International Journal of Interactive Mobile Technologies (iJIM) – eISSN: 1865-7923 – Vol. 15, No. 02, 2021 Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: A Meta- Analysis Study https://doi.org/10.3991/ijim.v15i02.18853 Dadang Juandi (), Yaya S. Kusumah Universitas Pendidikan Indonesia, Bandung, Indonesia dadang.juandi@upi.edu Maximus Tamur Universitas Katolik Indonesia Santu Paulus, Ruteng, Indonesia Krisna S. Perbowo University of Warwick, Warwick, United Kingdom Muhammad Daut Siagian Universitas Islam Sumatera Utara, Medan, Indonesia Rini Sulastri Universitas Serambi Mekkah, Aceh, Indonesia Habibi R. P. Negara Universitas Islam Negeri Mataram, Mataram, Indonesia Abstract—Hundreds of studies on Dynamic Geometry Software (DGS) in- fluence on mathematics learning with mixed results have been found in the lit- erature. Correspondingly, this meta-analysis study was conducted to assess the overall impact of DGS and analyze the characteristics of the identified studies to help educators decide under what conditions the use of DGS would achieve a higher level of effectiveness. This meta-analysis study investigated 57 effect sizes drawn from 50 journal articles and international proceedings between 2010 and 2020, using the Comprehensive Meta-Analysis (CMA) program as a calculation tool. Meanwhile, the Hedges coefficient is used to calculate the ef- fect size at the 95% confidence level. Based on a random-effect model with a standard error of 0.09, the analysis found an overall effect size of 1.07. This means that learning using DGS has a relatively high positive effect on math skills. Analysis of the study’s characteristics revealed that the DGS used was more effective by considering sample size, student-computer ratio, and educa- tion level. These facts can help educators use DGS in the future. Finally, the study’s implications and limitations are discussed, providing crucial infor- mation for further meta-analysis studies on DGS’s impact. Keywords—Dynamic Geometry Software, Meta-analysis, Mathematical abil- ity, Study Characteristics 18 http://www.i-jim.org https://doi.org/10.3991/ijim.v15i02.18853 https://doi.org/10.3991/ijim.v15i02.18853 mailto:dadang.juandi@upi.edu Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... 1 Introduction The advancement in computer technology has led to the application of software development in learning [1]-[3]. This further motivates teachers to take steps to inte- grate computers into the educational environment [4], [5], in order to improve the effectiveness and quality of the education system [6]-[8]. This development also pro- vides additional training and opportunities for students to explore their problem- solving attributes by seeking alternative solutions due to the unlimited computer use capabilities in the learning [9]-[11]. The use of computers has quickly attracted the interest of teachers and researchers in teaching mathematics [12]-[16] and one of the most widely applied software is Dynamic Geometry Software (DGS). This software allows users to make geometric figures and measure several variables from them to determine their properties, drag numbers through the screen, produce geometric constructions, hypotheses, and test them to make generalizations [17], [18]. Several studies have, however, been con- ducted to determine the effectiveness of DGS in mathematics classes [19]-[26]. Some studies have been conducted to examine DGS’s effectiveness on students’ mathematical abilities at various levels of education in Indonesia with several incon- sistent results. For example, [10]- [31] showed the use of DGS was more effective in improving students’ mathematical abilities than conventional methods of learning while [32]-[35] found that it was not better. Currently, there has not been a compre- hensive evaluation of the usefulness of DGS on students’ mathematical abilities have not been explored much. Meanwhile, educators and stakeholders need accurate infor- mation to determine the appropriate conditions for using DGS to achieve higher effec- tiveness levels. It is possible to fill this gap by undertaking a study that combines several quantita- tive findings to provide useful information for practice or policy [36], [37]. This method has been analyzed to consider its implications [38], and up to 2020, no re- search was found to have combined the results obtained in other studies to draw an objective conclusion. However, reviewing the literature in several studies allows for variation in results but also provides subjective conclusions [39], [40]. Meta-analysis is an objective method for reviewing the literature because of the use of its effect size as the unit of analysis [41]-[43]. Moreover, the effect sizes from each study would be combined to obtain an overall effect size [43], [44]. This technique eliminates the subjective interpretation of several empirical reports on the same topic [45], [46]. Finally, statistical procedures were used to determine the differences in DGS effectiveness based on study characteristics. Our previous meta-analysis research evaluated the effectiveness of constructivism- based mathematics learning [44] and mathematics software-based mathematics learn- ing [37]. We found that study characteristics such as study class and sample size in- fluenced the effect sizes of the two models on students’ mathematical abilities. How- ever, study characteristics such as the ratio between students and computers used have not been investigated. Even though several meta-analyses including [47]-[54] has been focused on computer effectiveness in general, only one study [55] focused ex- clusively on the effectiveness of DGS on students’ mathematical achievement. How- iJIM ‒ Vol. 15, No. 02, 2021 19 Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... ever, it has not included the ratio between students and computers used as characteris- tics of the analyzed studies. This study intends to complement previous research with the aim of (1) assessing the impact of using DGS on students’ overall mathematical abilities and (2) determin- ing differences in effectiveness based on research characteristics. These are necessary to help educators decide the most suitable conditions to use the software in improving students’ mathematical abilities. These goals were achieved by analyzing primary studies conducted on DGS effectiveness on students’ mathematical abilities using meta-analysis as a research tool with the following questions being the center of fo- cus: • Does the use of DGS in mathematics learning produce a large effect size on math- ematical abilities than conventional approaches? • Are there differences in effectiveness between DGS applied based on the following research years: (a) 2010-2012, (b) 2013-2015, (c) 2016-2018, and (d) 2019-2020? • Are there differences in effectiveness between the DGS implemented at the follow- ing educational levels: (a) Junior High Schools, (b) High and Vocational Schools, and (c) higher institutions? • Are there differences in effectiveness between DGS applied based on the following sample sizes: (a) less or equal to 30, and (b) more than 30? • Are there differences in effectiveness between the following types of DGS: (a) GeoGebra, (b) Cabri, (c) Sketchpad, and (d) Wingeom? • Are there differences in effectiveness between DGS applied based on students’ ratio to computers in the following settings: (a) individuals and (b) Groups? 2 Methodology 2.1 Research design This study was conducted to statistically evaluate and interpret the findings of pri- mary studies that have been conducted on the effect of DGS in mathematics learning on students’ mathematical abilities in Indonesia. This involves using a meta-analysis method with statistical analysis of quantitative data from individual studies [41], [42]. The overall effect size is determined to measure the effect of using DGS on students’ mathematical abilities. Effect sizes have many advantages over using only tests of statistical significance. [56]. The steps involved in the meta-analysis include identify- ing the problem, searching for related literature, coding the studies according to cer- tain criteria, conducting statistical analysis, and interpretations [38], [57]-[60]. In this research, this stage was also conducted. 2.2 Study search Empirical data is traced from an electronic database that includes the Educational Resource Information Center (ERIC), Springer Publishing, SAGE publishing, and 20 http://www.i-jim.org Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... google scholar. The keywords used include “dynamic geometry software, Cabri, Ge- oGebra, Geo sketchpad, and mathematical abilities.” Furthermore, Google Scholar and Portal Garuda were used to assess national journal articles using “dynamic geom- etry software, Cabri, GeoGebra, Geo sketchpad, and kemampuan matematis” as key- words. The results showed 129 studies had examined the effectiveness of DGS in learning mathematics in Indonesia between 2010 and 2020. 2.3 Coding process and inclusion criteria The information derived from each study was coded using a coding sheet, an in- strument used in meta-analysis to collect statistical information needed to transform effect sizes and obtain study characteristics from each identified primary study. The coding form was developed to maintain the analyzed studies’ reliability, and this re- quired filling of the coding form separately by two coders who were doctoral students with prior special training in meta-analysis. This coding considers the sample’s eligi- bility requirements under study, i.e., the literature studied is selected from experi- mental studies on the impact of DGS in Indonesia over the last decade (2010-2020). Moreover, samples with no means, standard deviation, and sample size statistics were excluded. This stage provides a total of 50 research articles that meet the eligibility for analysis, and due to the use of more than one experimental or control group in several studies, 57 effect sizes are analyzed. The formula for Cohen’s Cappa, denoted by Cohen κ (7), is a powerful statistic to test inter-coder reliability [61]. The formula is: 𝜅 = Pr(𝑎) − Pr⁡(𝑒) 1 − Pr⁡(𝑒) Where Pr (a) represents an actually observed agreement, and Pr (e) represents a co- incidence agreement. A deal level of 0.85 or greater is pre-determined to be consid- ered high. An agreement rate of 0.92 was obtained for this study. Thus, this meta- analysis is reliable. The studies included in the analysis process are presented in Ap- pendix 1. 2.4 Statistical analysis The statistical analysis steps in this study are based on the explanation of Boren- stein et al. (2009), namely: a) Calculating the effect size of each primary study b) Conducting heterogeneity tests and selecting the estimation model c) Examining publication bias d) Calculate the p-value to test the research hypothesis Further analysis, namely answering the second to sixth questions, has been carried out because the effect size estimation uses a random-effect model [61]. Software that helps data analysis is the Comprehensive Meta-Analysis (CMA) series 3. Cohen’s equation is a good estimate for the population but is biased towards studies that iJIM ‒ Vol. 15, No. 02, 2021 21 Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... contain small samples [62]. Therefore, the Hedges equation g is applied to avoid this bias while the effect size is interpreted using the classification developed by [63], which is presented in Table 1 below: Table 1. Cohen’s effect size classification Effect Size (ES) Interpretation 0,00 ≤ ES < 0,20 Ignored 0,20 ≤ ES < 0,50 Small 0,50 ≤ ES < 0,80 Moderate 0,80 ≤ ES < 1,30 Large 1,30 ≤ ES Very Large The CMA program provides an effect size for each study and combined effect size for each group of study characteristics as well as homogeneity between groups known as the Qb value (Qbetwen), resulting in statistically heterogeneous effect sizes Qb> χ2.95; p <0.05, the effect size homogeneity hypothesis is rejected [64]. This means that the study characteristic groups’ effect sizes do not measure the same population parameters [38] or that there is a statistically significant difference in the average effect size for each study characteristics group [47]. 3 Results 3.1 Research results regarding the first question The first objective of this analysis was to assess the effect of the use of DGS on students’ overall mathematical abilities. Therefore, on the basis of CMA-assisted calculations, the effect size and confidence interval limits were obtained and provided in Table 2. Table 2. Study effect sizes, confidence intervals, and standard errors Author Effect Size Confidence Interval Standard error Lower limit Upper limit Abduh & Sutarto, 2012 0.83 0.33 1.34 0.25 Hendriana, et al. 2019 1.23 0.74 1.75 0.25 Ramadani, et al. 2016 0.44 -0.01 0.90 0.22 Risnawati, 2012 1.17 0.59 1.79 0.30 Sari, 2013 0.13 -0.48 0.74 0.30 Nurhayati, 2013 1.75 1.18 2.38 0.30 Hartatiana, et al. 2017 0.70 0.36 1.04 0.17 Hartatiana, et al. a 2017 0.99 0.52 1.48 0.24 Hartatiana, et al. b 2017 0.91 0.41 1.42 0.25 Hikmah, et al. 2019 0.42 -0.06 0.90 0.24 Saumi & Amalia, 2017 1.76 1.06 2.53 0.36 Subroto, 2011 4.71 3.69 5.87 0.54 Syamsuduha, 2011 0.91 0.39 1.45 0.26 22 http://www.i-jim.org Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... Nuriadin a, 2015 2.05 1.40 2.77 0.34 Nuriadin b, 2015 0.68 0.12 1.25 0.28 Priyanto, et al. a 2018 0.50 0.01 1.00 0.25 Priyanto et al. b 2018 0.29 -0.20 0.78 0.24 Lexbin & Natalia, 2011 0.59 0.10 1.10 0.25 Aisyah, 2015 1.27 0.72 1.87 0.28 Anggroratri a, 2014 0.32 -0.27 0.93 0.30 Anggroratri b, 2014 0.16 -0.45 0.76 0.30 Annajmi a, 2016 2.10 1.58 2.67 0.27 Annajmi b, 2016 1.02 0.57 1.50 0.23 Atikasari, et al. 2013 0.97 0.48 1.48 0.25 Senjayawati, et al. 2018 1.08 0.56 1.62 0.26 Erana, et al. 2018 3.09 2.40 3.86 0.36 Farihah, 2015 1.32 0.79 1.88 0.27 Fitra & Sitorusn, 2019 0.97 0.38 1.58 0.30 Fitra & Syahputra, 2018 0.79 0.27 1.32 0.26 Habinuddin, 2018 0.63 0.25 1.03 0.19 Haris & Rahma, 2018 1.05 0.56 1.55 0.25 Jelatu et al, 2018 0.73 0.01 1.50 0.36 Khotimah, 2018 0.79 0.35 1.25 0.22 Priyono & Hermanto, 2015 0.10 -0.36 0.56 0.23 Ramadhani, 2017 0.48 0.03 0.95 0.23 Rosyid, 2018 2.99 2.30 3.75 0.36 Septian, 2016 1.96 1.38 2.59 0.30 Setyani & Lestari, 2015 0.10 -0.45 0.66 0.27 Siswanto, et al. 2017 1.61 1.04 2.21 0.29 Sumarni et al, 2017 5.50 4.49 6.65 0.54 Supriadi et al, 2014 2.36 1.75 3.03 0.32 Usman & Halim, 2017 1.12 0.64 1.62 0.24 Purwasih et al, 2020 0.44 -0.02 0.91 0.23 Kusumah et al, 2020 0.79 0.35 1.25 0.22 Juandi & Priatna, 2018 0.18 -0.30 0.68 0.24 Nurhayati et al, 2020 0.76 0.20 1.36 0.29 Sutrisno et al a, 2020 1.33 0.75 1.94 0.29 Sutrisno et al b, 2020 1.14 0.57 1.75 0.29 Hamidah et al, 2020 0.36 -0.17 0.89 0.26 Hindriyanto, et al. 2018 0.45 -0.05 0.96 0.25 Ikhsanudin a, 2014 1.61 1.05 2.21 0.29 Ikhsanudin b, 2014 0.76 0.24 1.29 0.26 Nurhidayah, et al. 2018 1.96 1.38 2.59 0.30 Surya, 2015 0.16 -0.28 0.61 0.22 Suryamiharja, 2017 0.73 0.28 1.20 0.23 Sya’diah, et al. 2014 0.54 0.05 1.03 0.24 Mayasary, et al. 2020 1.19 0.54 1.88 0.33 Table 3 shows the overall effect sizes ranged between 0.10 and 5.50, with a 95% confidence limit, while Figure 1 shows the level of the effect size of the entire study based on [63] classification. iJIM ‒ Vol. 15, No. 02, 2021 23 Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... Fig. 1. Classification of effect sizes Figure 1 shows the different effect sizes obtained from the studies conducted on us- ing DGS in mathematics learning, while Table 3 illustrates the results of the descrip- tive meta-analysis according to the estimation method. Table 3. Description of the meta-analysis results according to the estimation model Model n Z P Q I-squared Table value (p=0.05) Effect Size Confidence Interval Lower limit Upper limit Fixed-effects 57 25.96 0.00 394.93 85.82 0.92 0.85 0.90 Random-effects 57 11.34 0.00 394.93 85.82 1.07 0.89 1.26 As shown in Table 3, the mean effect size was calculated to be 0.92, and this was classified as a high level according to [63]. The estimation method is determined through the effect size homogeneity test, which shows the Q value to be 394.93, and it is found to be more than 74.56 (df = 56; p = 0.05) in table tabel χ2. This means that the effect sizes between studies differ. Therefore, the estimation model to determine the impact of using DGS on students’ mathematical abilities as a whole could be evaluated using the random-effects model. The random-effects model in Table 3 showed the lower limit was 0.89 while the upper limit was 1.26 while the average was 1.07 at a 95% confidence interval. This was classified as a very high level, according to [63]. Moreover, the significance test results gave z value as 11.34 and p = 0.00, indicating that the use of DGS in mathe- matics learning resulted in a larger effect size than conventional approaches. The challenge in meta-analysis research is to avoid publication bias, namely the fact that statistically significant articles have a higher chance of being published and that researchers also rarely (6%) try to publish insignificant research [65]. This ten- dency leads to an over-representation of significant studies, similar to the loss of stud- ies that actually exist [38], [66], [67]. Therefore, a study funnel plot was included in determining the existence of publication bias in this study, and the result is presented in Figure 2. 3 6 13 14 8 13 0 5 10 15 no level low level moderate level high level very high level excellent levelN u m b e r o f e ff e c t si z e s Level of Effect Size The number of studies 24 http://www.i-jim.org Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... Fig. 2. Funnel plot related to the effect sizes of the studies included in the meta-analysis Figure 2 shows that the scattered effect’s size is not entirely symmetrical in the middle of the funnel plot. Therefore, Trim and Fill tests were carried out to evaluate the extent of the effects associated with publication bias in the effect sizes obtained from the meta-analysis conducted according to the random effects of the model, and the results are presented in Table 4. Table 4. Trim and Fill test results Studies Trimmed Point Confidence Interval Q Value Lower Limit Upper Limit Observed values 1. 07 0.89 1.26 394.93 Adjusted values 0 1. 07 0.89 1.26 394.93 Table 4 shows there was no difference between the size of the observed and virtual effects created according to the random effect model conducted to correct the impacts of publication bias. Thus, there is no publication bias in this study 3.2 Research results regarding the second question Descriptive statistics about the second question are illustrated in Table 5. Table 5. Effect size according to a year of study Year N Effect Size %95 Confidence Interval Heterogeneity Test Lower limit Upper limit Qb value p 2010-2012 5 1.07 0.82 1.33 2013-2015 16 0.81 0.67 0.95 8.10 0.04 2016-2018 26 1.01 0.91 1.11 2019-2020 10 0.82 0.65 0.99 iJIM ‒ Vol. 15, No. 02, 2021 25 Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... Table 5 shows the effect sizes between study groups based on the study year var- ied. The statistical value of Q obtained from the homogeneity test was 8.10, and since this is greater than 7.81 (df = 3; p = 0.05) in table χ2, the effect size distribution has a heterogeneous structure. This, therefore, means the effect size of mathematical ability using DGS in mathematics learning between study groups differs based on the year of the study. 3.3 Research results regarding the third question Descriptive statistics about the third question are presented in Table 6 Table 6. The effect size of the study according to the educational stage Educational Stage N Effect Size %95 Confidence Interval Heterogeneity Test Lower limit Upper limit Qb value p College 8 1.05 0.83 1.27 JHS 33 0.95 0.86 1.04 7.07 0.02 SHS 16 1.76 0.64 0.89 Table 6 shows the effect sizes between study groups based on education levels also varied. The Q statistical value obtained from the homogeneity test was 7.07, and since it is greater than 5.99 (df = 2; p = 0.05) in table χ2, the effect size distribution has a heterogeneous structure. This, therefore, means the effect size of mathematical ability using DGS in mathematics learning between study groups differs based on the level of research education. 3.4 Research results regarding the fourth question Descriptive statistics about the fourth question are presented in Table 7 Table 7. Effect sizes of the studies according to the sample size Sample Size N Effect Size %95 Confidence Interval Heterogeneity Test Lower limit Upper limit Qb value p 0 – 30 23 1.09 0.86 1.11 4.81 0.04 31 and over 34 0.89 0.80 1.97 Table 7 shows there was a variation in the effect sizes between study groups based on sample size. This was associated with the Q statistical value obtained from the homogeneity test to be 4.81, and since this was greater than 3.81 with 1 degree of freedom and p = 0.05 in table χ2, the effect size distribution has a heterogeneous structure. This means the effect size of the mathematical ability recorded using DGS in mathematics learning between study groups differs based on the size of the re- search sample. 26 http://www.i-jim.org Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... 3.5 Research results regarding the fifth question Descriptive statistics about the fifth question are presented in Table 8. Table 8. Effect sizes of the studies according to the type DGS DGS type N Effect Size %95 Confidence Interval Heterogeneity Test Lower limit Upper limit Qb value p CABRI 12 0.90 0.76 1.05 GEO SKETCHPAD 6 0.73 0.51 0.94 6.19 0.10 GeoGebra 31 0.98 0.89 1.08 WINGEOM 8 0.80 0.62 0.62 Table 8 indicates there was a variation in the effect sizes between study groups based on DGS type. This was associated with the 6.19 obtained as the statistical value of Q from the homogeneity test, and due to the fact that this is smaller than 7.81 (df = 3; p = 0.05) in table χ2, the effect size distribution has a homogeneous structure. Therefore, there was no difference in the effect size of mathematical ability using DGS in mathematics learning between study groups based on the type used. 3.6 Research results regarding the sixth question Descriptive statistics about the sixth question are presented in Table 9. Table 9. Effect sizes of the studies according to the student and computer ratio Student and Computer Ratio N Effect Size %95 Confidence Interval Heterogeneity Test Lower limit Upper limit Qb value p Individual 20 1.10 0.98 1.22 12.83 0.00 Group 37 0.83 0.74 0.91 Table 9 shows a variation in the effect sizes between study groups based on student and computer ratios used in learning. The statistical value of Q obtained from the homogeneity test was 12.83, and since this is greater than 3.84 (df = 1; p = 0.05) in table χ2, the effect size distribution has a heterogeneous structure. This, therefore, means there is a difference between the effect size of mathematical ability using DGS in mathematics learning for study groups differs based on the ratio of students and computers used in the process. 4 Discussion This study analyzed 57 effect sizes, and according to the random-effects model, the combined effect size was found to be 1.07. This shows that the use of DGS in mathe- matics learning has a high positive impact compared to conventional methods. It shows the average student treated using DGS exceeded the 84% mathematical ability of those in conventional classes, which were initially equivalent. Based on the inter- iJIM ‒ Vol. 15, No. 02, 2021 27 Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... pretation table from [68], the average students ranked 16th in the experimental group were equivalent to those ranked 6th in the control group. This finding is in line with previous meta-analysis studies conducted by [52] to compare the effectiveness of DGS-based through the analysis of 587 primary studies and found a combined effect size of 1.02. Even though the number of studies included in this present research was ten times smaller than the sample size, very similar results were obtained, reflecting the overall trend. Another previous meta-analysis study compared the effectiveness of math software used on students’ math abilities by ana- lysing 51 primary studies, and an effect size of 1.102 was found [37]. Some other related studies showed the use of computers in learning influences students’ mathe- matical abilities [47]-[54], [64]. Therefore, the results of this study and other related research shows using DGS in mathematics learning can improve and a very high effect on students’ mathematical abilities. The results also indicate that more study characteristics are related to effect size. The strongest relationship was found for the following variables: year of study, level of education, sample size, and student to computer ratio. The effect size does not differ based on the type of DGS used in learning. Significant differences were observed between the study groups based on the re- search year as observed in the effect size value of 0.82 considered as high level found for the latest year study group, which is smaller than for the oldest year, which was 1.07 and considered very high level. This is very surprising and contradicts previous predictions that the effect size of using DGS on the mathematical abilities of latest year students is greater due to the continuous update of the software and improvement in teachers’ quality. However, it is supported by previous studies that the effect size of studies in older study groups was greater than those in newer study groups [47], [49]. The higher values obtained for, the older study groups are associated with the Haw- thorne effect, which occurs when students are stimulated to make greater efforts simp- ly due to the novelty of the treatment [47]. As of 2010, the use of DGS in mathemat- ics learning was new in Indonesia. The results showed a strong relationship between the DGS effectiveness and edu- cation level. The effect size of the software’s application in tertiary institutions and SHS was found to be greater than on JHS. This was in line with the findings of [55], which showed significant differences in effect size for different school levels but not the same with the results of [37] and [49] that there was no significant difference. The analysis also showed a strong relationship between DGS effectiveness and sample size, as observed in the effect size variations between small (0-30), which was 1.09, and large sample sizes (31 and over) with 0.89. This means a small sample size should be considered more in teaching settings. This is in line with the findings of [37] and [53] that the effect size of the study group in small samples was greater than those in large samples. However, it is different from the results of [49], [52], [55] that study groups in small samples had smaller effect sizes. This variation, therefore, needs to be further investigated. This meta-analysis also showed there was no significant difference in effect size based on the type of DGS used. This means every type of DGS is effective in mathe- matics learning, with the largest combined effect size of 0.98 was GeoGebra from 31 28 http://www.i-jim.org Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... studies. However, this characteristic of this study has not been extensively investigat- ed in the previous meta-analysis. A significant relationship was also found between the DGS effectiveness and stu- dents’ ratio to the computers used. This was associated with the extraordinary differ- ence in effect sizes for individuals (one student uses one computer), which was 1.10, and the 0.83 recorded for group implementation (one computer used by more than one student). This, therefore, means individual versions should be considered more in teaching settings. These results are in line with [47] that learning using computers individually has a larger effect size than a collective use. 5 Conclusion This study was conducted by integrating the findings of the effects of using DGS on students’ mathematical abilities, both as a whole and in several key study charac- teristics. The results of the analysis reveal that the use of DGS has a high positive impact on students’ math abilities. The assessment of the DGS effectiveness based on study characteristics showed it is more effective under certain conditions. First, it was found to be very effective in sample conditions less than or equal to 30. Second, it provides classrooms with a sufficient number of computers, allowing students to use them individually, which is recommended for a higher level of effectiveness. Third, DGS’s use was recorded to be more effective in high schools and colleges than in junior high schools. Some differences in effect sizes were observed in terms of the year the studies were conducted. Most recent study groups were found to have smaller values compared to older studies. This shows the consideration of the Hawthorne effect in the mathematics teaching process. Meanwhile, different types of DGS can be used without any exception. Even though the use of DGS was found to have a very high effect on students’ mathematical abilities, the results were only based on studies with certain criteria, with some similar studies not analysed due to inadequate required statistical infor- mation. For this study’s purpose, only five research characteristics were examined and they include the year the study was conducted, level of education, sample size, type of DGS, and the ratio of students to computers. Meanwhile, some others, such as the study’s location, treatment duration, teacher’s role as a tutor or instructor, and com- puter’s role as an addition or a substitute for the teacher. Consequently, these conclu- sions do not reflect the overall effectiveness of using DGS in mathematics learning. Therefore, for further research, a detailed investigation is required to determine DGS’s effectiveness using some of the characteristics that have not been investigated. 6 Acknowledgment Results This research was funded by a graduate school grant (HSPS-2019) under the Uni- versitas Pendidikan Indonesia, Bandung, Indonesia. iJIM ‒ Vol. 15, No. 02, 2021 29 Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... 7 References [1] H. Bakirci, A. K. Bilgin, and A. Şimşek, “The effects of simulation technique and work- sheets on formal operational stage in science and technology lessons,” Procedia - Soc. Be- hav. Sci., vol. 15, pp. 1462–1469, 2011, https://doi.org/10.1016/j.sbspro.2011.03.311. [2] C. S. Koong and C. Y. Wu, “The applicability of interactive item templates in varied knowledge types,” Comput. 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Maximus Tamur is a doctoral student in mathematics education at the University of Pendidikan Indonesia. He is also a lecturer in the mathematics education study program of the Universitas Katolik Indonesia, Santu Paulus Ruteng, and the vice- chairman of the Indonesian Mathematics Educators Association (IMES) for the Prov- ince of East Nusa Tenggara Indonesia (email: maximustamur@unikastpaulus.ac.id) Krisna S. Perbowo is a mathematics education doctoral student at Warwick, Unit- ed Kingdom. (email: k.perbowo@warwick.ac.uk) Muhammad Daut Siagian is a mathematics education doctoral student at the mathematics education university. He is a lecturer in the mathematics education study program of the Islamic University of North Sumatra, Medan, Indonesia (email: mds iagian@fkip.uisu.ac.id) Rini Sulastri is a mathematics education doctoral student at the mathematics edu- cation university. He is also a lecturer in the mathematics education study program, 34 http://www.i-jim.org https://doi.org/10.11613/bm.2012.031 https://doi.org/10.12738/estp.2014.5.2311 https://doi.org/10.12738/estp.2014.5.2311 https://doi.org/10.1177/1745691612459059 https://doi.org/10.1007/s12564-016-9433-x https://doi.org/10.1007/s12564-016-9433-x mailto:yayaskusumah@yahoo.com mailto:maximustamur@unikastpaulus.ac.id mailto:k.perbowo@warwick.ac.uk mailto:mdsiagian@fkip.uisu.ac.id mailto:mdsiagian@fkip.uisu.ac.id Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... Serambi Mekkah University, Aceh, Indonesia (email: rini.sulastri@serambimekkah.a c.id) Habibi R. P. Negara is a doctoral student in mathematics education at the mathe- matics education university. He is also a lecturer in the mathematics education study program of the Mataram State Islamic University, Mataram, Indonesia (email: habibi- perwira@uinmataram.ac.id) Article submitted 2020-09-25. Resubmitted 2020-10-19. Final acceptance 2020-10-21. Final version published as submitted by the authors. 9 Appendix A: List of the Studies Included Author Year Title of the Study Toto Subroto 2011 The Use of Cabri 3D Software As Virtual Manipulation Tool in 3- Dimension Geometry Learning To Improve Junior High School Students’ Spatial Ability Dodi Syamsuduha 2011 The Effect of Sketchpad’s Geometric Assisted Cooperative Learning Towards Increased Critical Thinking Ability Marchasan Lexbin & Stevi Natalia 2011 Improvement of Geometric Comprehension Ability of Junior High School Students through a Realistic Mathematical Approach Aided by Sketchpad Geometer’s Software M. F. Abduh, Kartono, & Hery Sutarto 2012 The Effectiveness of Tapps Learning Model Assisted by Facebook Learning and Cabri on Achieving Problem Solving Capabilities Risnawati 2012 The Effect of Learning Using Inductive-Deductive Approaches Assisted by the Cabri Geometry Program Against the Improvement of Students’ Mathematical Representation Ability Diah Prawitha Sari 2013 Improving Students’ Critical Mathematical Thinking Ability and Self Regulation Through Utilization of the Cabri Geometry II Program in the Tutorial Learning Model Nurhayati 2013 Effect of Application of Constructivism Approach with Cooperative Learning Model Assisted by 3D Cabri Program on Reasoning Ability and Mathematical Connection of High School Students in Tasikmalaya City Gias Atikasari & Ary Woro Kurniasih 2013 The Effectiveness of Cooperative Learning Model with Geogebra Assisted TTW Strategy on Mathematical Creative Thinking Ability of Class VII Students in Triangle Material Astin Stasia Anggroratri 2014 The Effectiveness of Geogebra Assisted Mathematics Learning with a Laboratory Approach compared to the Classical Approach for Stationary Values and Drawing Curves in Class XI High School Nanang Supriadi, Yaya S. Kusumah, Jozua Sabandar, & Jarnawi D. Afgani 2014 Developing High-Order Mathematical Thinking Competency on Hi gh School Students ‘ Through Geo Gebra-Assisted Blended Learning Ikhsanudin 2014 The Effect of Use of Wingeom’s Assisted Cooperative Learning Type on the Geometry Problem-Solving Capabilities of High School Students Halimah Sya’diah, & Prahesti Tirta Safitri 2014 The Effect of Quantum Software Assisted by Wingeom’s Software on Students’ Mathematical Reasoning Abilities Ishaq Nuriadin 2015 Contextual Learning Assisted by Geometer’S Sketchpad Program in Improving Mathematical Communication and Communication Capabilities of Junior High School Students Nida Aisyah 2015 The influence of the problem based learning model assisted by geogebra software on the ability to solve mathematical problems iJIM ‒ Vol. 15, No. 02, 2021 35 mailto:rini.sulastri@serambimekkah.ac.id mailto:rini.sulastri@serambimekkah.ac.id mailto:habibiperwira@uinmataram.ac.id mailto:habibiperwira@uinmataram.ac.id Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... Umi Farihah 2015 The Effect of Geogebra Interactive Program on Motivation and Student Learning Outcomes on the Material of Straight Line Equation Graphs Setio Priyono & Redi Hermanto 2015 Improving students’ mathematical representation ability by using problem-based learning (PBL) models assisted by Geogebra software media Nanik Setyani, Himmawati Puji Lestari 2015 The Effectiveness of Mathematics Learning Using Geogebra Assisted CPS (Creative Problem Solving) Model in terms of Learning Achievement and Creativity of Class VIII Students of SMP PGRI Tegalsari Purworejo Regency Edi Surya 2015 Junior High School Mathematics Learning Based on Malay Culture and Wingeom Software Iqbal Ramadani, Zulkarnain, & Sehatta Saragih 2016 The Effect of Van Hiele Learning Model Assisted 3D Cabri Software on Mathematics Learning Outcomes of Mainstay Class Its Mtsn Students The Effect of Van Hiele Learning Model Assisted 3D Cabri Software Against Learning Outcomes Annajmi 2016 The Effect of Van Hiele Learning Model Assisted 3D Cabri Software on Mathematics Learning Outcomes of Mainstay Class Its Mtsn Students The Effect of Van Hiele Learning Model Assisted 3D Cabri Software Against Learning Outcomes Ari Septian 2016 Application of Geogebra to Improve Mathematical Problem Solving Ability of Students in the Mathematics Education Study Program at Suryakancana University Hartatiana, Darhim, & Nurlaelah 2017 Improving Junior High School Students’ Spatial Reasoning Ability Through Model Eliciting Activities with Cabri 3D Hartatiana, Darhim, & Nurlaelah 2017 Student’s Spatial Reasoning through Model Eliciting Activities with Cabri 3D Fazrina Saumi & Rizki Amalia 2017 Application Of Brain Based Learning ( BBL ) Models Based On Saintific Approach With 3D Cabries In Geometry Material To Increase The Ability Of Mathematics Communications For Students Of SMAN 1 Karang Baru Ramadhani 2017 Difference Between Increasing Mathematical Self Efficacy Between Students Who Get Geogebra Assisted Guided Learning Learning Without Geogebra Assisted At SMPN 22 Medan Rizki Dwi Siswanto & Yaya S Kusumah 2017 Improvement of Spatial Geometry Ability in Junior High School Students through Guided Inquiry Learning Assisted by Geogebra Sumarni, Anggar T. Pratitno, & Mita Nurpalah 2017 Development of Economic Mathematics Teaching Materials Based on Learning Cycles Assisted by Geogebra Software to Improve Student Learning Outcomes Muhammad Rizal Usman & Nur Humairah Halim 2017 Improving the Mathematical Creative Thinking Ability of High School Students Through Inquiry Learning Assisted by Geogebra Software at the Subject of Linear Programs Bagja Nugraha Suryamiharja 2017 The Effect of Application of Learning Model of 3D Wingeom Software Assisted Learning Against Improvement of Students’ Mathematical Concepts Understanding Budi H. Priyanto, Abduloh, & Mokhammad R. Yudhanegara 2018 The Role of Teaching Material Based on Van Hiele Theory on Students’ Mathematical Representation Ability Eka Senjayawati & Martin Bernard 2018 Application of Search Solve Create Share Model to Develop Mathematical Reasoning Abilities Using Geogebra Software 4.4 Erana, Rifqi Hidayat, & Desy Lusiyana 2018 Implementation of Geogebra Software Version 4.4 Learning Cycle Learning Model in an Effort to Improve Mathematical Concepts and Mathematical Disposition of Middle School Students Awaluddin Fitra & Muhammad Romi 2018 The Effect of Geogebra on Student Learning Outcomes in SPLDV Material in Class VIII of Kemala Bhayangkari 1 Medan Middle School 36 http://www.i-jim.org Paper—The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: ... Syahputra Endang Habinuddin 2018 Ability Improvement In Understanding Derivative Calculus Using Geogebra Abd Haris & Arif Rahma 2018 Student Spatial Ability Through Problem Based Learning With Geogebra Software Silfanus Jelatu, Sariyasa, & I Made Ardana 2018 Effect of GeoGebra-aided REACT strategy on understanding of geometry concepts Khotimah 2018 Improving Mathematical Literacy Skills Using Metacognitive Guidance Approach Assisted by Geogebra Abdul Rosyid & Uba Umbara 2018 Implementation of the Missouri Mathematics Project Learning Model Assisted by GeoGebra to Improve Mathematical Communication Skills of Middle School Students Dadang Juandi & Nanang Priatna 2018 Discovery learning model with geogebra assisted for improvement mathematical visual thinking ability Yunio Hindriyanto & Metya Dwi Kurniasih 2018 The Influence of Generative Learning Model Assisted with Wingeom Software to Student ‘ s Mathematical Learning Outcomes Fadillah Nurhidayah, Ervin Azhar, & Hella Jusra 2018 The Effect of Jigsaw Cooperative Learning Model Assisted by Wingeom Software on Mathematics Learning Outcomes of Students in Negeri Negeri 163 Jakarta Benny Hendriana, Ishaq Nuriadin, & Listya Rachmaeni 2019 The Influence Of Brain-Based Learning Model With Cabri 3d On Student ‘ S Ability Of Spatial Mathematics Rezkiyana Hikmah, Sri Rezeki, & Bayu Jaya Tama 2019 Use of 3D Cabri to Increase Students’ Mathematical Representation Ability Awaludin Fitra & Martua Sitorus 2019 Effect of Geogebra Application Assisted Learning on Student Learning Outcomes in Class VIII Junior High School Kemala Bhayangkari 1 Medan Ratni Purwasih, Ratna Sariningsih, & Indah Puspita Sari 2020 Self Efficacy of Students’ High Order Thinking Mathematics Ability Through Geogebra Softwere Assisted Learning Yaya S. Kusumah, Dedek Kustiawati, & Tatang Herman 2020 The Effect of GeoGebra in Three-Dimensional Geometry Learning on Students’ Mathematical Communication Ability Yanti Nurhayati, Nur Eva Zakiah, & Asep Amam 2020 Integration of contextual teaching learning (CTL) with geogebra: can it improve students’ mathematical connection skills? Sutrisno, Nita Zuliyawati, Rina Dwi Setyawati 2020 The Effectiveness of Problem-Based Learning and Think Pair Share Learning Models Assisted by Geogebra on Mathematical Problem Solving Capabilities Nur Hamidah, Lis Nur Afidah, Lutfi Wahyu Setyowati, Sutini, & Junaedi 2020 The Effect of Geogebra Learning Media on Quadratic Function Material on the Motivation and Learning Outcomes of Students N. Mayasary, C. Hasanudin, & A. Fitrianingsih 2020 The use of wingeom software in geometry subject, how is the learning outcomes of junior high school students? iJIM ‒ Vol. 15, No. 02, 2021 37