International Journal of Interactive Mobile Technologies (iJIM) – eISSN: 1865-7923 – Vol 16 No 24 (2022) Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics Problem Solving and Creative Thinking Ability https://doi.org/10.3991/ijim.v16i24.35749 Dessy Noor Ariani(), Mohamad Syarif Sumantri, Firmanul Catur Wibowo Universitas Negeri Jakarta, Jakarta, Indonesia dessynoorarianii@gmail.com Abstract—This research uses the Android module based on a strategy called "inquiry-based learning" and "flipped classroom" to help people utilize their cross-disciplinary skills in complex real-world situations. This experiment showed how the Android module-based inquiry flipped classroom learning af- fects math pre-service teachers' ability to solve mathematical problems and think creatively in geometry. In the third term, 123 students were randomly as- signed Android module-based inquiry flipped classroom learning, PowerPoint module-based conventional flipped learning, or conventional learning. The study found that math pre-service teachers were much better at solving mathe- matics problems and creative thinking when using Android module-based in- quiry flipped classroom learning because its use effectively extends learning time, permits the acquisition of more knowledge, and encourages a collective responsibility for learning in order to engage in the process of deeper learning. This type of learning also helps them learn how to deal with real-world prob- lems that they may face in their future jobs. This implication can guide instruc- tional designers on how to help students solve math problems and think crea- tively. Keywords—Android module, inquiry flipped classroom learning, mathematics problem solving, mathematics creative thinking 1 Introduction The development of professional and competent teachers, especially mathematics teachers, needs to undergo tremendous and rapid change to address the development of education. Learning innovations must be carried out continuously and match the demands of learning through integrated and well-structured activities to create a large academic and quality culture. High-order thinking competencies, such as problem- solving and creative thinking skills, are critical in the 21st century and have been highlighted by several scholars [1], [2]. In fact, teacher education programs world- wide have been criticized for being too theoretical, not preparing future teachers for the classroom, and not having a professional focus [3]. There is also a need for teach- ers to be able to recognize, evaluate, and explain their choices and actions [4]. There- 32 http://www.i-jim.org https://doi.org/10.3991/ijim.v16i24.35749 mailto:dessynoorarianii@gmail.com Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… fore, lecturers must create active, flexible, student-centered, and collaborative learn- ing in higher education. A range of technologies have been used to encourage student involvement. The development of smartphone applications has been made possible in mobile learning to complement educational activities [5]. Combining mobile technology, contextual learning techniques, and relevant learning designs can create a relaxing online learn- ing experience [6]–[8]. An excellent way to create socially engaging and constructiv- ist learning environments, for instance, is to use Android learning material on mobile devices, according to a recent study [9]–[11]. Android is one of the popular operating systems for smartphones and tablets. An- droid allows everyone to create and develop Android applications for every need[12]. Android learning material on mobile devices may create a socially engaging and con- structivist learning environment for students [10], [11]. In addition, the Android mod- ule is a convenient, effective, and interactive alternative learning source that can be accessed anytime and from any location via a smartphone [13]. Therefore, an Android module may be utilized in a technology-based classroom to achieve specific learning goals[14]. Moreover, an Android module is more attractive and interactive because it combines digital media formats, such as animations, videos, links, buttons, and others [12]. The “flipped classroom” (FC) is one of the change strategies that can accelerate technology innovation in math education. The flipped classroom strategy provides learners with more flexible study times and multiple assessments to enable students to learn more [15]. Traditional teacher-centered learning is challenged by the flipped classroom strategy, which changes teachers into advocates and facilitators who assist students in teamwork or individual learning [16]. The flipped classroom combines face-to-face learning with ICT-supported learning outside the classroom and has the opposite order of learning to conventional lectures [17]. Students acquire knowledge or skills individually or collectively before class, and then teachers mainly provide questions and guided collaborative learning activities in class [18]. As a result, for various topics such as science and mathematics, this teaching strategy can enhance brainstorming and interaction with peers, develop students' skills in communication and independence in learning, and transform students' learning habits for the better [19]–[21]. As a teaching method, FC is described as a teaching reform that uses mobile tech- nology to modify teaching ideas, instruction objectives, teaching time, and teaching mode so that instructors educate students in class and students complete their assign- ments at home [22]. Students can access lecture videos, notes, slides, and articles outside the classroom, while teachers can connect and interact with their students through the web of Learning Management Systems (LMS) and encourage deep learn- ing through in-class activities. Flipping the classroom allows for additional time for active learning and problem-solving activities [23]. Moreover, a recent meta-analysis by L. Zheng et al. [24] suggests combining flipped classroom strategies with other educational models, such as inquiry-based learning, to optimize the effectiveness of flipped classroom situations. For example, in STEM education, inquiry-based learning can be optimally utilized in flipped class- iJIM ‒ Vol. 16, No. 24, 2022 33 Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… room circumstances because the freed-up in-class time can allow students to hypothe- size, investigate, discuss, and justify problem-solving strategies [25]. There are several ways to facilitate learning through inquiry by flipping a class- room. In a productive failure-based flipped classroom, students are still expected to complete mathematical exercises despite their failures [26]–[28]. Students are then required to watch a video at home to put together what they have learned instead of using a video to learn how to solve a problem as homework [28]. As in any flipped classroom, the application does this during the course. When implementing an in- quiry-based flipped classroom, teachers must carefully consider the arrangement of in-class and out-of-class stages. However, few studies have investigated the efficacy of assisting mathematics lecturers with teaching methods for inquiry-based flipped learning [29], [30]. In addition, inquiry-based learning in flipped classroom settings has received little attention in scientific and mathematics education research. There- fore, combining inquiry-based learning with flipped classroom strategies may result in more time for investigation during class [31]. This research is very important because problem-solving and creative thinking are two skills that need to be mastered and possessed by prospective elementary school teachers [32]. This skill is a basic ability that students should also master. This ability is becoming increasingly urgent due to the demands of an increasingly competitive workforce and complex problems. However, some results indicate a lack of students' ability to solve mathematical problems [33], [34]. Therefore, the systematic study of the process of creating and resolving problems and the ways to organize problem- solving procedures for learning mathematics has become a research priority [2]. Although proficient problem-solving can be enormously useful in both instances, prior research indicates that students frequently struggle with both tasks [35]–[37]. Mathematical creative thinking (MCT) is also an essential competence for pre-service mathematicians and is usually based on an underlying process or a visible product. Creativity, when taught within the context of the 21st century, can assist students in their capacity to adjust to the continuously shifting world that surrounds them[38]. Mathematical problem-solving and the generation of new ideas require creative think- ing (CT) [38]. This process involves identifying which objects' regular properties have changed and how they have changed [39]. This strategy encourages students to find meaning in participating and reflecting on events [40]. A critical cognitive skill for students is recognizing when they have not fully thought through the potential drawbacks of a proposed solution [41]. Therefore, this study examines the effect of Android module-based inquiry flipped classroom learning on elementary pre-service mathematics problem-solving and creative thinking skills. 2 Methods 2.1 Research design This study utilized a quasi-experimental design with a control group design for both the pre-test and post-test. Eight weeks were devoted to the experiment during the 34 http://www.i-jim.org Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… third semester of the 2020-2021 academic year. Geometry topics in mathematics classes were taught using Android module-based inquiry flipped classroom learning in experiment group 1. Group 2 of the experiment used a PowerPoint module-based conventional flipped classroom strategy, while the control group engaged in conven- tional learning. The experiment was conducted in a classroom with the same teacher for each group to avoid unanticipated results. The iSpring Suite and Website to Apk Bulder application were used to generate an Android geometry module-based inquiry for flipped classroom learning. The Android geometry module-based inquiry for flipped classroom learning was designed to be accessible offline, but its video was only accessible online. The purpose of the videos being posted on Youtube is to reduce application size and make the application easier to install on smartphones. Figure 1 shows the content of the Android geometry mod- ule. Fig. 1. An Android geometry module-based inquiry flipped classroom learning 2.2 Participants The activity was implemented during the third semester of elementary pre-service education for the geometry course, which had a total of 123 students. Before the ex- periment, the three classes were randomly divided into two experimental groups and a control group. They consisted of 41 students in Experimental Group-1 (Android mod- ule-based inquiry flipped classroom learning, named the AMIFC group), 41 in Exper- imental Group-2 (PPT module-based conventional flipped learning, named the PMCFC group), and 41 in the control group (conventional learning, named the CL iJIM ‒ Vol. 16, No. 24, 2022 35 Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… group). Their report shows that they have a similar background, age, and knowledge of geometry. 2.3 Data collection instrument This study collected quantitative data through math problem-solving and creative thinking tests. Seventy study participants provided reliability estimates for each in- strument. Field [42] stated a Cronbach's coefficient of .70 or higher indicates internal consistency reliability and all study instruments met or exceeded this standard. Before and after the study, all groups were given the mathematics problem-solving and crea- tive thinking skills test to see how well they had done. The processing time for prob- lem-solving skill assessments administered before and after the test is limited to 45 minutes with different questions. Researchers developed the Mathematics Problem-Solving Skills Test (MPSST) to assess the problem-solving abilities of third-year elementary mathematics pre-service teachers enrolled in a geometry course during the third semester of their study. Three professionals in the field of mathematics teaching had taken the MPSST and approved its content. The MPSST was divided into four sub-scales adapted from Polya [43]. These sub-scales included understanding the problem, generating a solution plan, implementing the solution plan, and concluding. Understanding the problem was the first sub-score, followed by developing a solution strategy, implementing the plan, and solving the problem. The results of Cronbach's alpha also showed that the ques- tionnaire for the usability test was reliable (alpha = 0.912). In their third semester of pre-service education, students taking a geometry course were given the Mathematics Creative Thinking Skills Test (MCTS), which research- ers developed to gauge their mathematics creative thinking capabilities. For the MCTS, three experts in math education confronted each other and verified the test's content. Four indicators of MCT fluency, flexibility, elaboration, and originality are used in the MCTS guidelines [44], [45]. Fluency refers to a person's ability to devise numerous solutions when solving a mathematical problem[46] and flexibility refers to the ability to modify one's problem-solving strategy if one becomes stuck[45]. The term "elaboration" refers to the ability of a specific solution path to allow for extend- ed reasoning. As the last point, originality refers to the individual’s ability to find a distinct and unusual path for their degree of knowledge [46]. Furthermore, Cronbach's Alpha results demonstrated that the questionnaire for the usability test was reliable (alpha = 0.744). 2.4 Data analysis Data from the tests measuring mathematics problem-solving and creative thinking skills were analyzed using the Shapiro-Wilk distribution test, which revealed whether or not the data was normally distributed. Pre- and post-test values were both greater than or equal to 0.05. As a covariate variable, the pre-test scores of the three groups were used in an ANOVA parametric test to determine any differences with the post-test scores. For 36 http://www.i-jim.org Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… further analysis, only variables with a normal distribution were considered. At this point, we used an analysis of variance (ANOVA) to see whether the groups with a normal distribution differed significantly in their pre-and post-test scores. 3 Results The Shapiro-Wilk test was conducted to determine normality, while the homogene- ity test was conducted as a prerequisite for the ANOVA test. The results of the Shapiro-Wilk test indicated that both the pre-test and post-test data had a normal dis- tribution. In addition, variance homogeneity tests revealed that the pre-and post-test data originated from the same group. 3.1 Impact of the Android module-based inquiry flipped classroom learning implementation on mathematics problem solving skills A paired t-test was performed for each group to determine gain scores and signifi- cant differences between the pre- and post-tests. The paired t-test indicated a statisti- cally significant mean difference for each group. Additionally, pre- and post-test scores across groups were statistically significant at the 0.00 level (see Table 1). Table 1. Paired samples T-test Treatment Pre-test Post-test Mean Differences t df Sig. (2-tailed) AMIFC 4.7 9.8 5.1 23.43 40 .000** PMCFC 4.6 8.6 4.0 36.54 40 .000** CL 4.6 7.3 2.7 11.93 40 .000** The information on Table 1 shows the statistical value of IFL, t= 23.433, and p- value = .000< .05; CFL, t = 36.54, and p-value = .000< .05; CL t= 11.93 and p-value = .000< .05 Thus, it is concluded that there was a significant difference in mathemati- cal problem-solving skills for the pre-tests and post-tests of all treatments. In addition, the mean differences for the Android Module-Based Inquiry Flipped Classroom Learning (AMIFC), PPT Module-based Conventional Flipped Learning (PMCFC), and Conventional Learning (CL) were 5.1, 4.0, and 2.7 points, respectively. So, the Android Module-Based Inquiry Flipped Classroom Learning obtained the highest mean difference in improving mathematics problem-solving compared to PMCFC and CL. After a paired T-test, ANOVA (analysis of variance) was used to analyze whether there were significant differences between the three study groups. Based on Table 2, the value of F is 18.961 with a p-value of 0.000 <0.05, which means there is a significant difference in mathematics' problem-solving skills means between AMIFC, PMCFC, and CL. To find out whether there is a significant differ- ence in the average value of problem-solving skills between the research groups, a post-hoc test was carried out, as shown in Table 3. iJIM ‒ Vol. 16, No. 24, 2022 37 Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… Table 2. ANOVA test of mathematics problem solving skills Sum of Squares df Mean Square F Sig. Between Groups 119.63 2 59.81 18.96 .000 Within Groups 378.54 120 3.15 Total 498.16 122 Table 3. Post-Hoc analysis of mathematics problem solving skills (I) Class (J) Class Mean Difference (I-J) Std. Error Sig. Tukey HSD AMIFC PMCFC 1.29* .44 .010 CL 2.39* .44 .000 PMCFC AMIFC -1.29* .44 .010 CL 1.10* .44 .035 CL AMIFC -2.40* .44 .000 PMCFC -1.10* .44 .035 Based on the post hoc test results in Table 3, it can be explained that the mathemat- ics problem-solving skills of the AMIFC group paired with the PMCFC group had a significant difference of p = .010 < 0.05, while the AMIFC paired with CL also had a significant difference p = 0.000 < 0.05. Based on these calculations, this study indi- cates that Android module-based inquiry flipped classroom learning significantly impacts the mathematics problem-solving skills of elementary mathematics pre- service teachers. 3.2 Impact of the Android module-based inquiry flipped classroom learning implementation on mathematics creative thinking skills The paired t-test indicated a statistically significant mean difference for each group. Additionally, pre and post-test scores across groups were statistically signifi- cant at the 0.00 level (see Table 4). Table 4. Paired samples T-test mathematics creative thinking skills Treatment Pre-test Post-test Mean Differences t df Sig. (2-tailed) AMIFC 4.6 9.6 5 13.400 40 .000** PMCFC 4.4 8.3 3.9 15.095 40 .000** CL 4.4 7.2 2.8 9.448 40 .000** Table 4 shows the statistical value of AMIFC, where t= 13.400, and p-value = .000< .05; PMCFC, t = 15.095, and p-value = .000< .05; CL t= 9.448 and p-value = .000< .05 Thus, it is concluded that there was a significant difference in the mathe- matical creative thinking skills pre-tests and post-tests for all treatments. In addition, the mean differences for the Android Module-Based Inquiry-Flipped Classroom Learning (AMIFC) = 5, PowerPoint Module-based Conventional Flipped Learning 38 http://www.i-jim.org Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… (PMCFC)= 3.9, and Conventional Learning (CL) = 2.8. Thus, the Android module- based inquiry flipped classroom learning had the highest score in improving mathe- matics creative thinking skills in elementary school mathematics pre-service than the other two methods. After a paired T-test, ANOVA (analysis of variance) was used to examine the effect of inquiry-based flipped classroom learning on pre-service mathe- matics creative thinking, as described on Table 5. Table 5. ANOVA test of mathematics creative thinking skills Sum of Squares df Mean Square F Sig. Between Groups 117.382 2 58.691 15.051 .000 Within Groups 467.951 120 3.900 Total 585.333 122 Based on Table 5, the value of F = 15.05 with a p-value of 0.000 <0.05 means there is a difference in mathematics creative thinking skills using AMIFC, PMCFC, and CL. To find out whether there is a significant difference in the average value of creative thinking skills between the research groups, a post-hoc test was carried out, as shown in Table 6. Table 6. Post-Hoc analysis of mathematics creative thinking skills (I) Class (J) Class Mean Difference (I-J) Std. Error Sig. Tukey HSD AMIFC PMCFC 1.293* .436 .010 CL 2.390* .436 .000 PMCFC AMIFC -1.293* .436 .010 CL 1.098* .436 .035 CL AMIFC -2.390* .436 .000 PMCFC -1.098* .436 .035 *. The mean difference is significant at the 0.05 level. Based on the post hoc test results in Table 6, it can be explained that the mathemat- ics creative thinking skills of the AMIFC group paired with PMCFC had a significant difference p = .010 < 0.05. Likewise, the AMIFC paired with CL also had a signifi- cant difference p = 0.035< 0.05. Based on these calculations, this study indicates that Android module-based inquiry flipped classroom learning significantly impacts the mathematics creative thinking skills of elementary mathematics pre-service teachers. 4 Discussion This study applied the Android module-based inquiry flipped classroom learning to help students acquire considerable knowledge and foster mathematics problem- solving and creative thinking in a control class. According to the study's objectives, using the Android module-based inquiry flipped classroom learning in geometry courses improved pre-service teachers' mathematics problem-solving and creative thinking skills in the short and long term after eight weeks of implementation. Several iJIM ‒ Vol. 16, No. 24, 2022 39 Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… studies indicate that the ability to recognize and express complex relationships in a mathematical problem, as well as to draw different generalizations from these rela- tionships and employ various problem-solving strategies, is an essential component of mathematical creativity [47], [48]. These study results revealed that the Android module-based inquiry flipped classroom learning, used in the experimental group, had more positive effects on mathematics problem-solving and creative thinking skills than in other groups. These results consistently demonstrate the effectiveness of the suggested method. This section describes how Android module-based inquiry flipped classroom learning helps advance teachers' mathematics problem-solving and creative thinking skills in elementary mathematics pre-service. First, the Android module-based inquiry flipped learning is a transformation of the conventional module that uses ICT to make the existing modules more interesting and interactive. This is because we can add illustrations, animations, audio, and video to it. Students follow the steps in the program from start to finish. Students can improve their learning outcomes (self-assessment) by incorporating exam facilities or interac- tive evaluation into the Android module-based inquiry flipped learning, allowing for greater student interaction with course materials. Android learning material on mobile devices may create a socially engaging and constructivist learning environment for students [9]–[11]. In addition, the Android module is a convenient, effective, and interactive alternative learning source that can be accessed anytime and from any location via a smartphone [13]. Therefore, it may be utilized in a technology-based classroom to achieve specific learning goals[14]. Second, discussions are facilitated in inquiry-based learning by having students as- sume collective responsibility for learning and by giving them numerous opportuni- ties to communicate with their classmates. In an inquiry-based flipped learning class, frequent communication practice and collective responsibility for learning appear to be potent methods for enhancing students' modes of learning. After participating in group discussions in class, students began to feel a sense of collective responsibility for their studies. They were required to discuss problems with group members and share their various approaches to find better solutions and enhance their understand- ing. The discussion consists of articulating and refining one's understanding and ideas and listening to others. Therefore, under the lecturer's guidance, inquiry-based learn- ing provides the opportunity to develop these essential skills through direct experi- ence. This finding supports previous studies that examine the impact of IBL on stu- dents' critical thinking skills [49]. In addition, it was discovered that students with an active learning style benefit more from the proposed approach than students with a reflective learning style in terms of learning achievement. Several studies also show that inquiry-based learning with the help of technology can improve students' motiva- tion to learn their learning outcomes, their satisfaction with school, and their self- confidence [50]–[52]. Third, flipped classroom learning gave students more time to learn from easily ac- cessible modules[53], [54]. With this extra time, students can learn everything they need about the geometry course from an Android module. When class time is regular- ly extended for all students, students' problem-solving skills improve dramatically. As previously stated, students were required to study the Android module (including 40 http://www.i-jim.org Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… learning materials, lecture videos, and quizzes) before each class session. As a result, they were able to solve and discuss problems in class. Finally, flipped learning saves students time in the classroom by making the lecturer's explanations of concepts available. Out-of-class time contributed to the reduction of in-class time for each student. This extra time to learn can benefit all students, and the majority will see an improvement in their grades. Several studies have reported similar results: flipped classroom learning can improve students' motivation[55], student performance in mathematics instruction [15]. In addition, a recent study on flipping mathematics classes by Cevikbas and Kaiser [56] indicates that well-designed flipped classroom scenarios can improve students' mathematical thinking and comprehension by em- ploying a variety of teaching methods. Fourth, several studies state that inquiry-based learning can optimize the effective- ness of flipped classroom situations [24], [57]. Moreover, integrating inquiry-based learning into the flipped classroom increases student engagement, motivation, satis- faction, and decreases anxiety [58]. In sum, Android module-based inquiry flipped classroom learning greatly affects how students develop their mathematics problem-solving and creative thinking skills. It works best when students are aware of and responsible for their actions. Pre-service teachers learned in a way that would stick with them for a long time. This was done by developing their ability to learn independently through inquiry-based flipped learn- ing and by repeating and reinforcing what they had learnt through the Android mod- ule, including video, learning materials, and quizzes outside of school. Students will learn independently based on their ability to comprehend the learning materials of- fered for them. In addition, when the teaching and learning process is conducted online, students can regulate their study time and find comfortable studying environ- ments [59], [60]. Students can also repeat information that they have not fully com- prehended. Consequently, learning activities become more student-centered when this paradigm is used. Therefore, they have many resources in the Android module for inquiry-based learning in class. 5 Conclusion This study aims to examine the effect of Android module-based inquiry flipped classroom learning on elementary pre-service mathematics problem-solving and crea- tive thinking skills. The study found that math pre-service teachers were much better at solving mathematics problems and using creative thinking when using Android module-based inquiry for flipped classroom learning. In this study, Android module- based inquiry flipped classroom learning is beneficial for enhancing problem-solving and creative thinking skills in geometry because its use effectively extends learning time, permits the acquisition of more knowledge, and encourages a collective respon- sibility for learning in order to engage in the process of deeper learning. However, additional time and effort are required to prepare Android modules, select appropriate problems, and create a conducive environment for discussion under this combined approach. In addition, Android module-based inquiry flipped classroom learning can iJIM ‒ Vol. 16, No. 24, 2022 41 Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… be implemented in K-12 or higher education institutions in other countries and cul- tures, with both introverted and extroverted students. 6 Acknowledgment The authors would like to thank the Research Institutes and Community Service (LPPM), Universitas Negeri Jakarta, and the Directorate General of Higher Educa- tion, Ministry of Education, Culture, Research, and Technology Indonesia which has provided funds in the Doctoral Dissertation Research Scheme. 7 References [1] F. Erdogan and F. Yildiz, “Investigation of Pre-Service Mathematics Teachers’ Creative Thinking Tendencies.,” Int. Online J. Educ. Teach., vol. 8, no. 4, pp. 2297–2316, 2021, https://eric.ed.gov/?id=EJ1318733 [2] M. Santos-Trigo, “Problem-Solving in Mathematics Education BT - Encyclopedia of Mathematics Education,” S. Lerman, Ed. Cham: Springer International Publishing, 2020, pp. 686–693. https://doi.org/10.1007/978-3-030-15789-0_129 [3] H. W. Afdal, “‘Research-based’ and ‘profession-oriented’ as prominent knowledge discourses in curriculum restructuring of professional programs,” High. Educ., vol. 74, no. 3, pp. 401–418, 2017, https://doi.org/10.1007/s10734-016-9998-7 [4] K. Spernes and H. W. Afdal, “Scientific methods assignments as a basis for developing a profession-oriented inquiry-based learning approach in teacher education,” Eur. J. Teach. Educ., pp. 1–15, May 2021, https://doi.org/10.1080/02619768.2021.1928628 [5] R. D. Siswantoa, A. M. Hildab, and E. Azharc, “Development combinatorics realistic mathematics education application based on the android mobile,” Development, vol. 5, no. 6, 2019, https://www.ijicc.net/index.php/volume-5-2019/178-vol-5-iss-6 [6] S. Papadakis and M. Kalogiannakis, Eds., Mobile Learning Applications in Early Childhood Education. IGI Global, 2019. https://doi.org/10.4018/978-1-7998-1486-3 [7] L. Lisana and M. F. Suciadi, “The Acceptance of Mobile Learning: A Case Study of 3D Simulation Android App for Learning Physics,” Int. J. Interact. Mob. Technol., vol. 15, no. 17, pp. 205–214, 2021, https://doi.org/10.3991/ijim.v15i17.23731 [8] H. H. Batubara, M. S. Sumantri, and A. Marini, “Developing an Android-Based E- Textbook to Improve Learning Media Course Outcomes,” Int. J. Interact. Mob. Technol., vol. 16, no. 17, pp. 4–19, Sep. 2022, https://doi.org/10.3991/ijim.v16i17.33137 [9] M. Drolia, E. Sifaki, S. Papadakis, and M. Kalogiannakis, “An Overview of Mobile Learning for Refugee Students: Juxtaposing Refugee Needs with Mobile Applications’ Characteristics,” Challenges, vol. 11, no. 2, p. 31, 2020, https://doi.org/10.3390/challe1102 0031 [10] S. Papadakis, “The impact of coding apps to support young children in computational thinking and computational fluency. A literature review,” Frontiers in Education, 6, 657895. https://doi.org/10.3389/feduc.2021.657895 [11] N. Nurhasanah, S. Masitoh, F. Arianto, and N. Ayubi, “Development of Android Application-Based Early Childhood Learning Devices (PAUDPEDIA) During the COVID-19 Pandemic,” Int. J. Interact. Mob. Technol., vol. 16, no. 09, pp. 231–238, May 2022, https://doi.org/10.3991/ijim.v16i09.31703 42 http://www.i-jim.org https://eric.ed.gov/?id=EJ1318733 https://doi.org/10.1007/978-3-030-15789-0_129 https://doi.org/10.1007/s10734-016-9998-7 https://doi.org/10.1080/02619768.2021.1928628 https://www.ijicc.net/index.php/volume-5-2019/178-vol-5-iss-6 https://doi.org/10.4018/978-1-7998-1486-3 https://doi.org/10.3991/ijim.v15i17.23731 https://doi.org/10.3991/ijim.v16i17.33137 https://doi.org/10.3390/challe11020031 https://doi.org/10.3390/challe11020031 https://doi.org/10.3389/feduc.2021.657895 https://doi.org/10.3991/ijim.v16i09.31703 Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… [12] Asmianto, M. Hafiizh, D. Rahmadani, K. Pusawidjayanti, and S. Wahyuningsih, “Developing Android-Based Interactive E-Modules on Trigonometry to Enhance the Learning Motivation of Students,” Int. J. Interact. Mob. Technol., vol. 16, no. 02, pp. 159– 170, Jan. 2022, https://doi.org/10.3991/ijim.v16i02.27503 [13] D. Handayani, E. Elvinawati, I. Isnaeni, and M. Alperi, “Development Of Guided Discovery Based Electronic Module For Chemical Lessons In Redox Reaction Materials,” Int. J. Interact. Mob. Technol., vol. 15, no. 07, p. 94, Apr. 2021, https://doi.org/10.3991/ ijim.v15i07.21559 [14] Sutarto, A. Muzaki, I. D. Hastuti, S. Fujiaturrahman, and Z. Untu, “Development of an Ethnomathematics-Based e-Module to Improve Students’ Metacognitive Ability in 3D Geometry Topic,” Int. J. Interact. Mob. Technol., vol. 16, no. 03, pp. 32–46, Feb. 2022, https://doi.org/10.3991/ijim.v16i03.24949 [15] X. Wei et al., “Effect of the flipped classroom on the mathematics performance of middle school students,” Educ. Technol. Res. Dev., vol. 68, no. 3, pp. 1461–1484, 2020, https:// doi.org/10.1007/s11423-020-09752-x [16] S.-C. Cheng, G.-J. Hwang, and C.-L. Lai, “Critical research advancements of flipped learning: a review of the top 100 highly cited papers,” Interact. Learn. Environ., pp. 1–17, May 2020, https://doi.org/10.1080/10494820.2020.1765395 [17] N. T. T. Thai, B. De Wever, and M. Valcke, “Feedback: an important key in the online environment of a flipped classroom setting,” Interact. Learn. Environ., pp. 1–14, Sep. 2020, https://doi.org/10.1080/10494820.2020.1815218 [18] Y. Zengin, “Investigating the use of the Khan Academy and mathematics software with a flipped classroom approach in mathematics teaching,” J. Educ. Technol. Soc., vol. 20, pp. 89–100, 2017, https://www.jstor.org/stable/90002166 [19] L. Zhao, X. Liu, and Y.-S. Su, “The Differentiate Effect of Self-Efficacy, Motivation, and Satisfaction on Pre-Service Teacher Students’ Learning Achievement in a Flipped Classroom: A Case of a Modern Educational Technology Course,” Sustainability, vol. 13, no. 5, p. 2888, Mar. 2021, https://doi.org/10.3390/su13052888 [20] M. Jahr, “Teaching Mathematical Modelling and Programming with GAMS in Dual Management Master Curricula Using Flipped Classrooms and Open Book Exams,” in Operations Research Forum, 2022, vol. 3, no. 3, pp. 1–12. https://doi.org/10.1007/s43069- 022-00162-8 [21] F. M. Zain, S. N. Sailin, and N. A. Mahmor, “Promoting Higher Order Thinking Skills among Pre-Service Teachers through Group-Based Flipped Learning,” Int. J. Instr., vol. 15, no. 3, pp. 519–542, Jul. 2022, https://doi.org/10.29333/iji.2022.15329a [22] J. He, “Research and practice of flipped classroom teaching mode based on guidance case,” Educ. Inf. Technol., vol. 25, no. 4, pp. 2337–2352, 2020, https://doi.org/10.1007/ s10639-020-10137-z [23] C. K. Lo and K. F. Hew, “A critical review of flipped classroom challenges in K-12 education: possible solutions and recommendations for future research,” Res. Pract. Technol. Enhanc. Learn., vol. 12, no. 1, p. 4, Dec. 2017, https://doi.org/10.1186/s41039- 016-0044-2 [24] L. Zheng, K. K. Bhagat, Y. Zhen, and X. Zhang, “The effectiveness of the flipped classroom on students’ learning achievement and learning motivation,” J. Educ. Technol. Soc., vol. 23, no. 1, pp. 1–15, 2020, https://www.jstor.org/stable/26915403 [25] B. Love, A. Hodge, C. Corritore, and D. C. Ernst, “Inquiry-Based Learning and the Flipped Classroom Model,” PRIMUS, vol. 25, no. 8, pp. 745–762, Sep. 2015, https://doi. org/10.1080/10511970.2015.1046005 iJIM ‒ Vol. 16, No. 24, 2022 43 https://doi.org/10.3991/ijim.v16i02.27503 https://doi.org/10.3991/ijim.v15i07.21559 https://doi.org/10.3991/ijim.v15i07.21559 https://doi.org/10.3991/ijim.v16i03.24949 https://doi.org/10.1007/s11423-020-09752-x https://doi.org/10.1007/s11423-020-09752-x https://doi.org/10.1080/10494820.2020.1765395 https://doi.org/10.1080/10494820.2020.1815218 https://www.jstor.org/stable/90002166 https://doi.org/10.3390/su13052888 https://doi.org/10.1007/s43069-022-00162-8 https://doi.org/10.1007/s43069-022-00162-8 https://doi.org/10.29333/iji.2022.15329a https://doi.org/10.1007/s10639-020-10137-z https://doi.org/10.1007/s10639-020-10137-z https://doi.org/10.1186/s41039-016-0044-2 https://doi.org/10.1186/s41039-016-0044-2 https://www.jstor.org/stable/26915403 https://doi.org/10.1080/10511970.2015.1046005 https://doi.org/10.1080/10511970.2015.1046005 Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… [26] J. Kerrigan, “Productive failure in the flipped mathematics classroom (dissertation),” Rutgers, The State University of New Jersey, 2018. https://doi.org/10.7282/T3QV3QX5 [27] Y. Song and M. Kapur, “How to Flip the Classroom – ‘Productive Failure or Traditional Flipped Classroom’ Pedagogical Design?,” Journal of Educational Technology & Society, vol. 20. International Forum of Educational Technology & Society, pp. 292–305, 2017. https://www.jstor.org/stable/jeductechsoci.20.1.292 [28] S. Schallert, Z. Lavicza, and E. Vandervieren, “Towards Inquiry-Based Flipped Classroom Scenarios: a Design Heuristic and Principles for Lesson Planning,” Int. J. Sci. Math. Educ., pp. 1–21, 2021, https://doi.org/10.1007/s10763-021-10167-0 [29] H. Sharkia and Z. Kohen, “Implementing the 5E inquiry model in an online platform of a flipped classroom environment,” 2022. https://hal.archives-ouvertes.fr/hal-03747804 [30] K. Wang, C. Zhu, S. Li, and G. Sang, “Using revised community of inquiry framework to scaffold MOOC-based flipped learning,” Interact. Learn. Environ., pp. 1–13, May 2022, https://doi.org/10.1080/10494820.2022.2071948 [31] B. Love, A. Hodge, C. Corritore, and D. C. Ernst, “Inquiry-Based Learning and the Flipped Classroom Model,” PRIMUS, vol. 25, no. 8, pp. 745–762, Sep. 2015, https://doi. org/10.1080/10511970.2015.1046005 [32] K. L. Purwanti and M. Mujiasih, “Kemampuan Literasi Matematika Siswa Madrasah Ibtidaiyah Ditinjau Dari Self-Efficacy,” J. Integr. Elem. Educ., vol. 1, no. 1, pp. 50–65, Mar. 2021, https://doi.org/10.21580/jieed.v1i1.6975 [33] R. Rasmitadila, R. Rachmadtullah, A. Samsudin, A. R. S. Tambunan, E. E. Khairas, and M. Nurtanto, “The Benefits of Implementation of an Instructional Strategy Model Based on the Brain’s Natural Learning Systems in Inclusive Classrooms in Higher Education,” Int. J. Emerg. Technol. Learn., vol. 15, no. 18, p. 53, Sep. 2020, https://doi.org/10.3991/ ijet.v15i18.14753 [34] Rasmitadila and R. Rachmadtullah, “Using of Jarimatika counting method (JCM) to slow learner students in a mathematics lesson,” J. Phys. Conf. Ser., vol. 1175, p. 012141, Mar. 2019, https://doi.org/10.1088/1742-6596/1175/1/012141 [35] T. García, J. Boom, E. H. Kroesbergen, J. C. Núñez, and C. Rodríguez, “Planning, execution, and revision in mathematics problem solving: Does the order of the phases matter?,” Stud. Educ. Eval., vol. 61, pp. 83–93, Jun. 2019, https://doi.org/10.1016/ j.stueduc.2019.03.001 [36] S. Osman, C. N. A. Che Yang, M. S. Abu, N. Ismail, H. Jambari, and J. A. Kumar, “Enhancing Students’ Mathematical Problem-Solving Skills through Bar Model Visualisation Technique,” Int. Electron. J. Math. Educ., vol. 13, no. 3, pp. 273–279, Oct. 2018, https://doi.org/10.12973/iejme/3919 [37] Rasmitadila, Widyasari, M. A. Humaira, A. R. S. Tambunan, R. Rachmadtullah, and A. Samsudin, “Using blended learning approach (BLA) in inclusive education course: A study investigating teacher students’ perception,” Int. J. Emerg. Technol. Learn., vol. 15, no. 2, 2020, https://doi.org/10.3991/ijet.v15i02.9285 [38] L. L. Hadar and M. Tirosh, “Creative thinking in mathematics curriculum: An analytic framework,” Think. Ski. Creat., vol. 33, p. 100585, Sep. 2019, https://doi.org/10.1016/ j.tsc.2019.100585 [39] A. Perry and E. Karpova, “Efficacy of teaching creative thinking skills: A comparison of multiple creativity assessments,” Think. Ski. Creat., vol. 24, pp. 118–126, Jun. 2017, https://doi.org/10.1016/j.tsc.2017.02.017 [40] H. A. Alismail and P. McGuire, “21st century standards and curriculum: Current research and practice.,” J. Educ. Pract., vol. 6, no. 6, pp. 150–154, 2015, https://eric.ed.gov/?id= EJ1083656 44 http://www.i-jim.org https://doi.org/10.7282/T3QV3QX5 https://www.jstor.org/stable/jeductechsoci.20.1.292 https://doi.org/10.1007/s10763-021-10167-0 https://hal.archives-ouvertes.fr/hal-03747804 https://doi.org/10.1080/10494820.2022.2071948 https://doi.org/10.1080/10511970.2015.1046005 https://doi.org/10.1080/10511970.2015.1046005 https://doi.org/10.21580/jieed.v1i1.6975 https://doi.org/10.3991/ijet.v15i18.14753 https://doi.org/10.3991/ijet.v15i18.14753 https://doi.org/10.1088/1742-6596/1175/1/012141 https://doi.org/10.1016/j.stueduc.2019.03.001 https://doi.org/10.1016/j.stueduc.2019.03.001 https://doi.org/10.12973/iejme/3919 https://doi.org/10.3991/ijet.v15i02.9285 https://doi.org/10.1016/j.tsc.2019.100585 https://doi.org/10.1016/j.tsc.2019.100585 https://doi.org/10.1016/j.tsc.2017.02.017 https://eric.ed.gov/?id=EJ1083656 https://eric.ed.gov/?id=EJ1083656 Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… [41] J. Sitorus and Masrayati, “Students’ creative thinking process stages: Implementation of realistic mathematics education,” Think. Ski. Creat., vol. 22, pp. 111–120, Dec. 2016, https://doi.org/10.1016/j.tsc.2016.09.007 [42] A. Field, Discovering Statistics Using IBM SPSS Statistics, Fifth Edit. London: Sage Publications Ltd, 2018. https://books.google.co.id/books?id=c0Wk9IuBmAoC&printsec= frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false [43] G. Pólya and J. H. Conway, How to solve it: A new aspect of mathematical method. Princeton University Press Princeton, 2011. https://books.google.co.id/books?id=z_hsbu 9kyQQC&dq=How+to+solve+it:+A+new+aspect+of+mathematical+method&lr=&source =gbs_navlinks_s [44] H. Nufus and M. Duskri, “Mathematical Creative Thinking and Student Self-Confidence in the Challenge-Based Learning Approach.,” J. Res. Adv. Math. Educ., vol. 3, no. 2, pp. 57–68, 2018, https://doi.org/10.23917/jramathedu.v3i2.6367 [45] M. Sahliawati and E. Nurlaelah, “Mathematical creative thinking ability in middle school students’,” in Journal of Physics: Conference Series, 2020, vol. 1469, no. 1, p. 12145. https://doi.org/10.1088/1742-6596/1469/1/012145 [46] J. S. Kozlowski, S. A. Chamberlin, and E. Mann, “Factors that Influence Mathematical Creativity,” Math. Enthus., vol. 16, no. 1–3, pp. 505–540, Feb. 2019, https://doi.org/ 10.54870/1551-3440.1471 [47] M. Schindler and A. J. Lilienthal, “Students’ creative process in mathematics: insights from eye-tracking-stimulated recall interview on students’ work on multiple solution tasks,” Int. J. Sci. Math. Educ., vol. 18, no. 8, pp. 1565–1586, 2020, https://doi.org/ 10.1007/s10763-019-10033-0 [48] R. Leikin and H. Elgrably, “Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers,” Int. J. Educ. Res., vol. 102, p. 101424, 2020, https://doi.org/ 10.1016/j.ijer.2019.04.002 [49] M. Duran and İ. Dökme, “The effect of the inquiry-based learning approach on student’s critical-thinking skills,” Eurasia J. Math. Sci. Technol. Educ., vol. 12, no. 12, pp. 2887– 2908, 2016. https://doi.org/10.12973/eurasia.2016.02311a [50] G. Hwang and C. Chen, “Influences of an inquiry-based ubiquitous gaming design on students’ learning achievements, motivation, behavioral patterns, and tendency towards critical thinking and problem solving,” Br. J. Educ. Technol., vol. 48, no. 4, pp. 950–971, Jun. 2017, https://doi.org/10.1111/bjet.12464 [51] Á. Suárez, M. Specht, F. Prinsen, M. Kalz, and S. Ternier, “A review of the types of mobile activities in mobile inquiry-based learning,” Comput. Educ., vol. 118, pp. 38–55, Mar. 2018, https://doi.org/10.1016/j.compedu.2017.11.004 [52] J.-C. Hong et al., “The effect of the ‘Prediction-observation-quiz-explanation’ inquiry- based e-learning model on flow experience in green energy learning,” Comput. Educ., vol. 133, pp. 127–138, May 2019, https://doi.org/10.1016/j.compedu.2019.01.009 [53] C. Santhanasamy and M. M. Yunus, “A Systematic Review of Flipped Learning Approach in Improving Speaking Skills.,” Eur. J. Educ. Res., vol. 11, no. 1, pp. 127–139, 2022, https://doi.org/10.12973/eu-jer.11.1.127 [54] F. Jafarkhani and Z. Jamebozorg, “Comparing Cooperative Flipped Learning with Individual Flipped Learning in a Biochemistry Course.,” J. Med. Life, vol. 13, no. 3, pp. 399–403, 2020, https://doi.org/10.25122/jml-2019-0149 [55] A. Dierdorp, “Evidence-Informed Teaching: Investigating Whether Evidence from ‘Flipping the Classroom’ Research Improves Students’ Motivation for Mathematics,” Education Sciences , vol. 11, no. 6. 2021. https://doi.org/10.3390/educsci11060257 iJIM ‒ Vol. 16, No. 24, 2022 45 https://doi.org/10.1016/j.tsc.2016.09.007 https://books.google.co.id/books?id=c0Wk9IuBmAoC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false https://books.google.co.id/books?id=c0Wk9IuBmAoC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false https://books.google.co.id/books?id=z_hsbu9kyQQC&dq=How+to+solve+it:+A+new+aspect+of+mathematical+method&lr=&source=gbs_navlinks_s https://books.google.co.id/books?id=z_hsbu9kyQQC&dq=How+to+solve+it:+A+new+aspect+of+mathematical+method&lr=&source=gbs_navlinks_s https://books.google.co.id/books?id=z_hsbu9kyQQC&dq=How+to+solve+it:+A+new+aspect+of+mathematical+method&lr=&source=gbs_navlinks_s https://doi.org/10.23917/jramathedu.v3i2.6367 https://doi.org/10.1088/1742-6596/1469/1/012145 https://doi.org/10.54870/1551-3440.1471 https://doi.org/10.54870/1551-3440.1471 https://doi.org/10.1007/s10763-019-10033-0 https://doi.org/10.1007/s10763-019-10033-0 https://doi.org/10.1016/j.ijer.2019.04.002 https://doi.org/10.1016/j.ijer.2019.04.002 https://doi.org/10.12973/eurasia.2016.02311a https://doi.org/10.1111/bjet.12464 https://doi.org/10.1016/j.compedu.2017.11.004 https://doi.org/10.1016/j.compedu.2019.01.009 https://doi.org/10.12973/eu-jer.11.1.127 https://doi.org/10.25122/jml-2019-0149 https://doi.org/10.3390/educsci11060257 Paper—The Impact of Android Module-Based Inquiry Flipped Classroom Learning on Mathematics… [56] M. Cevikbas and G. Kaiser, “Flipped classroom as a reform-oriented approach to teaching mathematics,” ZDM, vol. 52, no. 7, pp. 1291–1305, 2020, https://doi.org/10.1007/s11858- 020-01191-5 [57] S. Kaeophanuek and N. Chookerd, “A Development of the Flipped Learning Model Using the Critical Inquiry Process to Enhance Research Skills,” Int. Assoc. Online Eng., 2021, https://doi.org/10.3991/ijim.v15i03.17905 [58] N. Adhami and M. Taghizadeh, “Integrating inquiry-based learning and computer supported collaborative learning into flipped classroom: effects on academic writing performance and perceptions of students of railway engineering,” Comput. Assist. Lang. Learn., pp. 1–37, May 2022, https://doi.org/10.1080/09588221.2022.2046107 [59] N. Phurikultong and S. Tuntiwongwanich, “Using digital storytelling to enhance Thai student analytical thinking and learning achievement by use of a flipped classroom environment model and inquiry-based learning (IBL),” PalArch’s J. Archaeol. Egypt/Egyptology, vol. 18, no. 4, pp. 1829–1848, 2021, https://archives.palarch.nl/index. php/jae/article/view/6595 [60] S. Koes-H., F. S. Putri, E. Purwaningsih, and A. Y. Salim, “The influence of flipped classroom in inquiry learning to student’s critical thinking skills in impulse and momentum,” in AIP Conference Proceedings, 2020, vol. 2215, no. 1, p. 050008. https://doi.org/10.1063/5.0000503 8 Authors Dessy Noor Ariani is a doctoral student in Elementary Education at Universitas Negeri Jakarta, Jakarta, Indonesia. Her research focuses on elementary education teacher training and mathematics education (ORCID 0000-0002-1227-9307. email: dessynoorarianii@gmail.com). Mohamad Syarif Sumantri is a lecturer and head of the Elementary Education Doctoral Program at the Universitas Negeri Jakarta, Jakarta, Indonesia. His research focuses on elementary school educational technology, instructional media, and learn- ing strategy (email: syarifsumantri@unj.ac.id). Firmanul Catur Wibowo is a lecturer in the physics education program at the Universitas Negeri Jakarta, Jakarta, Indonesia. His research focuses on physics educa- tion, STEM, and educational technology (email: fcwibowo@unj.ac.id). Article submitted 2022-09-01. Resubmitted 2022-10-23. Final acceptance 2022-10-23. Final version published as submitted by the authors. 46 http://www.i-jim.org https://doi.org/10.1007/s11858-020-01191-5 https://doi.org/10.1007/s11858-020-01191-5 https://doi.org/10.3991/ijim.v15i03.17905 https://doi.org/10.1080/09588221.2022.2046107 https://archives.palarch.nl/index.php/jae/article/view/6595 https://archives.palarch.nl/index.php/jae/article/view/6595 https://doi.org/10.1063/5.0000503 mailto:dessynoorarianii@gmail.com mailto:syarifsumantri@unj.ac.id mailto:fcwibowo@unj.ac.id