Using Project Based Learning (PBL) Design to Expand Mathematics Students’ Understanding: A Case Study in Statistics Problem

This paper describes some activities that the author has designed using Project Based Learning (PBL) to develop students’ understanding of statistics. This study used a quasi-experimental method with a one group pretest-posttest quantitative research design. The subjects in this study are 30 students of class VII in SMP Negeri 6, Surabaya, Indonesia. The data collected using a questionnaire and a test. The validity of students’ response used product-moment correlations and the reliability test used the Cronbach’s Alpha formula, and the hypothesis was tested using the t-test (one sample t-test). The results showed that the positive response of students using PBL design to expand mathematics students’ understanding of statistics, namely 85.83%. Furthermore, there was a difference in the students’ learning outcomes before and after they learned through the PBL learning design, indicated by pretest the mean of score is 38.30 and a posttest mean score is 67.17. Besides that, tobserved of pretest is 15.931 and tobserved of posttest is 34.655, both are greater than ttable with a significant level α=0.05 is 2.042. Thus, we could be concludes that there as a difference the understanding of statistics students’ outcome before and after learning with PBL design.

lazy in understanding the material and even prefer to turn away from learning by playing. In particular statistical materials, some students are lazy in calculating data especially if the data is large. This if left unchecked will have an impact on the decrease in the academic value of students. Implementation of the model Based Project (PBL) is one alternative to overcome the above problems (Krajcik & Blumenfeld, 2006). The project-based learning model is one of the recommended of learning models in the implementation of curriculum 2013 in Indonesia. This is because PBL is a key strategy for creating independent thinkers and learners (Bell, 2010) and student-centered projects for active learning (Mosleh & Thom, 2017) that match the objectives of the 2013 curriculum. In addition PBL is also an innovative learning emphasizes complex activities with the goal of solving problems based on inquiry activities (Laviatin, 2008). Thompson and Beak (2007) also reported that they are students in a collaborative learning activity that challenges them as both individuals and group members. PBL allows students to learn by doing, applying their ideas while engaging in real-world activities through investigating questions, proposing hypotheses and explanations, discussing their ideas and finally developing solutions or outcomes (Diffily, 2002).
Some research results indicate that project-based learning has tremendous potential to train student' thinking processes (Thomas, 2000) that lead to students' creative thinking ability. So the students become enthusiastic in their learning, because the teacher acts as mediator and facilitator. The results of this study support the research conducted by Summers and Dickinson (2012) doing research and found that learners who learn to use project-based learning have higher learning achievement than the traditional learning. Leviatan (2008) also explained in his research that learning project-based is an innovative learning that emphasizes complex activities with the goal of solving problems based on inquiry activities. In addition, according to a study from Miswanto (2011) also shows that through a project-based learning model, students' learning outcomes on linear programming material become increasingly higher than before.
According to Markham et al. (2003), there are six aspects needed in PBL, namely: 1) authentic, real-world challenge; 2) academic all rigorous; 3) apply learning by using high-performances skills; 4) active exploration; 5) interact and make adult connections; 6) formal and informal assessment practices.
Besides that PBL also allows students to investigate questions, propose hypotheses and explanations, discuss their ideas, challenge the ideas of others, and try out new ideas (Krajcik & Blumenfeld, 2006).
Using PBL in learning, it is expected that students better understand and know that the things learned related to real life around them so that the concept of statistics learned will be recorded more strongly in the memory of students and learning outcomes will be better. In addition, this project-based learning model is expected to improve student learning outcomes and improve the ability to solve daily problems related to the subject matter of statistics that has been received.
The purpose of this research is to describe the Project Based Learning (PBL) design of mathematics students' in learning statistics.

Research Design
This study is a quantitative study with quasi experimental design using one-group pretest-posttest design that focuses on improving students' understanding in learning statistics to better outcomes before students get PBL learning. This research was conducted in class VII of SMP Negeri 6 Surabaya, Indonesia. This study is implemented for 2 months, February-April 2015.

Research Sample
The participants of the study were 1 class who were selected from cluster random sampling from 10 classes in the same grade from a junior high school at Surabaya city, Indonesia. The subjects in this study are 30 students of class VIIH, there are 15 are males and 15 are females. All students are in grade VII and aged between 12-13 years. Class VII H is the grade with the lowest average mathematics score compared to the other grade of the previous semester grade data.

Research Instruments and Procedures
The data collected using a questionnaire and a test. Pretest and posttest are the same questions consisting of 9 essays items. In our study, student activity categories to be observed include: 1) Listening or paying attention to teacher or friend explanations; 2) Observing, listening to, or view problems, events, or explanations in students worksheet; 3) Discussing or solving students worksheet or finding ways and answers in students worksheet; 4) Presenting the results of the discussion, providing feedback in groups; 5) Asking about the results of the discussion or observations to friends or teachers; 6) Making conclusions or summarize the learning materials in groups or together with teachers.

Data Analysis
The data analyses of our study are using validy, reliability, and hypothesis. The validity of students' response used product-moment correlations and the reliability test used the Cronbach's Alpha formula, and the hypothesis was tested using the t-test (one sample t-test).

Result
The results showed that the questionnaire of students responses filled by 30 students after following project-based learning on statistical materials obtained as follows: and 2 persons or 6.67% including very good qualification. The overall average score is 67.2 and is in good qualification. Different test results of student learning before and after given project-based learning are as follows: Based on the above Table shows that the average value posttest results are higher than the average value of pretest results with a difference of 28.9. Improvement of learning outcomes can also be seen in t-test results that there are differences in student learning outcomes before and after learning using the PBL model, this is evidenced by the t-test as follows.

Discussion and Conclusion
Response is an idea or feeling of students after following the lesson. According to Poerwadarminta (2003) Based on the above results, we can conclude that students' opinions about the use of project-based learning in improving students' mathematical understanding can be shown by the student's response is positive. While for difference of learning result of student before and after given PBL study can be shown with pretest average value is 38.30, mean value of posttest is 67.17. The difference in mean scores indicates that there is an increase in student learning outcomes. For test result t observed pretest and posttest value show bigger than t table , that is t count pretest=15.931, t-count posttest=34.655, and t table =2.042. Thus it can be concluded that there are differences in student learning outcomes before and after learning PBL, so that PBL can give effect to students' mathematical understanding so that student learning outcomes increase compared to previous tests.