Potential Challenges Based On Synchronous Online Course Integrated With Stem Context On Students’ Creative Thinking Abilities

The main focus of mathematics education in the current era is the development of mathematical thinking and problem-solving skills. This necessitates mathematics teachers to design learning experiences that encourage students to develop mathematical skills, such as creative thinking, as mathematics is crucial for thinking, observing, and organizing the world [1],[2],[3],[4]. Despite its importance, mathematics remains a challenging subject for students in Indonesia. The results of the PISA 2018 and TIMSS 2015 assessments indicate that Indonesia ranks 73rd out of 79 countries and 44th out of 49 countries, respectively [5],[6]. These results pose a challenge for mathematics educators, and teachers, as the frontline in the mathematics education process, need to address several challenges in the era of the industrial revolution and the 21st century.

Creativity, as one of the qualifications required by graduates in the era of the industrial revolution and the 21st century, plays a crucial role in the process of solving mathematical problems [7],[8],[9],[10],[11]. Creative teachers can complete their tasks quickly and efficiently, including preparing online learning during the COVID-19 pandemic, as the use of platforms such as e-learning or learning management systems (LMS) needs to be implemented to accommodate distance learning [12],[13],[14]. Consequently, students can explore self-learning as they can learn anytime, anywhere, and from any available internet sources, disregarding geographical differences and financial limitations. This can be accommodated through online learning [15],[16].

To ensure the achievement of students’ creative thinking skills during online lectures, an appropriate learning model needs to be prepared that accommodates students’ learning needs while maintaining educational quality. The Challenge-based on Synchronous Online Course integrated with STEM-Context (CBSO-STEM) learning model is an innovative approach in mathematics education that caters to students’ needs during online classes. The Challenge Based Learning (CBL) framework provides a unique atmosphere for the development of these skills through activities that guide students to solve given challenges. The challenges are framed within problems that students must solve through group discussions. Additionally, the role of Synchronous Online Course strategies allows students to interact directly with their peers or instructors through various platforms and learning management systems, facilitating the discussion of specific material-related issues. STEM itself, defined as learning activities and the context in which problems are presented, provides the best integration for skill development through meaningful and real-life learning processes, utilizing an engineering approach and technology to enable students to design solutions to the given challenges. The teaching and learning process is aligned with science and mathematics and relevant subjects, allowing students to collaborate and communicate problem-solving in their learning activities. The following is the syntax of the CBSO-STEM model and the STEM problem context presented in the Riemann Sum material.

STEM-Context on Riemann Sum Material

Big Idea

One of the fascinating features of the traditional Gadang house in Padang, West Sumatra, that captivates many people is its roof. Made of ijuk (black fiber) and shaped like buffalo horns, it symbolizes the victory of the Minangkabau people in buffalo racing competitions in Java. The curved and pointed shape of the roof is often referred to as “gonjong.” Before becoming a complete roof, the framework of the Padang house’s roof consists of individual parts that are assembled together. With the knowledge of integral calculus, we can calculate the area of the roof of the Gadang house in Padang, West Sumatra, along with its individual parts. The assembly of these roof parts is actually a concept of the Riemann sum partition.

Essential Question

Do you think we can find the area of ​​the roof of the Padang house? If so, how do you find the roof area of ​​a Padang house with the roof partitions?

STEM-Context on Integral Application Material

Big Idea

Have you ever noticed the shape of the steel cables hanging on a suspension bridge? Take a look at the image of the Akashi-Kaikyo Bridge above the Akashi Strait, connecting Maiko in the city of Kobe with Awaji Island in Japan. If you observe closely, the curve formed resembles a parabolic curve. By knowing the equation of this curve, we can easily determine the length of the cable needed without actually stretching the wire. Furthermore, we can also calculate the area bounded by the curve and the roadway. Integral calculus can be used to solve such cases.

Essential Question

How to determine the length of wire needed on the bridge? How do you determine the area of ​​the region bounded by the curve? Is it possible to solve in several ways/different resolution methods?

STEM-Context on Material Transcendental Functions

Big Idea

Bactrocera carambolae, commonly known as the Carambola fruit fly, is one of the pests frequently found in several fruit crops such as mango, orange, guava, starfruit, and others. Its presence is highly disruptive and challenging to control. In an experiment regarding the growth of fruit flies, a certain number of fruit flies were placed in an environment that supports their growth, meaning they have enough food, suitable temperature, and are inaccessible to predators. The experiment recorded the number of fruit flies present after t days as N(t), and then sought to find the relationship between t and N(t). The results of the experiment were recorded in the following list.

Essential Question

Based on the data, what function can represent the data? How can we obtain a function for the population of fruit flies based on the data? What is the geometric interpretation of the experiment’s results?

The implementation of the CBSO-STEM model in the Integral Calculus course was designed for sixteen sessions during the even semester of the 2021/2022 academic year. The implementation was carried out in three experimental classes, namely Class B of the Mathematics Education Study Program (S1), the Mathematics Study Program (S1), and the Applied Statistics and Computation Study Program (D3). After filling out a questionnaire regarding the implementation of online learning and taking a pretest in the first session, students will learn the Integral Calculus material for thirteen sessions by implementing the CBSO-STEM model. In the eighth and sixteenth sessions, students will take a midterm exam and a final exam as posttests. The following presents the descriptive statistical results related to students’ mathematical creativity.

The results indicate that the average scores of the experimental classes for each study program implementing the CBSO-STEM model are not significantly different, ranging from 49 to 57. Additionally, the average scores of the experimental classes for each study program implementing the CBSO-STEM model are higher than the average scores of the control class. The experimental classes for the Mathematics Education Study Program (S1), Mathematics Study Program (S1), and Applied Statistics and Computation Study Program (D3) obtained average scores of 56.04, 51.63, and 49.87, respectively, while the control class had an average score of only 38.69. Furthermore, there is an improvement in mathematical creativity in the experimental classes for each study program implementing the CBSO-STEM model, with increases of 0.31, 0.23, and 0.07, respectively. It is evident that there is a difference between the pretest and posttest scores in the experimental classes for each study program implementing the CBSO-STEM model. The minimum scores in the experimental classes are 15 for the Mathematics Education Study Program, 25 for the Mathematics Study Program, and 30 for the Applied Statistics and Computation Study Program, while the minimum score in the control class is 0. The maximum scores in the experimental classes are 90 for the Mathematics Education Study Program, 80 for the Mathematics Study Program, and 80 for the Applied Statistics and Computation Study Program, while the maximum score in the control class is only 75. Further statistical tests need to be conducted to determine the significance level and confirm the validity of these statements.

Based on the ANOVA test results according to Table 3 for mathematical creativity using Excel, the calculated t-value is 1.987. With α = 5%, the tabulated t-value is obtained as 3.067. Since the calculated t-value of 1.987 < the tabulated t-value of 3.067, H0 (null hypothesis) is accepted. Therefore, it can be concluded that there is no significant difference in the average mathematical creativity of the experimental classes from each study program implementing the CBSO-STEM learning model. In other words, the differences in classes implementing the CBSO-STEM model do not have an impact on students’ mathematical creativity.

Based on the results of the mathematical creativity test as presented in Table 4, the average score for the experimental class of S1 Mathematics Education and the average score for the control class are 56.04 and 38.69, respectively. The results were then tested using a t-test, resulting in a calculated t-value of 6.41 and a tabulated t-value of 1.66. Since the calculated t-value of 6.41 > the tabulated t-value of 1.66, H0 (null hypothesis) is rejected. Therefore, the average mathematical creativity of the experimental class in S1 Mathematics Education is higher than the average mathematical creativity of the control class. Thus, it can be said that the CBSO-STEM model has a better impact on the mathematical creativity of students in the S1 Mathematics Education program.

Based on the results of the mathematical creativity test as presented in Table 4, the average score for the experimental class of S1 Mathematics and the average score for the control class are 51.63 and 38.69, respectively. The results were then tested using a t-test, resulting in a calculated t-value of 6.25 and a tabulated t-value of 1.66. Since the calculated t-value of 6.25 > the tabulated t-value of 1.66, H0 (null hypothesis) is rejected. Therefore, the average mathematical creativity of the experimental class in S1 Mathematics is higher than the average mathematical creativity of the control class. Thus, it can be said that the CBSO-STEM model has a better impact on the mathematical creativity of students in the S1 Mathematics program.

Based on the results of the mathematical creativity test as presented in Table 4, the average score for the experimental class of D3 Applied Statistics and Computation and the average score for the control class are 49.87 and 38.69, respectively. The results were then tested using a t-test, resulting in a calculated t-value of 4.77 and a tabulated t-value of 1.66. Since the calculated t-value of 4.77 > the tabulated t-value of 1.66, H0 (null hypothesis) is rejected. Therefore, the average mathematical creativity of the experimental class in D3 Applied Statistics and Computation is higher than the average mathematical creativity of the control class. Thus, it can be said that the CBSO-STEM model has a better impact on the mathematical creativity of students in the D3 Applied Statistics and Computation program.

Based on the results of the mathematical creativity test as presented in Table 5, the average pretest score for the experimental class of S1 Mathematics Education and the average posttest score for the experimental class of S1 Mathematics Education are 36.88 and 56.04, respectively. The results were then tested using a t-test, resulting in a calculated t-value of 7.62 and a tabulated t-value of 1.66. Since the calculated t-value of 7.62 > the tabulated t-value of 1.66, H0 (null hypothesis) is rejected. Therefore, the average posttest mathematical creativity of the experimental class in S1 Mathematics Education is higher than the average pretest mathematical creativity of the experimental class in S1 Mathematics Education. In other words, there is a significant improvement in mathematical creativity in the S1 Mathematics Education experimental class that has implemented the CBSO-STEM model. Furthermore, after calculating the Ngain, a value of 0.3036 with a moderate criteria is obtained. Thus, it can be said that the CBSO-STEM model has an impact on improving the mathematical creativity of students in the S1 Mathematics Education program.

Based on the results of the mathematical creativity test as presented in Table 5, the average pretest score for the experimental class of S1 Mathematics and the average posttest score for the experimental class of S1 Mathematics are 37.79 and 51.63, respectively. The results were then tested using a t-test, resulting in a calculated t-value of 6.80 and a tabulated t-value of 1.66. Since the calculated t-value of 6.80 > the tabulated t-value of 1.66, H0 (null hypothesis) is rejected. Therefore, the average posttest mathematical creativity of the experimental class in S1 Mathematics is higher than the average pretest mathematical creativity of the experimental class in S1 Mathematics. In other words, there is a significant improvement in mathematical creativity in the S1 Mathematics experimental class that has implemented the CBSO-STEM model. Furthermore, after calculating the Ngain, a value of 0.2224 with a low criteria is obtained. Thus, it can be said that the CBSO-STEM model has an impact on improving the mathematical creativity of students in the S1 Mathematics program.

Based on the results of the mathematical creativity test as presented in Table 5, the average pretest score for the experimental class of D3 Applied Statistics and Computation and the average posttest score for the experimental class of D3 Applied Statistics and Computation are 46.45 and 49.87, respectively. The results were then tested using a t-test, resulting in a calculated t-value of 1.39 and a tabulated t-value of 1.67. Since the calculated t-value of 1.39 ≤ the tabulated t-value of 1.67, H0 (null hypothesis) is accepted. Therefore, the average posttest mathematical creativity of the experimental class in D3 Applied Statistics and Computation is equal to the average pretest mathematical creativity of the experimental class in D3 Applied Statistics and Computation. In other words, there is no significant improvement in mathematical creativity in the D3 Applied Statistics and Computation experimental class that has implemented the CBSO-STEM model. Furthermore, after calculating the Ngain, a value of 0.0639 with a low criteria is obtained. Thus, it can be said that the CBSO-STEM model has an impact on improving the mathematical creativity of students in the D3 Applied Statistics and Computation program with a low level of success.

After attending Integral Calculus lectures by implementing the CBSO-STEM model, students were asked to fill out a questionnaire regarding their response to the implementation of the CBSO-STEM learning model. The questionnaire consisted of 40 items classified into several aspects related to the implementation of the CBSO-STEM model in the Integral Calculus lectures. These aspects include (1) the aspect of synchronous activity implementation, (2) the aspect of Learning Management System (LMS) implementation, (3) the aspect of Virtual Meeting implementation, (4) the aspect of discussion activity implementation, (5) the aspect of teaching materials availability implementation, (6) the aspect of instructional video availability implementation, (7) the aspect of student-centered activity implementation, (8) the aspect of assignment implementation, and (9) students’ opinions on the implementation of the CBSO-STEM model. The following are the results of students’ responses to the implementation of the CBSO-STEM model in Integral Calculus lectures.

The score for the aspect of synchronous activity implementation is 3.36 with a Good category, the score for the aspect of Learning Management System (LMS) implementation is 3.36 with a Good category, the score for the aspect of Virtual Meeting implementation is 3.31 with a Good category, the score for the aspect of discussion activity implementation is 3.49 with a Very Good category, the score for the aspect of teaching materials availability implementation is 3.41 with a Very Good category, the score for the aspect of instructional video availability implementation is 3.37 with a Good category, the score for the aspect of student-centered activity implementation is 3.22 with a Good category, the score for the aspect of assignment implementation is 3.45 with a Very Good category, and the score for the aspect related to students’ opinions on the implementation of the CBSO-STEM model is 3.25 with a Good category. These results indicate that students have a positive response to the implementation of the CBSO-STEM model with a final score of 3.36 (Good category).

The innovation of the CBSO-STEM learning model provides an alternative solution for online learning that takes into account the needs of students while ensuring the quality of learning outcomes. The CBSO-STEM model has the potential to develop creative thinking skills and other necessary skills for students.

Challenge Based Learning provides students with opportunities to develop the 4C skills [17]. Group discussion activities provide students with experiences of working effectively in teams. In its implementation, students work together to solve challenges, with each group member actively contributing ideas to overcome the provided challenges, thereby fostering collaboration skills among students [18], [19].

At the beginning of the learning process, students are presented with the Big Idea. The conveyed Big Idea should have a meaningful connection between the content and the students’ lives, thus motivating them to learn. Then, students are asked to generate Essential Questions related to the presented Big Idea. This learning experience allows students to ask questions and develop their critical thinking skills. Subsequently, students are required to solve the given challenge. The challenge should be developed from a situation or activity that creates a sense of urgency and prompts students to take action. This learning experience can encourage students to develop critical thinking skills [20], [21].

In solving the challenges, students are provided with several guides such as guiding activities, guiding questions, and guiding materials that allow students to make decisions in order to develop their responsibility. Students are given a safe space to think creatively, try new ideas, experiment, fail, receive feedback, and try again. Throughout the process of solving the challenges, each solution presented by the students is valued, and there is a need for evaluation for each process. This learning experience can develop students’ creativity. The findings reveal that the implementation of the Challenge Based Learning model can enhance mathematical creative problem-solving abilities, creative thinking skills of students, and mathematical creativity [22], [23], [24], [25], [26]. Furthermore, it is added that almost 88% of students agree that they have become creative individuals after participating in the Challenge Based Learning experience [27] because Challenge Based Learning can be developed in highly flexible and creative situations and provide a safe space for all students to think creatively, try new ideas, experiment, fail, receive feedback, and try again [28].

The results of the challenge solutions are well-documented by the students, which will be useful for ongoing reflection, informative assessment, evidence of learning, portfolio, and storytelling of their Challenges. After successfully finding solutions to the challenges, students are encouraged to publish their findings. The students’ findings will be evaluated by both students and teachers to obtain the best challenge solutions. This publishing activity provides students with an opportunity to express their opinions, ideas, criticisms, and suggestions in written or oral form, thus developing students’ communication skills [29].

STEM-based learning is based on real-life problems that guide learners to seek solutions to social, economic, and environmental issues [30]. When integrating STEM into mathematics education, several aspects need to be considered: (1) using meaningful and real-life learning related to the learners’ daily lives; (2) challenging the potential of learners using an engineering design approach to develop critical and creative thinking skills through interconnected activities; (3) assisting learners with technology design and learning from failures in designing solutions within the engineering design with existing designs; (4) implementing a teaching and learning process aligned with science, mathematics, and relevant subjects such as language, humanities, and social sciences; and (5) training learners to collaborate and communicate problem-solving in learning activities [31].

Synchronous classroom activities are an appropriate choice because students can interact directly with each other to discuss a learning topic, and both the teacher and students can interact with each other even when they are in different locations. Online communication helps students stay connected to the course and their fellow students through platforms like WhatsApp Group. This is called synchronous learning because the system allows students to ask questions to the teacher or their peers instantly through instant messaging and provides students with immediate feedback from their teachers [13]. Furthermore, the teacher will provide feedback through virtual meetings.

The effectiveness of the learning model is then analyzed based on several criteria. The research results show that (a) the CBSO-STEM model shows similar average mathematical creativity of students in the experimental classes of each implemented study program, (b) the average mathematical creativity of students with the CBSO-STEM model is better than the average mathematical creativity of students with the expository model, (c) the CBSO-STEM model shows an improvement in the mathematical creativity of students who implemented the CBSO-STEM learning model, and (d) students have a positive response to the implementation of the CBSO-STEM learning model. In other words, it can be concluded that the implementation of the CBSO-STEM model is effective in developing students’ mathematical problem-solving abilities.

The implementation of the CBSO-STEM model is one alternative solution in the context of online learning. The application of this model can be further developed to enhance other abilities/skills of students, considering the needs of graduate qualifications in the era of Industry 4.0 and IT development.

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