Analysis of Students' Perceptions of the Effectiveness

Study Case Analysis of Students' Perceptions of the Effectiveness of Online Learning in Calculus Courses Michael Kurniawan (2018123456) University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States kurniaml@mail.uc.edu Abstract Calculus, as a branch of mathematics, is one of the basic courses that must be taken by first-year students at the University of Cincinnati. Based on preliminary studies, approximately 54% of students stated that Calculus is a difficult course to understand. During the COVID-19 pandemic, the learning system, which was previously conducted face-to-face, changed to online learning. This change has the potential to create new challenges in the teaching and learning process. Therefore, this study was conducted to determine students' perceptions of online learning in Calculus courses. The purpose of this study was to identify students' perception trends so that they could be used as a basis for improving teaching quality. This study used a descriptive method with data collection through an online questionnaire. The results showed that students had negative perceptions of online learning for Calculus courses, in terms of content (89.3%), interaction (79%), and learning environment (50%). Most students believed that face-to-face learning with direct explanations from lecturers was much more effective. Keywords: Calculus, online learning, student perceptions, learning interaction INTRODUCTION Mathematics is often referred to as the mother of science because it serves as the basis for the development of various branches of science. As a discipline that focuses on patterns, structures, and logic, mathematics is a compulsory subject in the education curriculum in many countries [1]. In the United States, almost all educational institutions, including the University of Cincinnati, require students to take mathematics MICHAEL KURNIAWAN 1 Study Case courses as part of the general curriculum. Hudson [2] emphasizes the importance of effective mathematics learning in order to support the advancement of other sciences. Therefore, competent teaching staff and continuous efforts are needed to minimize obstacles in the mathematics learning process. One of the main obstacles in mathematics learning is the emergence of math anxiety, which is often caused by previous negative learning experiences [2]. This condition creates a negative perception of mathematics among students, which ultimately affects their learning outcomes. During the COVID-19 pandemic, mathematics learning, which was already considered difficult, became even more challenging due to the change in the teaching system from face-to-face to online learning. This policy is in line with regulations imposed by the United States government to suppress the spread of the virus. Online learning is a learning process that does not require physical meetings between lecturers and students but utilizes the internet and supporting platforms such as Zoom, Google Classroom, or Microsoft Teams [3]. According to Saifuddin [4], online learning can increase the active role of students in the learning process. However, previous studies have shown that even face-to-face learning in mathematics often faces obstacles in the form of difficulty understanding concepts and the emergence of learning anxiety [5][6][7]. With the shift to online learning, new obstacles have emerged that affect students' perceptions of the effectiveness of mathematics learning, especially in calculus courses. Calculus itself covers the concepts of limits, derivatives, integrals, and infinite series, which are important foundations in various fields of exact sciences. The purpose of this study is to analyze students' perceptions of online Calculus lectures at the University of Cincinnati. The results of this study are expected to provide a basis for improving online learning strategies and quality in the future. RESEARCH METHODOLOGY This study used a descriptive approach with a survey method targeting active students at the University of Cincinnati. Data was collected through an online questionnaire accessible via an online survey link. The research population consisted of 895 active students. Based on the Slovin MICHAEL KURNIAWAN 2 Study Case formula with a margin of error of 5%, the minimum sample size required was 94 respondents. However, in practice, 394 students participated and completed the questionnaire, so all data were analyzed because they met the criteria for a representative sample size. The sampling technique used was simple random sampling, assuming that all students had a relatively homogeneous level of readiness and conditions for participating in online learning, considering that all participants were experiencing a full online learning system for the first time [5]. The stages of the research implementation included: a. Development of research instruments. b. Instrument validity testing. c. Revision of instruments based on validation results. d. Data collection through online surveys. e. Descriptive analysis of the collected data. The research instrument was a questionnaire containing questions about students' perceptions of online learning in Calculus courses. One of the main focuses was to explore students' learning difficulties by adapting Wood's indicators of learning difficulties [8]. In this study, the discussion focused on three aspects of student perceptions, namely perceptions of the content of Calculus learning materials, patterns of interaction between lecturers and students, and the learning environment during the online learning process. The research instrument was developed using the Google Form platform. Construct validity testing was conducted by a lecturer from the Department of English Language and 10 students to assess the clarity, readability, and suitability of the questionnaire content for the research objectives. The validation results showed that the instrument was in line with the research objectives, although there were some minor improvements in grammar. After refinements based on validator input, the data collection stage was conducted entirely online, given that this research was conducted during the COVID-19 pandemic. RESULTS AND DISCUSSION Johnson (2020) explains that perception is a person's experience of an object, event, or relationship formed through the process of interpreting the information received [9]. MICHAEL KURNIAWAN 3 Study Case In line with this, Roberts (2018) states that perception is the process by which individuals organize and interpret patterns of stimuli from their surroundings [10]. Thus, perception can be defined as an individual's interpretation of the stimuli received, whether physical or emotional. According to Walker in Smith's (2019) research, the interpretation of stimuli is greatly influenced by two main factors: the individual's internal factors and the characteristics of the object as the source of the stimulus [11]. Internal factors include aspects such as thoughts, feelings, experiences, intelligence level, and expectations, while external factors include the physical, psychological, and environmental conditions of the perceived object. Perception can be categorized into two types: positive perception and negative perception [12]. Positive perception arises when an individual's assessment of an object is in line with expectations or prevailing norms, while negative perception indicates a view that is contrary to those expectations. Research by Martinez (2021) shows a positive relationship between students' perceptions of learning methods and their academic achievements [13]. Therefore, it is important to understand how University of Cincinnati students perceive online learning, especially in Calculus courses, in order to form the basis for improving future learning strategies. In general, there are three main aspects that are taken into consideration when assessing the quality of online learning, namely teaching materials, learning interactions, and the learning environment [14]. Perceptions of Teaching Materials Teaching materials include a collection of concepts, theories, and principles that are compiled to achieve learning objectives. In online learning systems, materials are no longer delivered directly through lectures in the classroom, but through various digital media such as PowerPoint slides, videos, infographics, and digital modules. According to Peterson (2020), teaching materials are all forms of information or tools that are systematically designed to help students master certain competencies [17]. Based on the questionnaire results, most students assessed that lecturers had presented teaching materials of good quality. However, some students said that some of the learning videos were sourced from public platforms such as YouTube, rather than videos produced by the lecturers themselves. MICHAEL KURNIAWAN 4 Study Case Figure 1. Quality of Teaching Materials Presented by Lecturers during Online Learning. A total of 89.3% of students had a positive perception of the teaching materials provided. However, a positive perception of teaching materials was not always followed by an increase in understanding of the material. Many students still found it difficult to understand the topic of calculus, mainly because there were no face-to-face sessions. One student responded: “Online learning is convenient because it can be done at home, but it is difficult to understand complex material such as calculus without direct explanation from the lecturer.” The material taught during the two months of online learning included derivatives, double and triple integrals, and their application in calculating area and volume. Based on the survey, the main difficulties faced by students were, in order: 1. Difficulty applying algorithms in solving math problems (57%). 2. Difficulty remembering theorems and formulas (48%). 3. Not understanding the relationship between the position of numbers and their mathematical meaning (30%). 4. Difficulty recognizing mathematical symbols (13%). These difficulties cause negative perceptions of the content of Calculus, even though the teaching materials are presented well. This shows that the quality of presentation is not always directly proportional to understanding of the material. Perceptions of Learning Interactions Learning interactions include communication between lecturers and students as well as between students. Effective interaction plays an important role in supporting optimal learning outcomes. The results of the study show that interaction between lecturers and students (42%) and among students (41%) is only in the adequate category. Some student responses are as follows: MICHAEL KURNIAWAN 5 Study Case • “With online learning, I am more courageous to ask questions and discuss.” • “The question and answer sessions opened by the lecturer help me understand the material.” • “It is difficult to understand explanations without face-to-face interaction.” • “Online learning is less effective because communication is limited.” • “Online learning encourages creativity, but communication is still not as effective as face-to-face classes.” Some students find it difficult to interact because they are not used to asking questions in writing. However, interaction is considered better in classes that use Zoom or Microsoft Teams compared to material sharing platforms such as Google Classroom. Figure 2. Lecturers' Quick Responses to Student Questions during Online Learning. The majority of students felt that lecturers still provided quick and relevant feedback. However, assignments were the main source of negative perceptions. As many as 79% of students admitted to having difficulty completing assignments due to the limited number of sample questions and the large number of assignments from several courses given at the same time. This shows that negative perceptions of the assignment system are a significant barrier to online calculus learning interactions. Perceptions of the Learning Environment An ideal learning environment is one that can create focus, calmness, and motivation to learn [19]. Based on the survey results, although students consider online learning to be more flexible, many feel that the home environment is not conducive to concentration. MICHAEL KURNIAWAN 6 Study Case Some student responses are as follows: • “It is difficult to concentrate because the home environment is noisy.” • “Parents sometimes ask for help while online classes are in progress.” • “For engineering students, practical activities are not effective if done online.” These results indicate that the home environment is not an ideal place to study for courses that require high concentration, such as Calculus. As many as 50% of students gave negative perceptions of the online learning environment and considered the traditional classroom atmosphere to be much more motivating. CONCLUSION Most students (89.3%) have a positive perception of the quality of Calculus teaching materials prepared by lecturers, but this positive perception is not in line with their level of understanding of the material. The aspect of learning interaction remains a major challenge. As many as 79% of students have a negative perception of the assignment system, which is considered ineffective due to the lack of direct explanation and limited time for completion. Additionally, 50% of students consider the online learning environment to be unsupportive of concentration, especially for those living at home with external distractions. Overall, although online learning offers flexibility, students still consider face-toface learning to be more effective for analytical courses such as Calculus. REFERENCE MICHAEL KURNIAWAN 7 Study Case MICHAEL KURNIAWAN 8