International Journal of Interactive Mobile Technologies (iJIM) – eISSN: 1865-7923 – Vol. 15, No. 08, 2021 Paper—The Effect of Online Project-Based Learning Application on Mathematics Students' Visual … The Effect of Online Project-Based Learning Application on Mathematics Students' Visual Thinking Continuum in Covid-19 Pandemic https://doi.org/10.3991/ijim.v15i08.21565 Sapti Wahyuningsih (*), Abd. Qohar, Darmawan Satyananda Universitas Negeri Malang, Java, Indonesia sapti.wahyuningsih.fmipa@um.ac.id Noor Azean Atan Universiti Teknologi Malaysia, Johor, Malaysia Abstract—The COVID-19 pandemic led to the implementation of the Work from Home (WFH) policy. The impact of this policy is to replace the process of teaching and learning activities by using an online learning system. In this in- dustrial era 4.0, the integration of web applications is very much needed in problem-solving learning. One that can be used to integrate web applications in learning through project-based learning. The focus of this research is to study the effects of online project-based learning applications on mathematics stu- dents' visual thinking continuum. Instruments used in the form of rubric virtual mind maps, audio-visual and virtual posters are used to observe students' visual thinking continuum. The instrument was analyzed with the Rasch measurement model software named WINSTEPS. This study used one group pretest-posttest design to see the effect of integrating web applications in learning through pro- ject-based learning analyzed using SPSS. The results of instrument analysis for rubric virtual mind maps, audio-visual products, and virtual posters on measure person obtained good person reliability, MNSQ infit, and MNSQ OUTFIT the average rating is very good. For the ZSTD infit and the ZSTD outfit, the aver- age value is close to 0.0 so that the quality of the person's reliability is good. The results of the conformity quality of the items with the model studied from the fit order items obtained the value of Outfit mean square (MNSQ), Outfit Z- standard (ZSTD), and the value of Point Measure Correlation (Pt Mean Corr) for the three instruments met good criteria. The results of the analysis of paired samples test from 54 respondents obtained p <0.05 so that the base learning project has the effect of increasing students' visual thinking continuum. Imple- mentation of online project-based learning in mathematics learning is an alter- native that can be used to improve students' creative problem-solving skills in online learning. Keywords—Project-based learning, visual thinking, visual learning, visual communication, and Rasch measurement model 4 http://www.i-jim.org Paper—The Effect of Online Project-Based Learning Application on Mathematics Students' Visual … 1 Introduction 1.1 Background The existence of the COVID-19 pandemic led to the implementation of the Work From Home (WFH) policy. This policy is an attempt by the government with the goal that the public conduct physical distancing, to reduce the spread of COVID-19. Edu- cation in Indonesia has also become one of the areas affected by the COVID-19 pan- demic. The Ministry of Education in Indonesia issued a policy by dismissing schools and universities and replacing the teaching and learning process by using an online learning system. Not only in Indonesia, but had the impact of this pandemic also felt in other countries. Italy utilizes virtual teaching policies on campus [1], just as the adaptation of education and training in medicine in the Department of Medicine, Pe- relman School of Medicine at the University of Pennsylvania [2]. The impact of increasingly sophisticated technology disruption and the demand for online learning, forcing students and teachers to master the technology that supports the learning system. This requires the support of the adaptation of learning strategies. Some of them can be seen in New Zealand that use blended learning [3], virtual learn- ing in Harvard Medical School [4], online use of modules to teach nursing students [5], online learning in developed countries [6] examined elementary teachers' use of online learning [7], [8], and online education [9]. Adaptation of learning strategies for mastering concepts online can use mind maps. Some related research discusses mind maps, such as mind mapping in the learning models [10], e-learning in mind maps of the Czech and Kazakhstan universities [11], and the use of virtual mind mapping [12]. The effectiveness of mind maps in educa- tion can be seen in [13]–[19]. The mind map is a visual thinking application that has an important role in learning mathematics. Creativity and visual thinking contribute to the learning of mathematics. This can be seen in [20], creative problems with visual thinking in [21], and the implementation of creative and visual media problems in schools [22]. Subsequent research developed from visual thinking to the visual thinking continu- um. A discussion of the visual thinking continuum can be seen in [23]. The visual thinking continuum on the implementation of learning includes visual thinking, visual learning, and visual communication. Some studies on visual learning for example [24] – [27]. Visual learning has an important role in learning, applied in the form of audio- visual media. In addition to visual thinking and visual learning, visual communication also has an important role. Some studies on visual communication for example [28]– [31]. Visual communication applications in this study can be in the form of posters that can facilitate the delivery of problem-solving. This can be seen in several studies [8], [32] – [34]. In the era of the industrial revolution, 4.0 web application integration is needed in the learning process of problem-solving. One learning model that can be integrated with web applications is project-based learning (PBL). This learning model can help students to have creative thinking, sharpen problem-solving skills, practice interact- ing, and assist in investigations that lead to solving real problems. The focus of learn- iJIM ‒ Vol. 15, No. 08, 2021 5 Paper—The Effect of Online Project-Based Learning Application on Mathematics Students' Visual … ing involves students in problem-solving investigations and activities of meaningful tasks that have great potential to provide a more interesting and meaningful learning experience for students. Some previous studies on project-based learning development can be seen in [35] – [42]. PBL has a positive effect on learning and its results, this can be seen in [43] – [45]. Researches on linking PBL with ICT are in [46] – [49]. While research on the combination of online learning with project base learning is discussed by [47],[49] – [51]. Through the teaching and learning process, student creativity can be nurtured and developed in facing problems solving problems. The characteristics of the graph theory application course can be applied to real problems. The choice of the PBL model is following the characteristics of this course. Based on the positive impact of the PBL and the characteristics of the course, the PBL model is implemented in learning the application of graph theory. Students determine projects that are solved by conducting field surveys in relevant industries or institu- tions. E-project products made by students in the form of virtual mind maps, audio- visuals, and virtual posters are discussed in this article. Rasch model is used to ana- lyze the quality of the instruments. 1.2 Literature review Virtual mind maps as the implementation of visual thinking is needed in identify- ing and understanding the structure of the subject, presenting an overall picture of something in a shorter time, improving recording information speed, supporting and improving creative problem-solving. Each virtual mind maps is very unique that easy to remember and deliver brief information because it only uses keywords. Students design virtual mind maps in working on projects shared online using mobile devices. Previous studies that support this opinion are [10] – [12], [16], [17], [19]. Visual learning is implemented by audio-visual media. Media that displays motion is informative, educative, and instructional, which provide meaningful experiences, aside to develop and expand the horizons of critical thinking. Previous studies that support this opinion are [24]– [27], [52], and [53]. The virtual poster is one form of visual communication. The virtual poster is illus- trations of simplified object images so that they can highlight the power of messages and visuals, using colors to express the idea of a particular fact or event. Students design the virtual poster in working on projects shared online using mobile devices. Some studies that support this opinion are [30], [33], [34]. 2 Research Objectives To know the effect of online project-based learning on the Application of Graph Theory course, research objectives: 1). Analyze the visual thinking continuum in- strument using the Rasch measurement model, 2). To examine the effects of online project-based learning on students' visual thinking continuum. 6 http://www.i-jim.org Paper—The Effect of Online Project-Based Learning Application on Mathematics Students' Visual … 3 Research Methodology 3.1 Research design The goal of the Application of Graph Theory course is for students can make a problem-solving project by applying a concept in graph theory. Data on the problem is a real problem taken from field surveys in the industry. The product of this e- project is in the form of virtual mind maps to describe concepts and problems, audio- visual products of problems and solutions, and virtual posters to communicate project results. The purpose of this research is to explore aspects of planning, designing, analyzing, developing, implementing, and evaluating students' visual thinking contin- uum process in completing projects of this course. The qualitative approach in this study is used to analyze aspects of visual thinking, visual learning, and visual communication of student projects. The quantitative ap- proach in this study used one group pretest-posttest design to see the effect of inte- grating web applications in learning through project-based learning. 3.2 Participants Participants of this study are 54 students of the mathematics department (6th se- mester) taking courses in the Application of Graph Theory in even semester 2019- 2020. There are two classes, namely TE1 (24 students) and TE2 (30 students). 3.3 Measurement instrument The instruments used in this study are the assessment rubric of the virtual mind maps media, audio-visual media, and virtual poster media. The results of each rubric are analyzed by the Rasch measurement model using WINSTEPS software. The re- sults of summary statistics from the Rasch model provide information about the quali- ty of the instruments and the quality of the student's response patterns to the instru- ments. Meanwhile, the level of conformity of items with the model is examined from the fit order item. The use of the Rash model can be seen in [54]–[59] and [60] 4 Results / Findings Examples of e-projects in the form of virtual mind maps of student designs are shown in Figure 1 and examples of products in the form of virtual posters are shown in Figure 2. iJIM ‒ Vol. 15, No. 08, 2021 7 Paper—The Effect of Online Project-Based Learning Application on Mathematics Students' Visual … Fig. 1. Examples of student mind map products Fig. 2. Examples of student poster products The following is a summary of statistics in the form of a measured person to see the quality of student response patterns and misfit orders to see the suitability of the measurement model. Table 1. Measured Person Mind maps and Table 2 Misfit Order Mind maps are the Rasch modeling analysis results for the mind maps rubric. Table 3. Measured Person Audio-visual, and Table 4. Misfit Order Audiovisual is the Rasch modeling analysis results for the audiovisual rubric. Table 5. Measured Person Poster and Table 6. Misfit Order Poster is the Rasch modeling analysis results for the poster rubric. 8 http://www.i-jim.org Paper—The Effect of Online Project-Based Learning Application on Mathematics Students' Visual … Table 1. Measured Person Mind maps MEASURE INFIT OUTFIT MNSQ ZSTD MNSQ ZSTD MEAN 1.66 0.98 0.05 0.98 0.06 SEM .42 0.02 0.05 0.02 0.05 P.SD 3.07 0.15 0.34 0.16 0.37 S.SD 3.10 0.15 0.35 0.16 0.37 MAX 5.18 1.09 0.51 1.17 0.54 MIN -3.38 0.00 -1.45 0.00 -1.45 REAL RMSE Person RELIABILITY 0.89 Table 2. Misfit Order Mind maps Entry Number TOTAL COUNT MEASURE INFITMNSQ ZSTD OUTFIT MNSQ ZSTD PT MEASURE CORR. Item 3 54 0.11 1.05 0.53 1.05 0.35 0.61 K3 5 54 0.19 1.03 0.34 1.05 0.38 0.72 K5 4 54 0.02 1.01 0.11 1.02 0.17 0.54 K4 2 54 -0.16 1.01 0.14 1.00 0.07 0.66 K2 1 54 -0.16 0.83 1.53 0.78 1.40 0.66 K1 MEAN 54.0 0.00 0.99 - 0.1 0.98 -0.1 P.SD 0.0 0.14 0.08 0.7 0.10 0.7 Table 3. Measured Person Audiovisual MEASURE INFIT OUTFIT MNSQ ZSTD MNSQ ZSTD MEAN 1.68 0.98 0.06 0.97 0.06 SEM 0.41 0.02 0.06 0.02 0.06 P.SD 2.95 0.15 0.41 0.16 0.43 S.SD 2.98 0.15 0.41 0.16 0.43 MAX 4.42 1.09 0.79 1.12 0.80 MIN -3.72 0.00 -1.43 0.00 -1.43 REAL RMSE Person RELIABILITY 0.90 Table 4. Misfit Order Audiovisual Entry Number TOTAL COUNT MEASURE INFIT MNSQ ZSTD OUTFIT MNSQ ZSTD PT MEASURE CORR. Item 3 54 0.00 1.10 1.13 1.06 0.45 0.54 C3 4 54 0.25 1.10 1.07 1.06 0.47 0.55 C4 2 54 0.00 1.05 0.56 1.06 0.50 0.69 C2 5 54 -0.08 0.93 0.72 0.95 0.32 0.64 C5 6 54 -0.25 0.91 -1.01 0.87 0.94 0.68 C6 1 54 0.08 0.85 -1.64 0.83 -1.22 0.64 C1 MEAN 54.0 0.00 0.99 -0.1 0.97 -0.2 P.SD 0.0 0.15 0.10 1.1 0.09 0.7 iJIM ‒ Vol. 15, No. 08, 2021 9 Paper—The Effect of Online Project-Based Learning Application on Mathematics Students' Visual … Table 5. Measured Person Poster MEASURE INFIT OUTFIT MNSQ ZSTD MNSQ ZSTD MEAN 0.56 0.97 0.04 0.97 0.03 SEM 0.45 0.02 0.07 0.03 0.08 P.SD 3.28 0.17 0.52 0.18 0.55 S.SD 3.31 0.18 0.53 0.19 0.56 MAX 3.91 1,19 0.94 1.22 1.02 MIN -3.91 0.00 -1.35 0.00 -1.35 REAL RMSE Person RELIABILITY 0.91 Table 6. Misfit Order Poster Entry Number TOTAL COUNT MEASURE INFIT MNSQ ZSTD OUTFIT MNSQ ZSTD PT MEASURE CORR. Ite m 2 54 -0.15 1.09 1.15 1.08 0.69 0.66 K2 4 54 -0.15 1.06 0.79 1.04 0.33 0.57 K4 1 54 0.02 1.04 0.46 1.01 0.15 0.77 K1 3 54 0.43 0.92 -0.83 0.88 -0.87 0.71 K3 5 54 -0.15 0.84 -2.09 0.83 -1.45 0.75 K5 MEAN 54.0 0.00 0.99 -0.1 0.97 -0.2 P.SD 0.0 0.22 0.10 1.2 0.09 0.8 To see the effect of integrating web applications in learning through project-based learning analyzed using one group pretest-posttest. The pretest and posttest data nor- mality test was performed with the Kolmogorov-Smirnov before performing the mean difference test for the pretest-posttest. Table 7 the results of the pretest and post-test normality test. The results of the mean difference test for the pretest-posttest are given in Table 8. The results of the analysis of paired samples test from 54 respondents obtained p <0.05 so that the base learning project has the effect of increasing students' visual thinking continuum. Table 7. Pretest and posttest normality Kolmogorov-Smirnov test Pretest Posttest N 54 54 Mean 79.1852 85.2778 Std. Deviation 2.21550 1.84715 Absolute .108 .144 Positive .097 .144 Negative -.108 -.115 Test Statistic .108 .144 Asymp. Sig. (2-tailed .167c .007c Test distribution is Normal Test distribution is Normal 10 http://www.i-jim.org Paper—The Effect of Online Project-Based Learning Application on Mathematics Students' Visual … 5 Discussions Table 8. The mean difference test Paired Differences t df Sig(2- tailed) Std Error mean 95% Confidence interval of the diff Mean S. D Lower Upper Pre-Post Test -6.093 1.533 0.209 -6.511 -6.511 -29.207 53 0.000 The Rasch measure model can be used to analyze instruments such as referring to previous research for validation [61] and [62], ability [57], and reliability level for each student's responses [58]. The results of measured persons for virtual mind mapss, audiovisuals, and virtual posters are shown in Table 1, Table 3, and Table 5. These results indicate the quality of student response patterns to the instrument. Person reli- ability criteria are shown in Table 9 refer to [63]. The results of the measured person for the virtual mind maps, audiovisual, and vir- tual poster are shown in Table 1, Table 3, and Table 5. These results indicate the qual- ity of student response patterns to the instrument. Person reliability criteria are shown in Table 9 below. Table 9. Criteria Person Reliability Criteria Person Reliability Poor <0.67 Fair 0.67 – 0.80 Good 0.81 – 0.90 Very Good 0.91 – 0.94 Excellent >0.94 From the person measure table, the person reliability value for the virtual mind maps is 0.89 (Good), the person reliability value for audiovisual is 0.90 (Good), the person reliability value for the virtual poster is 0.91 (Very Good). Other data that can be used to see the quality of student responses are the mean INFIT MNSQ, OUTFIT MNSQ with ideal criteria of 1.00, and mean INFIT ZSTD, OUTFIT ZSTD with ideal criteria of 0.0. In Table 1, for the virtual mind maps, the mean INFIT MNSQ and OUTFIT MNSQ is 0.98, the mean INFIT ZSTD is 0.05 and the mean OUTFIT ZSTD is 0.06. In Table 3, for the audiovisual, the mean INFIT MNSQ is 0.98 and mean OUTFIT MNSQ is 0.97, the mean INFIT ZSTD and OUTFIT ZSTD is 0.06. In Table 5, for the virtual poster, the mean INFIT MNSQ and OUTFIT MNSQ are 0.97, the mean INFIT ZSTD is 0.04 and the mean OUTFIT ZSTD is 0.03. The results of the Rash model analysis for the person measure show that the overall student response pattern is good. The results of the misfit orders for virtual mind maps, audiovisual, and virtual posters are shown in Table 2, Table 4, and Table 6. These results indicate the suitabil- ity level of the instrument with the ideal measurement model. The criteria for fit items are shown in Table 10 refer to [63]. iJIM ‒ Vol. 15, No. 08, 2021 11 Paper—The Effect of Online Project-Based Learning Application on Mathematics Students' Visual … Table 10. Criteria of the misfit orders Indikator Ideal criteria Infit Means Square (Infit MNSQ) 0.5 < Infit MNSQ < 1.5 Outfit Mean Square (outfit MNSQ) 0.5 < outfit MNSQ < 1.5 Infit Z-standard (infit ZSTD) -2.0 < infit ZSTD < +2.0 Outfit Z-standard (outfit ZSTD) -2.0 < outfit ZSTD < +2.0 Point measure correlation (Pt Measure Corr) 0.4 < Pt Measure Corr < 0.85 In Table 2, the mind maps misfit order can be seen that all items K1, K2, K3, K4, K5 fulfill 0.5