, statistical information, sampling method, research region, year of publication, and type of publication were retrieved from study papers that matched the criteria of inclusion and went as a result of study selection step. The data extraction technique includes two coding specialists in meta-analysis to guarantee that the information or data obtained from the process of extraction was legitimate and reliable (Nugraha & Suparman, 2021). Thus, reliable and credible data increased the likelihood that this meta-analysis would produce outstanding findings.

Statistical Analysis
Because the class capacitys in the intervention group (RME) in this meta-analysis were relatively modest, effect sizes were computed using Hedge's g equation (Borenstein, 2009;Harwell, 2020). The collected effect sizes were interpreted using Thalheimer & Cook (2002) classification. The following shows the categorization of effect sizes, as shown in Table 1. Every publishing of study findings was tainted by publication bias. As a result, publication bias and sensitivity analyses were necessary to guarantee that the statistical data contained in each main study was reliable (Furuya-Kanamori & Doi, 2020;Bernard et al., 2014). In this meta-analysis research, funnel plots were employed, and fill and trim tests (Harwell, 2020). Furthermore, the evidence on effect size stability and normality were tested using analysis of sensitivity in the CMA software's "One study removed" option (Bernard et al., 2014).
Meta-analysis research included two impact models: fixed effect models and random effect models (Borenstein, 2009;Cheung, 2015). This study uses a random effect estimation model, this is due to variations in the effect size and moderator variables to be analyzed (Haidich, 2010;Paloloang et al., 2020). The discovery of heterogeneous effect size data suggested that a study characteristics analysis was necessary to investigate the variables most likely to cause heterogeneity in effect size data (Borenstein, 2009;Siddiq & Scherer, 2019). In addition, in the null hypothesis study, the p-value of Z statistics was utilized to explain the substantial influence of RME deployment on improving Indonesian students' MRA.

C. RESULT AND DISCUSSION
The investigation's search yielded 213 abstracts from Semantic Scholar, Google Scholar, Education Resources Information Center (ERIC), and Directory Open Access Journal databases (DOAJ). 213 main study titles were discovered, including 147 from the Google scholar database, 49 from the Semantic scholar database, eight from the DOAJ database, and nine from the ERIC database. Description of the primary study search and selection results visualization is presented in Figure 2.

Extracting Data Results
The findings of the twenty-five primary studies that met the inclusion criteria as well as the study selection would be obtained. The following shows the findings of data extraction from twenty five preliminary studies, as shown in Figure 2.
Studies included in the meta-analysis (n=25) Full text article exluded (n=11), did not provide all statistical data (n=6), and control class not conventional learning (n=5) Full text article assessed for eligibility (n=36) Records exluded based on abstract and study design not quasi-experimental (n=134) Records after duplicates removed (n=170) Record identified through database searching (n=213)

Analysis of Publication Bias and Sensitivity
The following is the Hedge Standard Error Funnel Plot, as shown in Figure 3. The funnel plot graphic illustrates the distribution data of effect size from the primary studies in this meta-twenty-five analysis. Figure 3 depicts the data on effect size distribution from the twenty-five prior studies included in this investigation. The fill and trim test findings in Table 3 reveal that no impact size data in this meta-analysis research should be added or cut. This conclusion interprets significant evidence from the twenty-five main studies of the  Table 3. As a result, examination of multiple publication bias offered significant indication that the data on effect size from the twenty-five meta-analysis comprised primary studies were free of publication bias. Outliers can significantly contribute to the distortion of averages and variation in a collection of effect sizes. As a result, A sensitivity analysis might be used to discover factors that may produce a grouping of aberrant effect sizes (Bernard et al., 2014). The total effect incorporated in the model of random effects was g = 1.064; 95% CI = [0.773;1.354]; n = 25; SE = 0.148, as shown in Table 4. The greatest mean produced by utilizing the tool "One study removed" in CMA software with the random effect model was g = 01.354; n = 25; SE = 0,148, while the lowest average was g = 0,774; n = 25; SE = 0,148. These findings imply that the effect size collection is highly robust and appropriate and that it is unaffected by an unusual combination of effect size and class capacity.

Each Primary Study's Overall Effect Size
The following shows the total effect of RME adoption in enhancing each study's MRA of Indonesian students, as shown in Table 4. According to Table 4, the range of impact sizes of RME implementation in improving MRA of Indonesian students was between -0,391 and 2,708. According to the effect size categorization, there were two studies with insignificant effect sizes, six studies with moderate effect sizes, eight studies with high effect sizes, four studies having extremely high effect sizes, and five research with ideal effect sizes. A null hypothesis study was performed to examine if the deployment of RME significantly improves the MRA of Indonesian students. The following shows the findings of the null hypothesis test, as shown in Table 5. According to Table 5 contains an analysis of the null hypothesis test, the application of RME considerably improved the Indonesian students' MRA throughout the twenty-five main studies examined. The twenty-five prior studies' effect size was 1,064, indicating a large impact size. It suggests that the RME application has a pretty favorable influence on improving the MRA of Indonesian students. This finding was in line with meta-analysis performed research by Tamur et al. (2020), which included from 72 research published in national and international publications, 95 effect sizes were calculated or sessions between 2010 and 2019.
The findings of this investigation are as follows: According to Thalheimer & Cook (2002), the total size of the effect is 1.104, which is classed as extremely high. This demonstrates that using RME substantially impacts students' mathematical ability more than the traditional technique. Similarly, Juandi et al. (2022) evaluated 54 impact sizes from 38 separate research completed over the last two decades, including 6140 participants, and discovered that currently uses RME had a considerable significant effect on students' mathematical ability.
Some academics conceptually endorsed the influence of RME deployment on improving students' MRA in Indonesia. Mathematics starts with real-world problems, and formal mathematics is formed by mathematizing real-world problems (Gravemeijer & Terwel, 2000;Laurens et al., 2018;Nasution & Dur, 2017). Teaching mathematics must be closely related to reality and experience (Heuvel-panhuizen, 2003); the knowledge of teaching mathematics must be enjoyable and beneficial for students; thus, connections between reality and math must be made (Heuvel-panhuizen, 2003;Turgut, 2021;Fendrik, 2021).
The usage of models aimed at concrete models that progress to abstract models allows pupils to improve mathematical reasoning skills (Zaini & Marsigit, 2014). The average calculation of the twenty-five research examined reveals that the utilization of the RME approach significantly impacts students' mathematical reasoning ability. This is due to the combination of the RME approach's phases with measures of students' mathematical thinking (Fauziyah et al., 2016).
The RME technique can enhance intrinsic motivation, increase perseverance, and help students apply mathematical reasoning skills to the issues they confront (Anita Rahmatunisa, 2020;Ariati & Juandi, 2022a, 2022bTamur et al., 2020). The comparatively large effect size of RME implementation in improving the Indonesian students' MRA gives strong evidence that RME may be employed as effective learning in addressing students' poor MRA in studying mathematics. As a result, Indonesian mathematics instructors, particularly mathematics teachers, can use RME as among the most acceptable methods to enhance students' MRA.

The Analysis of the Study Characteristics
The study's variable features was the element responsible for the heterogeneous MRA of Indonesian students due to RME adoption. As a result, it was critical to investigate these aspects. The following shows the calculation results from the study characteristics analysis, as shown in Table 6. This meta-analysis examined three study characteristics: education level, class capacity, and technology assistance. Table 6 reveals that the p-value of Q statistics was more than 0.05 for all research characteristics. This suggests that the features of education level, class capacity, and technical assistance have no significant influence on the diverse effect size of RME implementation in improving the MRA of Indonesian students. This conclusion is comparable to that of (S. Turgut, 2021), who discovered that RME-based instruction did not demonstrate a significant difference in class capacity. Another meta-analysis investigation indicated a substantial difference between the two groups (Juandi et al., 2022;Turgut, 2021). The amount of primary studies included in the meta-analysis process was what distinguished this study from the previous one (Nugraha & Suparman, 2021).
This meta-analysis study classified education levels into three categories based on their characteristics: elementary, junior high, and senior high schools. The p-value of the three education level groups' Z statistics was less than 0.05. It reveals that RME application greatly improves the MRA of elementary, junior high, and senior high school students. Descriptively, primary school had a more significant impact size than others. Adopting the Realistic Mathematics Education method in elementary school is extremely helpful in enhancing mathematical thinking ability. This is consistent with earlier research that shows the Realistic Mathematics Education method is particularly effective in improving students' mathematical reasoning ability at the primary school level (Shoffa, 2022).
This meta-analysis study was divided into two groups depending on class capacity: less than or equal to 32 participants and more than 32 participants. Table 8 shows that the Z statistics p-value for the two class capacity groups was less than 0.05 for the null hypothesis test. It is interpreted that the use of RME considerably improves the MRA of Indonesian students, regardless of whether the class capacity is less than or equal to 32 participants or greater than 32 participants.
Furthermore, the effect of RME implementation on Indonesian students' MRA with a class capacity of less than or equal to 32 participants is smaller than the effect of performance on Indonesian students' MRA with a class capacity greater than 32 participants. This finding is reinforced by G. İ. Turgut (2022), who found that RME implementation with a class capacity of less than or equal to 32 students has a lower effect than RME implementation with a class capacity greater than 31 students. As a result, this meta-analysis study advises Indonesian mathematics instructors that using RME to improve students' MRA might be used in courses with small class capacity.
This meta-analysis research separated it into two categories based on technology-assisted RME and technology-assisted RME. The p-value of Z statistics for two technology-assisted was less than 0.05 for each group. This suggests that using RME improves the MRA of Indonesian students significantly. Furthermore, this meta-analysis study discovered that technologyassisted RME greatly influenced students' mathematical thinking ability. As a result, these data demonstrate that using technology in mathematics instruction greatly benefits instructors in enhancing students' mathematical reasoning abilities.

D. CONCLUSION AND SUGGESTIONS
The method of summarizing, estimating, and evaluating twenty-five primary research utilizing a meta-analysis study reveals indicates the use of RME has a significant influence on enhancing the MRA of Indonesian students. As a consequence of this meta-analysis study, Indonesian mathematics teachers should consider RME as one of the best approaches to improve students' MRA while applying mathematics teaching. The features of educational level, class capacity, and technological assistance had no significant influence on the varied effect size of RME implementation in improving students' MRA. However, the descriptive assessment of the research features This meta-analysis research indicates to Indonesian mathematics teachers that using RME to improve students' MRA should be limited to classrooms with less than 32 pupils, in primary schools and technologically assisted.