Project-based Learning Method in Advanced Mathematics for Engineering Students in Vietnam: Experimental Research

Mathematics and other sciences are considered difficult subjects by the majority of students. One of the reasons is that in the traditional classroom students are taught theory first and then they are asked to solve some exercises with algorithms, use less inference and rarely connect with activities in the real world. In the process of innovating teaching and learning methods, the use of project-based learning methods (PBL) has become popular in teaching and learning in universities in many countries around the world. This article uses the empirical research method with the application of project-based learning in the classroom at Hanoi Industrial University. The purpose of the study is to help students apply their knowledge and practical skills to participate in solving problems "The Robot Control Design Project". Research method: we talk with all the students in the class about the purpose of the project is to The Robot Control Design Project; Data collection method includes survey information from implemented projects and self-assessment of project-based learning of 48 third-year technical students at Hanoi Industrial University. The results show that students evaluate PBL positively because this method helps students have interesting practical experiences, while developing collaborative skills, problem solving and self-control in study. The results of the article can be used as a basis for future research in engineering classes to meet the increasing needs of learners for international integration.


Introduction
There have been significant fundamental changes in teaching and learning in universities in Vietnam in the past decade, in which, enhancing the role of the experimental process is commonly applied in teaching and learning in Engineering. Although these changes help learners become more active in the learning process, learners have not really mastered the learning process. The learner-centered approach in teaching and learning in Vietnam has not been fully applied and traditional teaching methods still exist when the teacher is still the main source of knowledge and the knowledge creation role of learners in the teaching process has not really been paid attention [1], [2].
In the era of globalization, learners have to master the process of acquiring knowledge for international integration, traditional teaching methods are no longer suitable when learners need to "learn with practice", construct and share knowledge, positive experience and real learning situations [3], [4], [5], [6], [7], [8]. One of the most innovative methods of teaching and learning in an engineering class is using Project Based Learning (PBL).
According to Jason Ravitz, Nate Hixson, Mary English, John Megendoller (2012) [9], PBL provides opportunities for students to learn deeply content knowledge and 21st century skills. While PBL practices vary depending on grade level and subject area, projects should allow some level of student voice and choice, and must be planned, managed, and evaluated carefully to connect rigorously academic content to the 21st century Skills (such as collaboration, communication, and critical thinking) through students' products and presentations [10], [11].
PBL method can meet the requirements of learners for the process of building knowledge and practical experience; however, this method is still quite new and is not yet popular in teaching and learning technical majors in Vietnam. Therefore, this article applies project-based teaching methods in Advanced Maths for students in engineering to help students not only have theoretical understanding but also practical experience, develop collaboration skills, problem solving skill and self-regulation in learning, thereby improving autonomy in learning.

The Concept of Project-based Learning Method
PBL has become popular in teaching and learning in many countries around the world, such as teaching about traditional culture, teaching preserving intangible heritages, teaching about ecological environmental protection, etc. In the context of technical teaching, PBL is used equivalent to many different terms such as project work, project method, project approach, project-oriented approach, project-based instruction [12] or experiential learning [14], [13].
PBL is simply defined as a learning strategy organized with learning projects [15], [16], [17]. Buck Institute of Education [18a], Blumenfeld, Fishman, Krajcik, Marx and Soloway (2000) [6], an American research and development organization, defines PBL as "a teaching method in which learners acquire knowledge and skills by working for a long period of time to study and answer a real, compelling, complex question, problem, or challenge".

Characteristics of Project-based Learning Method
Thomas [15] raised 5 criteria of PBL including: (1) centrality; (2) motivation; (3) tectonics; (4) autonomy in learning and (5) reality. The uniqueness of PBL is the construction of a final product that shows the learners' knowledge, understanding and attitude towards the problem being researched and that the problem is presented by the learner in many different forms such as videos, pictures, reports, models and other artifacts [18].
According to Cocco [19], PBL is a learner-centered approach, based on three constructivist principles: context-specific learning, active learning, and sharing knowledge and understanding. During the PBL process, learners are given the opportunity to "build knowledge by solving real world problems through questioning and discussing, designing and conducting investigation, gathering, analyzing and explaining information, data, draw conclusions and report results " [21]. Teaching in this form of questioning allows learners to gain meaningful learning experiences and achieve a common goal through collaborative development and presentation of a final product [20]. PBL is also a form of experiential learning, in which learners participate consciously and actively think about the learning process [22], [23]. The Robot Control Design projects in this experimental study demonstrate the above characteristics of PBL.

The Benefits of Project-based Learning
Project-based learning method brings many practical benefits to learners. First of all, PBL helps promote learners' self-regulation learning in the process of systematically documenting and thinking [24]. PBL helps learners gain autonomy through goal setting, planning and organization and become more excited about learning [25]. Thus, PBL contributes to the development of learners' autonomy capacity in learning.
In addition, PBL also creates conditions for learners to develop collaboration skills. Collaboration skills are central to the teaching and learning process [26]. PBL offers learners the opportunity to "interact and communicate with each other ... in a real context" [27]. Markham [28] thinks that collaboration skills in PBL are similar to teamwork skills in professions; this will help learners to equip them with effective teamwork skills, which will help them work better in future work.
In particular, PBL helps learners develop high-level problem solving and critical thinking skills [29]. These are very important, transformable, lifelong skills that learners always need outside of the classroom. The ability of learners to solve problems formed during project design and construction helps learners participate more actively in the learning process thanks to increased awareness [30]. Because PBL consists of highly practical work, it is more meaningful to learners in increasing the learners' interest and motivation to participate in the project and to promote learning [31].

Research Methods
In order to promote PBL's preeminence in teaching and learning engineering, an empirical study on PBL was conducted with 48 third-year engineering students of Hanoi Industrial University. The Robot Control Design Project was selected as an experimental research for the 530 Project-based Learning Method in Advanced Mathematics for Engineering Students in Vietnam: Experimental Research following reasons: (1) the survey subjects were third-year students with knowledge of theory and practice from a basic level or higher; (2) The author of the article who is also a lecturer of this module can evaluate his own teaching method through research on his own teaching activities.

Research Questions
The empirical study answers the following questions: (1) How do students work on robot control design projects? (2) What is the student's experience with the project-based learning method?
To answer the research questions above, robot control design projects are conducted with student groups for 10 weeks during a semester. The students participating in the study were divided into 4 groups, each group of 12 students. To delve deeply on the topic of robotic control design, groups of students choose their own ideas of whether to build or improve certain related equipment to carry out the project.

Implementing Project
To achieve the goals of PBL, the robot control design project consists of 4 specific implementation steps. We recommended a number of steps to implement a project because "when the projects are structured to help students actively plan projects early, students gradually develop a sense of ownership and pride in project". Therefore, students are instructed in detail about 4 steps to implement a robot control design project from group formation, topic selection to information research on topic, group work, and correct the trainer's responses, present the final product to the class, and evaluate the project. To avoid selecting the same topic, all of the groups have to apply for a project topic before working on their robot control design project.
Steps to implement robot control design project Instruction: Students do a robot control design project for 10 weeks in the following stages (Diagram 1).

Steps:
Step 1: Project construction Teachers and students propose ideas on the topic of Robot Control Design for a learning project by presenting a situation with a real problem or a task to solve. The project can be proposed by a teacher, student or student group, but it is the student who decides to choose, however, it should be ensured that the content is suitable for the purpose of learning, the content of the program and the facts, in accordance with the capacity of students. The teacher can also recommend a number of topics for students to choose from.
Students clearly define the goals of the Robot Control Design project, the requirements to be achieved of the project.
Teachers divide groups or let students group themselves to suit the task of the Robot Control Design project, according to the capacity of each student.

Step 2: Make an implementation plan
Students actively discuss project goals, tasks to be performed in the project, then divide the work into small packages for each group or individual to take on a part of the work. Tasks of each group and individual must be very specific and detailed about the content of the work, how to proceed, and the time of completion.
Basing on project goals, project implementation time funds and student deployment plans teachers give comment, and correct to help students implement in the right direction.

Step 3: Project implementation
During this period, groups of students positively and actively perform assigned tasks by applying the knowledge learned and self-researching.
With the feature of Advanced Math for engineering, in order to carry out the Robot Control Design project, students need to know about other basic knowledge related to the project such as mechanics, electricity. Therefore, acquiring relevant specialized knowledge is an important task in project implementation.
While working on a learning project, students need to increase communication between team members, between group and group. Members of the group or between groups always have opinions of each other's feedback. Strengthen cooperation and exchange among team members, between groups. Especially, when doing projects, students always have to review the goals for timely adjustments.
Teachers always supervise and adjust students' activities so that all activities go according to plan, set targets, and ensure time progress.
During the project implementation phase, the qualities and abilities of the students are revealed and developed.  Question 6: What is a practical problem that leads to Laplaceization? Question 7: (Question of navigation) How is the Fourier transform applied in some areas such as signal processing, cryptography, frequency?

II. Implement a robot control design project Task 1: Students research theory-driven theory
Students in the research groups answer the content questions (questions 1,2,3) by writing their answers on the ballots. Under the organization of the group leader, group members exchange answer sheets for each other and then exchange ideas. After that, the group leader discussed and summarized on A0 paper.

Task 2: Research and answer content questions 4.
After studying the conceptual system and Laplace transforms, the groups work in the following order: + Each person should think to solve the above problem and write a draft; + Pass the draft paper to other people to see in a circle and make suggestions, whether the solution is complete or not; + Discuss in groups and give solutions to their groups;

Task 3: Research and answer content questions 5
To answer content question 5, students must be sure of what they have researched before. The method of organizing the implementation is the same as when performing task 2. In groups, divide it into pairs. Each person in the pair thinks about and drafts in a short time; exchanges drafts for each other, then comment, edit and agree on group the content answers.
The solution is summarized as follows:  Regarding the robot control product, the groups operate as follows: -Groups assign tasks to each individual in the group; -Calculate and design electrical circuit diagrams; -Prepare components such as battery source, capacitors, conductors, resistors; -After discussing for the whole group, the groups assemble the controller in the practice room.

Task 4: What is a practical problem that leads to Laplaceization?
+ The groups have prepared, learned the actual problems in advance, one group represented to give the situation as required above, the remaining groups commented with or denied and gave their own opinion. + Role swap groups make comments and discuss some real-world situations. + When approved, the team leaders record satisfactory example cases and synthesize. + The groups agreed in their groups to edit the content and presentation form of the report, synthesize the complete content of the report; write a final report. + Checking progress and completing products: Teachers regularly supervise, inspect and urge groups, promptly give instructions and directions of activities. Group record, edit, and perfect their own work.
Question 7: Students learn to see the Fourier transform plays an important role in the problems of converting discrete signals into amplitude and frequency components, which have great significance in signal processing, cryptography ,… This is the direction of research in the next project of the program.

Task 5: Present results and evaluation
-The groups synthesize the results and present their reports to the class. The teacher can appoint any member of the group to stand before the class to report so that the teacher can comment on the results of the group activities are effective or not, other members follow up, get out personal review.
-The groups display the products were hand-held robotic controls, demonstrate the maneuverability of the controller.
Product requirements: Compact, solid, beautiful appearance. Scientific design circuit, sufficient power supply, capacitor, inductor, frequency generator. Solid welds, conductors. Low cost. Some product pictures ( Figure 6

Step 4: Presenting results and reviews
The result of the Robot Control Design project is a product that students can introduce and present to the groups or to the class.
Teachers prepare facilities such as computers, projectors, fonts, boards, ... so that students can introduce the results. Evaluation of results can be made by individuals self-assessing the results of themselves, of groups, other individuals, or among groups of each other on the project implementation process, on the achieved products. The teacher is the last person to evaluate and make general comments on the project implementation and resulting products.  Table 1 contains questions for the purpose of studying self-assessment of groups of students participating in experimental research on project-based learning methods. Circle your opinion on questions 1-8 following the instructions below and state your opinion in sentences 9-10. Table 1. Self-assessment questionnaire

Scale (1) (2) (3) (4) (5)
1. I have found that the project-based learning method helps students be more excited, confident and effective in learning than the traditional presentation method. 2. I can develop autonomy in learning through team goal setting, project planning and implementation.

Data analysis
Regarding data analysis, descriptive methods are used to characterize robot control design projects. Quantitative analysis with calculation (one sample t-test) combined with qualitative analysis is applied to students' self-assessment of PBL.

Student Experience with Project-based Learning Methods
After implementing related projects on robot control design, generally all groups of students have a positive assessment of PBL with an average value of 4 or more, which is statistically significant difference with p <.05. (Table 2). According to the results in Table 2, students agree the most that PBL helps students to be inspired, confident and learn more effectively than the traditional presentation method with the highest mean (M = 4.60). With PBL's learner-centered approach, students find they have the opportunity to develop autonomy in learning through goal setting, group project planning, and implementation (M = 4.29).
The students all agreed on the benefits that PBL brought them through improving their ability to build knowledge and creativity (M

Difficulties and Students' Proposals on PBL
Although students appreciate PBL for the practical benefits that PBL brings, groups of students still have certain difficulties when implementing a robot control design project. First of all, PBL is completely new to student because they have never done a project before, except presentations in a traditional way. The challenge for the teams was to present a project related to designing a robot control. However, with the faculty input during project implementation, groups of students were able to self-adjust their projects by paying more attention to the presentation forms of the project combined with the specific products. In addition, at first, groups of students still had difficulty in the process of choosing a project topic because there was no consensus among the group. However, during the process of discussion, groups develop collaborative and teamwork skills, so the topic of groups is quickly agreed upon. Deeply researching the project topic is also a big challenge for groups of students who want to pick out the most prominent information about products of the project to present.
To carry out the robot control design project well, the groups made a number of constructive proposals.
Firstly, the project needs a lot of time to prepare the content and necessary tools and equipment. Therefore, students suggest groups need more time to improve the project after the teachers' feedback. Second, to avoid groups focusing heavily on one problem, students suggest robot control design projects should cover multiple disciplines; that will bring more color and variety to projects.
Third, students lack resources to prepare projects except for information gathered online; therefore, students suggest that the school library needs to equip more resources about the technical disciplines of countries around the world so that they can use them for their robot control design projects better.

Findings
PBL is applied to the class at Hanoi Industrial University through robot control design projects that bring positive results in learning for students similar to the results of some previous studies [32], [33], [34], [35]. However, the practical benefits that robot control design projects bring to students in this study are shown in the following specific aspects.

Building Knowledge
With the learner-centered approach in PBL, learners play an important role in the knowledge building process. Duffy [36] thinks that learners' need to construct new knowledge is the key to acquiring and cultivating knowledge, not the requirements imposed by teachers. PBL has applied the central principles of constructivist approach to learning and problem solving in practical contexts: "learning is a dynamic process in which learners construct their knowledge through combining new ideas with existing knowledge" [37], [38]. Based on this approach, student groups have created knowledge to build the content of robot control design projects without the imposition of knowledge of the teacher; the teacher is only the instructor, or the person who gives feedback on student robot control design projects. With PBL, students are empowered to truly master the process of creating and sharing knowledge, so they feel more excited and confident in the learning process.

Develop Collaboration and Teamwork Skills
Robot control design projects help students develop collaborative and teamwork skills through unifying the selection of project topics, assigning tasks to each team member to build project content and design vivid visual tools. Collaboration and teamwork skills on robot control design projects are very helpful for students in the future as they help students "become seasoned teamworkers, proficient in making group action plan… work together to solve the problem " [26], [2], [39], [11].

Autonomy in Learning
Through the implementation of a robot control design project, groups of students can set goals, plan and organize the team's project implementation. In particular, from the faculty feedback on the team's draft project, groups of students used more effective learning strategies to adapt the project in a better way. They restructure the project, adjust the original plan and apply new strategies to create better project products. This shows that students have the ability to develop self-regulation and cognitive process control during the implementation of a robot control design project. This ability helps students to be more aware of their responsibilities in the learning process, thereby improving autonomy in learning [40].

Experimental Learning
PBL is a form of experiential learning with positive and real-world learning situations. Experimental learning "emphasizes the important role of learners' experiences in the learning process" [41]. In robot control design projects, groups of students participate in experiential learning by doing action learning [42] with content design, self-study, and manual installation of the devices of the project as well as technical calibration for the equipment. Therefore, the robot control design projects help students to have an interesting experience in making products for application in life. Active learning activities in robot control design projects helps students benefit from discoveries and experiences through observations, interactions, and real-world exploration [41]. This experience enriches the students' knowledge and life experience in future work.

Conclusions
This study provides empirical evidence on the use of PBL by student robot control design projects. Despite certain difficulties during project implementation, as it was the first-time students were working on robot control design projects, the results showed that PBL offers many practical benefits and interesting experience for students, especially helps students build knowledge, improve collaboration and teamwork skills, improve self-regulation, control and develop autonomy in learning. These skills are very essential for learners and should be focused on developing so that students can integrate internationally in the age of globalization. In order to fully develop a learner-centered approach in PBL, teachers need to be more aware of the role of an instructor in student projects rather than as transmitting or imposing knowledge. Helping students overcome difficulties as well as responding to students' constructive suggestions when implementing projects, future PBL studies will surely bring about better results. From the practical benefits that PBL brings to students through robot control design projects, this study shows that PBL needs to be replicated and more popular in schools from high schools to universities in Vietnam to meet the increasingly high learning needs of learners for international integration.