THE EFFECTIVENESS OF PROBLEMBASED LEARNING PHYSICS POCKETBOOK INTEGRATING AUGMENTED REALITY WITH THE LOCAL WISDOM OF CATAPULTS IN IMPROVING MATHEMATICAL AND GRAPHICAL REPRESENTATION ABILITIES
Yogyakarta State University (Indonesia)
Received October 2022
Accepted July 2023
Abstract
This research aimed to reveal the effectiveness of using a ProblemBased Learning (PBL) physics pocketbook integrating augmented reality (AR) with the local wisdom of catapults in improving the mathematical and graphical representation abilities of high school students. This study is a quasiâ€‘experiment with a pretestposttest control group design. The data collection was carried out in two stages, namely empirical testing and effectiveness testing stages. The empirical test was conducted on 276 grade XII students, while the effectiveness test was conducted on three science classes of grade XI students of State Senior High School (SMAN) 10 Yogyakarta. The three classes consisted of 36 students in the experimental class, 36 students in the Contrast Class 1, and 36 students in the Contrast 2 Class. The mathematical and graphical representation abilities were measured through a test instrument that passes the analysis of the empirical test using the QUEST program. General Linear Model (GLM) was utilized to analyze the effectiveness test, which was supported by the SPSS software. The result of the General Linear Model (GLM) analysis in the experimental class showed a significant value of 0.000 on the mathematical and graphical representation ability variables. The findings of this study indicate that the use of the developed ProblemBased Learning physics pocketbook integrating augmented reality with local wisdom is effective in increasing the mathematical and graphical representation abilities of grade XI students, with an effective contribution of 82.6% and 84.4% each.
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Keywords â€“ Augmented reality, Graphical representation, Local wisdom, Mathematical representation, PBL, Pocketbook.
To cite this article:
Rahmasari, A., & Kuswanto, H. (2023). The effectiveness of problembased learning physics pocketbook integrating augmented reality with the local wisdom of catapults in improving mathematical and graphical representation abilities. Journal of Technology and Science Education, 13(3), 886â€‘900. https://doi.org/10.3926/jotse.1962 
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1. Introduction

The world of education has a major effect on increasing the potential of human resources in a nationâ€™s civilization. This increase is being complemented by the advances in science and technology. The field of science plays an important role in the advancement of science and technology. Science is classified as basic and it is important to learn; through science, we can know the benefits and applications of anything around us. One component of science that is important to learn is physics (Anwar et al., 2019; Diani, Yuberti & Syarlisjiswan, 2018).
The importance of learning physics usually does not go according to expectations. Most students consider the field of physics to be very difficult to learn, especially at the high school level (Simanjuntak, Marpaung, Sinaga & Siregar, 2021). The difficulties in secondary school physics are usually found in the materials related to material elasticity, especially in the multirepresentation abilities of students (Jannah, Sarwanto & Sukarmin, 2019). Material elasticity is the basic concept of physics that is poorly mastered by students (Rosiqoh, Barus, Bohori & Suhendi, 2020; Saâ€™diyah, Sarwanto & Sukarmin, 2017). Research reveals that understanding of the concept of material elasticity is still low (Batlolona, Diantoro, Wartono & Latifah, 2019). The reason is none other than the difficulty of students in answering problems related to Hookeâ€™s law submaterials, the arrangement of springs, and the modulus of elasticity (Batlolona, Diantoro, Wartono & Leasa, 2020; Saâ€™diyah et al., 2017).
The above research findings are supported by another finding that shows that the percentage of students who answered correctly in Hookeâ€™s legal problems was only 4%, while the other 96% answered incorrectly (Mustofa, 2018). In the submaterial of the modulus of material elasticity, the percentage of success in answering was only 57% (Saâ€™diyah et al., 2017). The difficulty continues, especially in the mathematical and graphical representation abilities in the material elasticity. Usually, students tend not to answer the questions with graphical and mathematical representation indicators (Jannah et al., 2019; Rosiqoh et al., 2020). This shows that there are still many students who have low mathematical and graphical representation abilities. Thus, it is necessary to strengthen studentsâ€™ conceptual understanding through the use of learning media that can represent abstract concepts in material elasticity.
Technological developments in the era of the industrial revolution 4.0 have produced many smartphonebased learning media (Aththibby, Kuswanto & Mundilarto, 2021; Bani & Masruddin, 2021; Liliarti & Kuswanto, 2018; Raras & Kuswanto, 2019; Saputra & Kuswanto, 2018; Shabrina & Kuswanto, 2018). The interest of students in accessing smartphones is one of the backgrounds for the development of the media (Sari, Riswanto & Partono, 2019). Several studies show that one of the learning media innovations by utilizing mobile technology that is being intensively used and developed is augmented reality (AR) (Fidan & Tuncel, 2019; Kholiq, 2020; LÃ³pezBelmonte, PozoSÃ¡nchez, FuentesCabrera & Romeroâ€‘RodrÃguez, 2020; Permana, Tolle, Utaminingrum & Dermawi, 2019; Suprapto, Ibisono & Mubarok, 2021). The application of augmented reality (AR) in learning process allows for the visualization of twodimensional things in three dimensions. So, objects look real (Arslan, KofoÄŸlu & Dargut, 2020; Bakri, Permana, Wulandari & Muliyati, 2020; Khan, Johnston & Ophoff, 2019). Therefore, augmented reality (AR) technology is able to facilitate and support the explanation of abstract physics concepts to students.
The selection of learning models is also important in overcoming these problems. The ProblemBased Learning (PBL) model is one of the learning models that is proven to help deepen scientific knowledge and revise conceptual understanding (Yuberti, Latifah, Anugrah, Saregar, Misbah & Jermsittiparsert, 2019). PBL tends to stimulate students with a problem. Stimulus in Problem Based Learning (PBL) is contextual which is taken in everyday life (Haryanti, Wilujeng & Sundari, 2020). This is in line with the characteristics of physics itself.
One of the characteristics of physics concepts that can be found in everyday life is local wisdom or community traditions. This is one of the factors that contribute to studentsâ€™ understanding of the physics concepts being taught (Jensen, Stentoft & Ravn, 2019; Qasem, 2016). Cultural diversity in Indonesia cannot necessarily be studied in a limited time. In overcoming this issue, it is necessary to have mobile applicationbased learning media with several integrations in the form of culture, PBL teaching models, and augmented reality (AR) technology to become a teaching medium. Thus, the development and implementation of media with the integration of these three things were carried out in order to increase studentsâ€™ mathematical and graphical representation abilities.
The media that is implemented is in the form of a ProblemBased Learning physics pocketbook integrating augmented reality by adding the local wisdom in the form of a catapults. The magnitude of the elasticity of the material in this medium is explained through the 3D augmented reality (AR) animation of the catapults. This is intended to grab studentsâ€™ attention and support studentsâ€™ understanding of material elasticity. Therefore, students are able to improve their mathematical and graphical representation abilities in learning physics, especially on the subject matter of material elasticity. The theoretical framework of this research is presented in Figure 1.
Figure 1. Theoretical Framework
2. Research Method
2.1. Research Design
This study is a quantitative quasiexperimental that involves three different classes using a pretestposttest control group design. The three classes consist of one experimental class, and two contrast classes (comparison). The experimental class is a class with treatment in the form of physics learning using a ProblemBased Learning physics pocketbook integrating augmented reality. Contrast Class 1 is a class that uses powerpoints media (PPT), while in Contrast Class 2, learning is carried out using school textbooks. The detailed can be seen in Table 1.
Group 
Pretest 
Treatment 
Posttest 
Experimental Class 
O1 
X1 
O2 
Contrast Class 1 
O1 
X2 
O2 
Contrast Class 2 
O1 
X3 
O2 
Notes: O1: Pretest; O2: Posttest; X1: Physics teaching by applying PBL physics pocketbook integrated with augmented reality (AR); X2: Physics teaching by applying PowerPoint media; X3: Physics teaching by applying textbooks used by teachers 
Table 1. Research Design
2.2. Research Sample
This study used two stages of testing with different samples. The empirical test phase aimed to determine the items of the material elasticity test that were valid and reliable, before being implemented in the research design class. The empirical test involved 276 grade XII students of three different high schools, namely State Senior High School (SMAN) 1 Comal, SMAN 2 Pemalang (Taman), and SMAN 3 Pemalang. Grade XII students were used as an empirical test sample because they had been given material elasticity lessons. The empirical test instrument consists of 15 questions. The details of these question indicators are shown in Table 2.
Indicator of mathematical representation ability 
Item number 
Question Indicator 
Reading mathematical symbols according to the problem 
1 
An event is presented when a child pulls a rubber catapult to shoot mangoes in his fatherâ€™s garden. Students were asked to determine the increase in length, the symbols of known quantities (stress, and modulus of elasticity). 
2 
2 springs used in an experiment are subjected to different forces and it is known that one of them increases in length. Students were asked to examine influential magnitude symbols and other spring length increase values 

3 
Students were asked to determine the symbol of the quantity that has an effect and examine the value of the increase in the length of the spring that occurs in parallel arrangements, when there is a picture and description about spring arrangements 

Determining mathematical equations according to the problem 
4 
A description of the problem regarding two types of elastic materials to make a catapultâ€™s rope has the same length, and the diameters of the two elastic materials are known. Students were asked to analyze the equation to find the overall increase in length of the elastic material, if the two elastic materials are connected as a slingshot rope with a stone load of w. 
5 
A problem regarding 4 family members who get into a car so that the springs of the car are compressed or experience a certain increase in length is presented. Assuming the spring is single. Students were asked to analyze the equation to find the spring constant of the car and the value of the spring constant in question 

6 
Students were asked to come up with the right equation in determining the ratio of length increases from spring arrangements carried out by students in an experiment 

Operating numbers or symbols in mathematical equations correctly 
7 
An event is presented about a rock climber who falls and hangs from a rope with a known initial rope length, diameter and length increase. Students were asked to analyze the Youngâ€™s modulus of the rope if the mass of the rock climber is known. 
8 
A problem is presented about a group of students conducting a Hookeâ€™s law experiment on a spring suspended by a load. With the experiment table containing the force value and the known length of the spring. Students were asked to assess the spring constant or spring rate based on the Hookeâ€™s law experiment table presented. 

9 
A picture of 3 springs arranged in parallel and in series is presented. The spring constant of each spring is known. Students were asked to analyze the mass of the load suspended in the arrangement of the 3 springs in the picture if the increase in length is known after being loaded. 

Indicator of graphical representation ability 
Item number 
Question Indicator 
Connecting graphs and mathematical formulas 
10 
A graph of the force relationship with the increase in length of an elastic rope on a catapult is presented. Students were asked to conclude at which point the rope changes its properties to become plastic based on the mathematical equation. 
11 
A graph of the relationship between the force and the increase in length of the three springs is presented. Students were asked to interpret which spring constant value is the largest of the three springs through the information on the graph. 

Modelling real objects or situations into graphics 
12 
Illustrations and descriptions of the problem of a child pulling a catapult are presented, but over time the catapult rope is no longer elastic. Students were asked to display a graph of the relationship between stress and strain when the applied stress exceeds the elasticity of the slingshot rope. 
13 
A table is presented with the results of Hookeâ€™s law experiment. The table contains information about the mass of the load suspended at the end of the spring and the increase in length. Students were asked to make a graph of the relationship between force and length increase according to the information in the table, and conclude. 

Processing information from a graph and calculating the physical quantity in question 
14 
A graph of the relationship between force and length increase is presented. Students were asked to analyze the value of the spring constant based on the information in the graph. 
15 
A graph of the relationship between force and length gain is presented in an experiment on Hookeâ€™s law. Students were asked to analyze the potential energy of the spring based on the information on the graph. 
Table 2. 15 Questions on Instrument of Empirical Test
The next stage was the effectiveness testing by involving 108 grade XI science students of SMAN 10 Yogyakarta. The sample was divided into three treatment classes. Each treatment class consisted of 36 students. The three classes were experimental class (grade XI Science 1), Contrast Class 1 (grade XI Science 3), and Contrast Class 2 (grade XI Science 2). The sample was established by using the random sampling technique.
2.3. Research Instrument
There are two types of research instruments, namely the teaching instrument and the data collection instrument. Teaching instrument is in the form of lesson plans and student worksheets, while the data collection instrument is in the form of a test. The essay test of the material elasticity to improve the mathematical and graphical representations abilities consists of three variable indicators with details presented in Table 3.
Variable 
Indicators 
Treatment 
Mathematical Representation 
Determining mathematical equations according to the problem 
Analyzing the equation to find the increase in the overall length of the elastic material, if the two elastic materials are connected as a catapult rope with a rock weight weighing w. 
Reading mathematical symbols according to the problem 
Determining the influential quantity symbol and examining the value of the increase in the length of the spring arrangement that occurs through image illustrations and stimulus descriptions. 

Operating numbers or symbols in mathematical equations correctly 
Assess the spring constant or spring constant based on Hookeâ€™s law experimental table presented. 

Graphical Representation 
Connecting graphs and mathematical formulas 
Comparing Youngâ€™s Modulus of the two catapult rope materials with mathematical equations by presenting a graph of the relationship between stress and strain on the two catapult ropes. 
Modelling real objects or situations into graphics 
Making a graph of the relationship between style and length increase according to the information in the table, and drawing conclusion 

Processing information from a graph and calculating the physical quantity in question 
Analyzing the potential energy of a spring based on the information on the graph 
Table 3. Indicators of Mathematical and Graphical Representation Matrix
2.4. Data Analysis
The analysis of empirical test was carried out on each item of the test using the QUEST program. The empirical test analysis with QUEST aimed to determine the validity and reliability of the test that was used. The result of the validity of the test items is seen through the Infit Mean of Square (INFIT MNSQ) value. The test items are said to meet the quality of the Rasch model and have INFIT MNSQ values in the range of 0.771.30 (Adams & Kho, 1996; Raymond & SiekToon, 1996). The summary of item estimates and the summary of case estimate values provide information about the testâ€™s reliability. The result of the two estimates was then interpreted using the criteria shown in Table 4 (Sumintono & Widhiarso, 2015).
Reliability Coefficient (R) 
Interpretation 
R < 0.67 
Low 
0.67 â‰¤ R < 0.80 
Adequate 
0.80 â‰¤ R < 0.90 
Good 
0.90 â‰¤ R < 0.94 
Very Good 
R > 0.94 
Outstanding 
Table 4. Reliability Interpretation Coefficient
Prior to the analysis of the effectiveness test, the prerequisite testing was conducted. The prerequisite test consisted of a normality test (ShapiroWilk) and a homogeneity test (Levene Statistics). The data that were proven to be homogeneous and normally distributed were then tested for effectiveness. The analysis of the effectiveness test in this study used the General Linear Model (GLM) technique assisted by the SPSS Program Version 25.
In general, the effectiveness test is useful to find out the magnitude of the effect of the use of the ProblemBased Learning (PBL) physics pocketbook integrating augmented reality with the local wisdom of catapults to improve studentsâ€™ mathematical and graphical representation abilities. The increase in mathematical and graphical representation abilities was analyzed using the General Linear Model (GLM) technique at the output of Pairwise Comparison based on the pretestposttest scores in each treatment class. An increase in the pretestposttest score can be seen through the significance value and the Mean Difference in the Pairwise Comparison output.
In this study, an analysis was also carried out to find out the magnitude of the effectiveness of the use of media. The effectiveness of using the ProblemBased Learning physics pocketbook integrating augmented reality can be seen through the output of Hotellingâ€™s Trace Multivariate Test. In the output, it can be seen that the effective contribution of media use is through the Partial Eta Squared value. The greater value of Partial Eta Squared indicates that the use of the media is very effective in affecting learning.
3. Findings and Discussion
3.1 Empirical Testing Result of Mathematical and Graphical Representation Tests
The test used in the empirical test for grade XII students consists of 15 questions for the variables of mathematical and graphical representation abilities. The results of the empirical test analysis obtained the reliability value of the test instrument in the sufficient and good categories. A detailed description of the reliability coefficient is presented in Table 5.
The analysis of the validity of the mathematical and graphical representation ability test revealed 12 items that met the quality of the Rasch model having an INFIT MNSQ value in the range of 0.771.30. There are three items that do not fit, namely numbers 1, 2, and 12. The details of the result of the analysis of the validity of the test instruments and their categories are presented in Table 6.
The three questions that do not fit the Rasch model as shown in Table 5 can be eliminated or discarded, taking into account the form of the instrument that is described as well as the number of indicators of mathematical and graphical representation abilities, which amount to 6. Thus, it is decided that the total items used for implementation in the research design class are six items. The six items on the test represent each variable indicator and are selected based on the items that fall into the fit category on the Rasch model.
Reliability 
Reliability Coefficient 
Category 
Summary of item estimate 
0.77 
Sufficient 
Summary of case estimate 
0.86 
Good 
Table 5. Analysis Result of Test Reliability
Item Number 
INFIT MNSQ 
Category 
1 
1.77 
Not Fit 
2 
1.33 
Not Fit 
3 
1.11 
Fit 
4 
0.98 
Fit 
5 
1.09 
Fit 
6 
1.21 
Fit 
7 
0.98 
Fit 
8 
0.89 
Fit 
9 
0.82 
Fit 
10 
0.86 
Fit 
11 
0.85 
Fit 
12 
0.69 
Not Fit 
13 
0.85 
Fit 
14 
0.84 
Fit 
15 
0.86 
Fit 
Table 6. Analysis Result of Test Validity
3.2. Test Result of the Effectiveness of Mathematical and Graphical Representation Ability
The data on the result of the effectiveness testing of the mathematical and graphical representation abilities were obtained by using an essay test that had passed the empirical test. The test in the form of pretestposttest was administered to each of the 36 grade XI science students according to the treatment in the research design. Prior to the effectiveness testing, prerequisite testing was conducted. The prerequisite test consisted of a normality test and a homogeneity test. The analysis of the normality test (ShapiroWilk) in this study obtained data that were normally distributed. This is due to the significance value gained being more than 0.05. This statistical test analysis was derived from pretestposttest scores of mathematical and graphical representations abilities. A summary of the range of studentsâ€™ pretest and posttest values along with the frequencies obtained can be seen in Table 7, 8 and 9.
The data in Table 7, 8, and 9 are input into the SPSS program according to the treatment class, namely the experimental class and the contrast class. The result of the normality test analysis in detail is presented in Table 10.
The next prerequisite test is the homogeneity test. The analysis of the homogeneity test (Levene statistic) in this study also obtained a significance value of > 0.05. This shows that there is a similarity of variance in the variable data of mathematical and graphical representation abilities, or the data are homogeneous. The result of the homogeneity test obtained can be observed in Table 11.
Pretest Score Range of Mathematical Representasion Ability 
F 
Posttest Score Range of Mathematical Representasion Ability 
F 
Pretest Score Range of Graphical Representation Ability 
F 
Posttest Score Range of Graphical Representation Ability 
F 
0 â€“ 9 
4 
0 â€“ 9 
0 
0 â€“ 9 
4 
0 â€“ 9 
0 
10 â€“ 19 
11 
10 â€“ 19 
0 
10 â€“ 19 
12 
10 â€“ 19 
0 
20 â€“2 9 
17 
20 â€“2 9 
0 
20 â€“2 9 
16 
20 â€“2 9 
0 
30 â€“ 39 
3 
30 â€“ 39 
0 
30 â€“ 39 
3 
30 â€“ 39 
0 
40 â€“ 49 
1 
40 â€“ 49 
0 
40 â€“ 49 
1 
40 â€“ 49 
0 
50 â€“ 59 
0 
50 â€“ 59 
0 
50 â€“ 59 
0 
50 â€“ 59 
0 
60 â€“ 69 
0 
60 â€“ 69 
1 
60 â€“ 69 
0 
60 â€“ 69 
1 
70 â€“ 79 
0 
70 â€“ 79 
12 
70 â€“ 79 
0 
70 â€“ 79 
12 
80 â€“ 89 
0 
80 â€“ 89 
10 
80 â€“ 89 
0 
80 â€“ 89 
10 
90 â€“ 100 
0 
90 â€“ 100 
13 
90 â€“ 100 
0 
90 â€“ 100 
13 
Total 
36 
Total 
36 
Total 
36 
Total 
36 
Table 7. Frequency Tables of PretestPosttest scores of Mathematical
and Graphical Representation Abilities in Experiment Class
Pretest Score Range of Mathematical Representasion Ability 
F 
Posttest Score Range of Mathematical Representasion Ability 
F 
Pretest Score Range of Graphical Representation Ability 
F 
Posttest Score Range of Graphical Representation Ability 
F 
0 â€“ 9 
1 
0 â€“ 9 
0 
0 â€“ 9 
1 
0 â€“ 9 
0 
10 â€“ 19 
2 
10 â€“ 19 
0 
10 â€“ 19 
2 
10 â€“ 19 
0 
20 â€“2 9 
4 
20 â€“2 9 
0 
20 â€“2 9 
4 
20 â€“2 9 
0 
30 â€“ 39 
10 
30 â€“ 39 
0 
30 â€“ 39 
10 
30 â€“ 39 
0 
40 â€“ 49 
7 
40 â€“ 49 
0 
40 â€“ 49 
7 
40 â€“ 49 
0 
50 â€“ 59 
3 
50 â€“ 59 
0 
50 â€“ 59 
3 
50 â€“ 59 
1 
60 â€“ 69 
5 
60 â€“ 69 
9 
60 â€“ 69 
5 
60 â€“ 69 
9 
70 â€“ 79 
3 
70 â€“ 79 
10 
70 â€“ 79 
3 
70 â€“ 79 
10 
80 â€“ 89 
1 
80 â€“ 89 
12 
80 â€“ 89 
1 
80 â€“ 89 
11 
90 â€“ 100 
0 
90 â€“ 100 
5 
90 â€“ 100 
0 
90 â€“ 100 
5 
Total 
36 
Total 
36 
Total 
36 
Total 
36 
Table 8. Frequency Tables of PretestPosttest scores of Mathematical
and Graphical Representation Abilities in Contras Class 1
Pretest Score Range of Mathematical Representasion Ability 
F 
Posttest Score Range of Mathematical Representasion Ability 
F 
Pretest Score Range of Graphical Representation Ability 
F 
Posttest Score Range of Graphical Representation Ability 
F 
0 â€“ 9 
4 
0 â€“ 9 
0 
0 â€“ 9 
4 
0 â€“ 9 
0 
10 â€“ 19 
4 
10 â€“ 19 
0 
10 â€“ 19 
4 
10 â€“ 19 
0 
20 â€“2 9 
10 
20 â€“2 9 
0 
20 â€“2 9 
10 
20 â€“2 9 
0 
30 â€“ 39 
10 
30 â€“ 39 
0 
30 â€“ 39 
10 
30 â€“ 39 
0 
40 â€“ 49 
5 
40 â€“ 49 
0 
40 â€“ 49 
6 
40 â€“ 49 
0 
50 â€“ 59 
2 
50 â€“ 59 
0 
50 â€“ 59 
2 
50 â€“ 59 
0 
60 â€“ 69 
1 
60 â€“ 69 
3 
60 â€“ 69 
0 
60 â€“ 69 
3 
70 â€“ 79 
0 
70 â€“ 79 
15 
70 â€“ 79 
0 
70 â€“ 79 
15 
80 â€“ 89 
0 
80 â€“ 89 
12 
80 â€“ 89 
0 
80 â€“ 89 
12 
90 â€“ 100 
0 
90 â€“ 100 
6 
90 â€“ 100 
0 
90 â€“ 100 
6 
Total 
36 
Total 
36 
Total 
36 
Total 
36 
Table 9. Frequency Tables of PretestPosttest scores of Mathematical
and Graphical Representation Abilities in Contras Class 2
Variable 
Treatment Class 
ShapiroWilk 

Statistic 
df 
Sig. 

Mathematical Representation Ability 
Experimental Class Pretest 
0.966 
36 
0.335 
Contrast Class 1 Pretest 
0.973 
36 
0.522 

Contrast Class 2 Pretest 
0.963 
36 
0.270 

Experimental Class Posttest 
0.951 
36 
0.115 

Contrast Class 1 Posttest 
0.959 
36 
0.196 

Contrast Class 2 Posttest 
0.969 
36 
0.398 

Graphical Representation Ability 
Experimental Class Pretest 
0.968 
36 
0.379 
Contrast Class 1 Pretest 
0.973 
36 
0.522 

Contrast Class 2 Pretest 
0.963 
36 
0.270 

Experimental Class Posttest 
0.951 
36 
0.115 

Contrast Class 1 Posttest 
0.970 
36 
0.419 

Contrast Class 2 Posttest 
0.969 
36 
0.398 
Table 10. Analysis Result of Normality Test
Variable 
Levene Statistic 
df1 
df2 
Sig. 
Mathematical Representation Ability 
1.439 
2 
105 
0.242 
Graphical Representation Ability 
1.293 
2 
105 
0.279 
Table 11. Analysis Result of Homogeneity Test
The successful prerequisite test then followed with an effectiveness test using the General Linear Model (GLM) technique facilitated by the SPSS Program Version 25. The effectiveness test in this study aimed to determine the increase and magnitude of the effective contribution of the use of the ProblemBased Learning physics pocketbook integrating augmented reality with the local wisdom of catapults on studentsâ€™ mathematical and graphical representation abilities. The result of the General Linear Model (GLM) analysis on the output of Pairwise Comparison obtained a significance value of <0.05, which is 0.000. The mean difference in the output has a negative value. This shows that the average posttest score in each treatment class is higher than the average of pretest score. Therefore, from those two findings, it can be stated that each treatment class had a considerable increase in pretestposttest scores of mathematical and graphical representation abilities. The result of the analysis in detail can be seen in TableÂ 12.
The effective contribution of the ProblemBased Learning physics pocketbook integrating augmented reality with local wisdom catapults and other media to physics teaching in the three treatment classes was analyzed through the General Linear Model (GLM) at the output of the Multivariate test type of Hotellingâ€™s trace. The result of the analysis obtained in detail can be seen in Table 13.
The values of partial eta squared in Table 13 show the effective contribution to the two variables from the implementation of the media for each treatment class. In the experimental class, it is known that the value of the partial eta squared of the mathematical representation ability of students is greater than that of the Contrast Class 1 and Contrast Class 2. The effective contribution is 0.826. This means that the use of the developed physics pocketbook integrating AR with local wisdom in the experimental class is able to increase mathematical representation ability by 82.6%. Meanwhile, PPT media and textbooks in Contrast Class 1 and Contrast Class 2 were able to increase mathematical representation ability by only 56.6% and 75.5%, respectively. In the variable of graphical representation ability, it is known that the partial eta squared value of the experimental class is 0.844. It can be interpreted that the use of the PBL physics pocketbook integrating AR with local wisdom in the experimental class is able to increase the graphical representation ability by 84.4%. Meanwhile, the increase in graphical representation ability in Contrast Class 1 and Contrast Class 2 using PPT media and textbooks is only 58.7% and 78.2%, respectively.
Variable 
Treatment Classes 

(J) Time 
Mean Difference (IJ) 
Sig. 
Mathematical Representation Ability 
Experimental 
Pretest 
Posttest 
63.722 
0.000 
Contrast 1 
Pretest 
Posttest 
33.333 
0.000 

Contrast 2 
Pretest 
Posttest 
51.250 
0.000 

Graphical Representation Ability 
Experiment 
Pretest 
Posttest 
63.639 
0.000 
Contrast 1 
Pretest 
Posttest 
32.583 
0.000 

Contrast 2 
Pretest 
Posttest 
51.806 
0.000 
Table 12. Analysis Result of Pairwise Comparisons
Variable 
Treatment Classes 
F 
Sig. 
Partial Eta Squared 
Mathematical Representation Ability 
Experimental 
499.440 
0.000 
0.826 
Contrast 1 
136.665 
0.000 
0.566 

Contrast 2 
332.064 
0.000 
0.755 

Graphical Representation Ability 
Experimental 
569.928 
0.000 
0.844 
Contrast 1 
149.405 
0.000 
0.587 

Contrast 2 
377.683 
0.000 
0.782 
Table 13. Analysis Result of Multivariate Test of Hotellingâ€™s Trace Type
3.3. Product of ProblemBased Learning Physics Pocketbook Integrating Augmented Reality with Local Wisdom of Catapults
In this study, elasticity topic was combined with the local wisdom of the catapult because it has the potential to attract the attention of students and increase knowledge about local wisdom in the form of the traditional catapult game. The combination is arranged in a learning media design in the form of ProblemBased Learning Physics Pocketbook Integrating Augmented Reality. The design of the media developed in this study can be seen in Figures 2 and 3.
Figure 2. Design of ProblemBased Learning Physics Pocketbook Integrating
Augmented Reality with Local Wisdom of Catapults