Students’ perceptions in undergraduate online math courses

Abstract The purpose of this qualitative study was to understand how undergraduate math students perceive their learning in an online learning environment. A review of the literature revealed a need for additional qualitative research on the perceptions of students in the online learning environment. The specific elements of interest were technology, communication, and assessment. The study used a qualitative descriptive case study design. Purposive sampling was used to sample six online undergraduate math students. Online questionnaires and follow-up interviews provided data for analysis. Interpretive analysis highlighted emergent themes to form a true representation of students’ perceptions. The results revealed that students perceived technology as a supportive tool that could not replace the need for teacher–student interaction and engagement. In addition, online students perceived communication as an essential classroom element. Participants considered online assessment measures ineffective without useful feedback. Educational stakeholders could use the study’s findings to make informed instructional design decisions that could increase student success rates in undergraduate online math courses. Also, researchers might use the study findings to identify instructional elements that could potentially lead to increased learning gains.


Introduction
The interest in online education and virtual learning style grows year by year. Although Internet access, increased enrollment of adult learners, and demand for flexible learning schedules are factors that have influenced the growth in online learning , the wished futuristic change in instructional styles has pushed universities to reshape the way of providing education and reviewed its systems and practices that have been used before for ensuring the continuum of learning life and the suitability to future situations. Also, this case has led institutions to seek new instructional methods in order to meet the various requirements of the e-learning environment by merging technologies and student collaboration to boost student learning (Archambault, Wetzel, Foulger, & Williams, 2010).
The change in circumstances of teaching and learning is a major feature in the current era. Online learning is the instructional model that provides learning as an alternative to a traditional instructional setting independent of time and location (Schachar & Neumann, 2010). The goal of this type of learning is to make a flexible framework that increases access to learning, enhances the quality of content, and achieves the instructional objectives (Croxton, 2014). While online learning has incorporated various modes of information delivery over the years, the distance learning has come with new technology, which increases the ability of individuals to communicate in live to in a face-to-face format from different locations (Bertram, 2017). However, students need to be competent and possess skills specific to the online learning environment in order to foster student learning, satisfaction, and achievement of outcomes (Frazer et al., 2017).
The practice of online learning in undergraduate programs is increasing. This is because the future of education is closely related to the use of technology in teaching and learning. In addition, the e-learning is a response to future education needs, increasing learning opportunities and enhancing digital awareness and the quality of educational content (Bonnel, 2008). For example, in King Khalid University (KKU), there are many initiatives and electronic digital courses and local and international educational platform, so the number of educational videos exceeded 5814, while the number of views reached about 4.7 million (S. Alshehri, 2019). Beside that, online learning positively affects general teaching subjects and mathematics. Hunter (2011) mentioned the effectiveness of e-learning in mathematics, and its contribution to exploring concepts and recalling mathematical rules in the long term. Also, the contribution of e-learning and Internet resources to learning mathematics at the university level is growing by simplifying mathematical concepts and providing multidimensional visual representations, enhancing mathematical communication, increasing the interaction of learners with visual representation, and moving mathematics education from the traditional level to the digital age (Aljaber, 2018).
The evolution of technology and instructional applications in education is a sign of this modern era. However, it requires skilled and motivated instructors to use it effectively (Tuncay & Uzunboylu, 2010). Although online learning at the university level has become increasingly acceptable over the last decade, there is no common rule or uniform mechanism to deliver the virtual instructional content between educational institutions. Instructional tools, which are developed by designers in higher education to improve the productivity and value of student learning, vary in their quality and appropriateness for learning task between educational institutions (Abrami et al., 2011). However, effectiveness, efficiency, and engagement are incorporated when using technology-assisted learning (Hunter, 2011).
Communication in an online education setting is an essential component for learning as it is being in two styles, which are synchronous and asynchronous. Students have the opportunities to collaborate simultaneously via synchronous communication, while the instructors get evidences of student understanding (Bertram, 2017). Interactions through tools of synchronous environment such as videoconferencing and chatting create a social presence without restrictions of location (Plante & Asselin, 2014). However, asynchronous communication is a solution when scheduling a group discussion or a team meeting becomes impossible. The success of asynchronous learning environment depends on students' participation in class discussions, commitment, discipline, and contribution to team projects (Richardson et al., 2016). However, online learning allows more communication and reflection than what might occur in traditional classroom discussions (Ferguson & DeFelice, 2010). Most recurrent themes in online learning were concentrated on different types of collaborative activities such as discussion boards, presence, and using a variety of instructional methods (Frazer et al., 2017). Other factors of distance learning include the ability to provide interactions and good relationship between faculty and students, positive messages, establishing mutual respect, encouragement, and time (Richardson et al., 2016). Besides that, online communication is a fundamental element when students' satisfaction of the course is evaluated (Ferguson & DeFelice, 2010).
Assessment is an essential ongoing process that identifies strengths and weaknesses of students' learning in math courses. The quality of assessment in an online setting creates a positive learning environment and supports a student's ability to self-regulate his academic performance (Croxton, 2014). It allows students to monitor their academic performance by receiving feedback from instructors and peers and provides strategies to make progress and improve their performance and skills and reflect on alternative learning strategies and future learning needs (Sancho & Excudero, 2012). Also, the assessment during the online course gives students more time for reflection, construction of self-knowledge, and goal setting (Bonnel, 2008). The instructors should provide learning support through their comments and feedback in the assessment in order to encourage students' learning and achievement. However, the application of online learning assessment may not be connected well to students' success (Bertram, 2017).
There is a gap in the literature of qualitative studies that focus on undergraduate student's perceptions in an online environment in mathematics. Plante and Asselin (2014) found that students preferred the online courses, but are less likely to enroll in them. Students believe that online learning is not as effective in preparing them to teach although it improves their technological skills and meets their academic requirements completely. The study of Carter et al. (2014) was focused on the views of students and faculty about meaningful e-learning via using a mixedmethod methodology. By answering questions regarding the experience of e-learning practice, four elements were mentioned, which are communication of student−faculty and student-student, course design, IT support, and institutional infrastructure to support e-learning. The researchers have assured the need for additional studies in the online learning that might increase learning gains (A. Alshehri, 2018;Xu & Jaggars, 2011). However, more qualitative studies are still needed to evaluate online learning and address the gap regarding the effectiveness of online learning (Zidan, 2015).

Problem statement
Teaching online math courses is not popular in undergraduate programs in Saudi Arabia due to the nature of math content and the learning style that is normally based on a face-to-face instructional method. However, Saudi universities have recently made necessary arrangements for implementing virtual instructional strategies in order to continue providing modern ways of the professional duties of learning. Online math learning would lead to a high rate of attrition among students (Bertram, 2017). According to Willging and Johnson (2009), approximately 20% of students enrolled in online math learning courses have a rise in attrition compared to students enrolled in the conventional class environment. Average attrition rates are 12 percent higher for online math courses than attrition rates for online programs across other disciplines (Golubski et al., 2013). In Web-based courses, the average graduation rate for math students is 12 per cent lower than in the face-to-face classes setting (Ashby et al., 2011).
Regardless of growth in the online learning, the particular issue is the lack of comprehension of students' perceptions in their learning and retention in an online mathematics environment. Also, there is no study that has conducted on undergraduate student perceptions for online learning of mathematics in Saudi Arabia. According to Eskey and Schulte (2012), the level of students' comfort about the structure of e-learning environment affects their enrollment decisions in online math courses. In addition, the success of online environment is highly dependent on the perceptions of stakeholders about it and the efforts they provide for such success (Bertram, 2017). However, there are economic consequences for educational institutions and students in the long term when attrition rates are high in the online education setting (Sancho & Excudero, 2012). Also, there is still a significant difference in student perceptions about what learning are elements and their effectiveness on their online learning although the policies and guidelines of online courses in KKU have been well established based on identified best practices (A. Alshehri, 2018). Thus, this study was conducted to explore undergraduate students' perceptions in online learning environment during a mathematics course.

Research questions
The following research questions were examined in this study: (1) How do undergraduate math students perceive technology in the online learning setting as it is related to their learning and attrition?
(2) How do undergraduate math students perceive communication in the online learning setting as it is related to their learning and attrition?
(3) How do undergraduate math students perceive assessment in the online learning setting as it is related to their learning and attrition?

Methodology
The purpose of this qualitative descriptive case study was to understand how undergraduate math students perceive their learning in the online learning environment. Six undergraduate math students from King Khalid University, Abha city, Saudi Arabia, have been involved in this study. Data collection instruments comprised virtual interviews as well as an online questionnaire, which were used to collect data relevant to the online instructional setting, which were technology, communication, and assessment.

Research design and procedure
The research design for this study was the qualitative descriptive case study design. A descriptive case study is appropriate when exploring a topic to comprehend meanings and patterns and attempting to select a representative sample that illuminates a specific phenomenon (Yin, 2014). The primary data collection instrument was individual interviews, which were applied by online questionnaires as well as participating in virtual interviews. For obtaining a clearer understanding of student perceptions, analysis involved the identification of common themes, patterns, and interrelationships, which may lead to meaningful change within the online mathematics learning environment.
Before the implementation, pilot testing was conducted for the interview and survey questions. According to Nerman (2011), researchers select to administer a pilot test to measure the suitability of the interview or survey procedure when conducting a qualitative examination. Three students who have taken math online courses participated in the pilot testing process to determine the reliability of the questionnaire. Those participants did not take part in the final research study. The pilot test attempted to identify ambiguous questions, leading questions, and potential bias in questions. However, results indicated the quality of questions relative to students' responses and there was no need to revise questions of the interview and survey.

Sampling
In this study, undergraduate math students were the target population. The purposive sample population included six undergraduate math students selected based on their relevancy in the study. The participants were all full-time students with experience learning via the online environment. As in earlier research, purposive sampling was suitable for their full-time learning experience via an online learning environment. They have taken two or more online undergraduate math courses. Undergraduate students of math department have received electronic invitation to be engaged in the study. The implementation of online invitations has led to enrich the data sample due to their ability to reach participants from various geographical regions. A description of the study and its objectives were included in the invitation letter. Also, a link of the questionnaire has been provided, which contained a statement of informed consent for participating in the study. Once participants indicated consent, they received access to the online questionnaire.

Instrumentations
The study used two data collection tools, which were the open-ended questionnaire and virtual interview. Having more techniques of data collection encourages thoughtful and honest responses and helps the researcher to measure multiple areas that would enhance the quality of the findings (Wahyuni, 2012). The open-ended questionnaire was used to collect data regarding students' perceptions of elements of their learning and attrition. The questionnaire contained semistructured questions regarding specific elements of technology, communication, and assessment. The questionnaire was built via Google Forms to ensure privacy and confidentiality of responses. Based on the answers to questionnaire questions, interview questions were formulated to encourage participants share their thoughts and follow-up their responses of the questionnaire questions in more detail.

Data collection
Data collection was completed in 7 weeks. The first level of data collection included a group discussion. The focus group was picked from the undergraduate students of King Khalid University who have taken undergraduate classes online during the first semester of 2022 school year. The group had valuable information about their experience in technology, communication and assessment.
A focused group was formulated through online interaction with the students of undergraduate mathematics department. An online invitation was sent to 63 students, and only 27 students filled the online forms sent to them with two reminders. Out of the respondents, one focus group of 12 students was formulated through random sampling. An online group was formed using Zoom platform, and questions that were already mentioned in the section of research questions were placed in front of the group. Responses were recorded using chat and opinions shared verbally by students.
Questionnaire-based virtual interviews, which can provide deep insights and related information regarding student perception of online learning in mathematics class, served as the second-level source for data collection. A semi-structured interview with random six participants was conducted. Interviewed students were not part of the already conducted focused group. Semistructured interviews are preferred when research seeks to understand the perception of respondents as suggested by Nicole and A A-O P (2021). An email was sent to randomly selected students using an online Google form. Responses from these forms were recorded along with their interview response. The interviewer did not try to influence respondents in any questions asked. Interviews were taken while the interviewer was open to any suggestions from the interviewees. Each interview lasted for almost 10-15 minutes, and those provided supplementary information related to participant's perception about online learning environment in mathematics class about communication, technology and assessment.
These online interviews and focus group discussions with online surveys offered accurate information and responses while reducing the cost and inefficiencies involved in face-to-face interviews. These interviews minimized the influence of gender, age, ethnicity, status, appearance, and behavior and helped in maintaining anonymity of respondents. Focus group interviews using online tools removed the problem related to geographic location, reduced cost and improved efficiency in terms of recording responses accurately.

Data analysis procedure
The qualitative approach helps in understanding phenomena and uncovers perceptions related to learning environments (Silverman, 2020). Focus group discussion using Zoom and semi-structured questionnaire surveys has been used in this study to collect data. Zoom has helped through its various features in order to effectively, efficiently and accurately record responses from the respondents during focused group discussions and one-to-one online interviews with students. The Google forms were used as the first point of contact because they are considered as a useful tool in conducting online surveys for qualitative research work.
In the online group discussion, which started our data collection, students had opportunity by giving them questions using Zoom Chat option and showing questions through Zoom slide share options. This method resulted in effective group discussion as suggested by the 12 students who participated in the group. Each student presented his/her opinion, which was recorded with the condition of anonymity. NVivo was used to develop themes and patterns identified through group discussion.
Individual interviews were conducted with the randomly selected students. Six participants were interviewed using Zoom, and the same were requested to complete Google forms. Interviews were conducted just to explain students about the scope and nature of research work. All six students duly filled out interview forms via Google. These forms were then tabulated using Microsoft Excel. These tabulated tables were then used to develop coding using NVivo software. A complete questionnaire was developed using Google forms for student responses. The questionnaire responses were then used to identify patterns and themes in the responses given by students.
All the data collected through online group discussion, Google questionnaire-based forms and interviews were converted into Microsoft Excel and Microsoft Word files. NVivo software was used in order to code all the responses collected from group discussion, questionnaire surveys and interviews. Primary coded data from group discussion and interviews were then used to analyze the student learning perception from online undergraduate mathematics class. Node and thematic analyses were developed using responses from group discussion and interviews. In order to compare the overall perception about online or physical classes, a sentiment analysis was also done using NVivo analytical tools. Node analysis evolved into three major thematic areas that were technology, communication, and assessment.

Results
Based on Nvivo analytics using word frequency tables, node analysis, and linkage comparison tables the following three major thematic areas were established. Table 1 shows the node analysis results. The table indicates that three themes emerged in two files, one generated through a focus group discussion of 12 randomly selected students and the second through questionnaires and interviews from six students. Student learning was the main title under which respondents linked assessment as the central theme by referring to it 15 times, communication as the other major theme by referring to it 37 times, and technology as another significant theme by referring to it 28 times.

Communication
Communication considered the essential theme per student references, included improvement in learning perception, role in online classes, and gaps that emerged as the significant communication elements under student learning. Student preference had a maximum influence on communication, whereas other factors like improvement in the learning experience, role in online classes, and communication gap also played an important role. Physical learning preference emerged as an essential element for communication in student learning. The second significant impact on student learning was played by technology recorded through responses in interviews and group discussions. Crucial elements related to technology, like the ease of use, connectivity, etc., emerged as the most critical influencer in technology for student learning perception. Other important areas included effects on students due to technology usage, problems faced, and student concentration. Some other factors, which referred to technology once, are excluded from the analysis. The third significant assessment theme had assessment influence, preference due to learning, cheating, and copying as central factors towards student learning perception from assessment.

Technology
Technology was explained further in terms of most crucial elements like communication, voice, clarity and other factors. Effects on students were the second most highlighted part from technology, indicating factors like lack of focus and badly affecting learning in certain cases. Technologyrelated problems and student concentration highlighted factors like affordability and liking with usage of social media and time-wasting questions.

Assessment
Assessment emerged as the third main theme under student learning from the responses recorded. Online experience of assessment was recorded, and analysis resulted in explaining student learning in terms of assessment in terms of conceptual understanding, preference due to learning and copying and cheating. Conceptual understanding was the significant part out of assessment learning perception; it highlighted that online assessments do not work well as NVivo analysis indicated a negative sentiment and words like bad. This indicated that online assessments are not as good as physical ones due to conceptual understanding. Other main nodes under assessment included preference due to learning and copying and cheating, which highlighted those surroundings, and physical assessment reduces cheating more than online one while increasing learning experience. Figure 1 shows the themes drawn using NVivo from the recorded responses from group discussion and interviews.
A node graph was generated based on the three identified themes through NVivo analysis to understand the main sub-themes falling under three of the major themes, as shown in Figure 1. There were two files used for this NVivo node analysis. The first file contained all notes from the focus group discussion of 12 students, and the second file had a response to the questionnaire survey, which ended with a followup interview to get responses from six students. File number indicates the number used by NVivo in developing node analysis against each main or sub-theme. Reference means total references made by respondents towards a particular main or sub-theme.

Questionnaire and group discussion findings
Questionnaire and group discussion analysis generated three different categories under student learning perception in an online mathematics learning environment. In order to check whether the assessment is explained by communication or communication can be defined by technology, comparison tables were created to check the linkage of themes. A comparison table for each category is generated using a response coding mechanism. The findings are divided into three main chapters as categorized during theme analysis. This theme includes Communication, Technology and Assessment, which explains student learning in an online environment as analyzed using questionnaire and group discussion responses. These linkage tables indicate that themes are mainly from student responses from focus group and questionnaire surveys and not from intertwined results generated from major themes. Comparison tables were also generated to validate major themes with sub-themes linkage. Each finding aligns with the relevant question asked during the interview or group discussion.

Communication
Communication-related responses were recorded from questionnaire-based interviews and group discussion. Communication response linkage indicates that most of the theme comes from student responses, interviews and focus group discussions, referring to Figure 1. One important linkage in the table is related to assessment, which refers to the linkage of communication with assessment. It is evident from research questions that learning works through assessment and communication; therefore, this linkage provides a logical explanation to the developed node. Questions 7-10 targeted communication in an online learning environment, whereas question number 03 from group discussion was about communication. Results were generated using analysis of all the responses through questionnaires, interviews, and focus group discussions. Figure 2 ishows association of communication with assessment and other elements related to it.

Comparison result
The comparison between the three main themes indicated that communication and assessment are associated, which is a finding in line with the initial research question as assessment is linked to communication when it comes to online learning. The association works through student learning. Communication is not associated with technology, and student learning has three themes: Communication, Assessment, and Technology. Comparison between communication and assessment is associated as shown in Figure 3 whereas following Figure 4 indicates that association between communication and technology works through student learning without any other association. Table 2 displays the results from word frequency analysis for the interview questions 7-10 and group discussion open-ended question # 3. The word "communication" occurs 33 times in these word frequency table data, with a weighted percentage of 3.46%. "Communicate" and "communication" are two words that are identical in the table, indicating that this term is frequently used  to exchange information or ideas in an online learning environment. Results indicate that communication is linked to student learning in an online learning environment. It also stresses that communication is one key aspect of the learning environment. Table 2 shows importance of communication in an online learning environment. Physical communication is preferred by students in comparison to online classes and physical classes improves learning experience over online classes. The importance of physical words is evident from the occurrence of physical words 85 times and the weighted Percentage of 8.91%.

Word frequency for communication
The frequent use of the word "communication" suggests that students are worried about their ability to interact effectively with peers and teachers in a virtual setting. The word indicates that they find communication difficult in the virtual learning setting. Additionally, "understand" is used frequently, demonstrating that the student's attention is on comprehending the information being taught in the virtual setting. The word indicates that students think it takes more work to understand the material in an online learning environment than in a traditional face-to-face setting. The term "problems" implies that there are difficulties that students are having in the online learning setting. The word suggests that online learning is more challenging than traditional face-to-face learning.
Overall, the word frequency table sheds light on how students view their learning setting and show that they have communication issues and encounter difficulties when using online learning platforms. These results can guide the development of interventions and strategies to enhance the learning experience for students in the virtual environment. Physical classes were preferred over online classes. There was an overall agreement among the participants that physical classes are focused and due attention can be given, whereas online  classes cause lack of focus and attention gets diverted due to disruptions. One respondent identified that communication in online classes does not work well as students connecting and reconnecting can cause disturbances during classes. One student stated that in physical classes they can ask direct questions therefore physical classes are better.
Interview Questions: Learning Perception Q7: How do you perceive mathematics learning in an online setting?
Students responded in agreement that it is hard to learn mathematics in an online learning environment. It was mentioned that in an online learning environment mathematics understanding and development is really hard as students cannot effectively comprehend mathematics. One of the students mentioned that if its hard due to mobility restrictions, then online mathematics learning is a useful way to learn mathematics.

Q8: Do mathematics online classes improve your learning experience or physical ones?
Interviews concluded that physical classes are better as most of the students advocated physical classes over online classes. Some respondents stated that physical classes are more interactive. One respondent stated that it is less easy to get bored and teacher interaction makes it easier to understand mathematics problems.

Q9: What is your opinion about the role communication plays in an online class?
Student interviews concluded that communication plays a very important role in online classes. One respondent stated that communication plays an important role because everything the students learn and everything students write in exams depend on communication from the teachers. Better communication means better marks.

Q10: Does online communication help you learn more than physical classes?
All students unanimously reported that physical classes are helpful over online classes. It was mentioned by respondents that physical classes encourage students to participate in classes. Students mentioned that physical classes are fluent and helpful in comprehending topics discussed in class.

Technology
In the case of technology, linkage does not work through association with communication rather linkage of technology as a major theme directly comes from students' responses through focus group discussion, interview responses, and questionnaires. Unlike assessment, association of communication with technology is not established in node analysis. This means technology works independently as a major theme, as specified earlier in the questions. Unlike assessment, technology has no association with communication when it comes to explaining.
The following comparison chart indicates the response linkage between communication, technology and assessment, as shown in Figures 5 and 6. This comparison suggests that technology and assessment are linked through student learning, while both are independent themes. Technology plays a significant role independently in student learning perception. Table 3 displays the results from word frequency analysis for the interview questions 7-10 and group discussion open-ended question # 3. Results indicate that communication is linked to student learning in an online learning environment. The table shows the importance of communication in an online learning environment. Students prefer physical communication to online classes; physical classes improve the learning experience.
The table suggests that technology plays a significant role in the learning process in the context of student learning perception in a learning environment. The word "technology" has the highest weighted Percentage at 5%, indicating that it is the most frequently mentioned word in the data set. The words "online" and "classes" are also in the top three, with weighted percentages of 4.26% and 4.63%, respectively, indicating that online classes and the use of technology in the learning environment are essential factors in student perception.
The word "screens" is mentioned with a weighted percentage of 1.48%, which may suggest that the use of screens in the learning environment is a concern for some students. The words "video" and "media" are also mentioned with a weighted percentage of 1.48%, indicating that the use of video and multimedia resources may be perceived as important for effective learning. The word "connectivity" is mentioned with a weighted percentage of 1.67%, suggesting that the quality of internet connectivity and access to technology may be an issue for some students. Similarly, the word "disturb" is mentioned with a weighted percentage of 0.93%, indicating that distractions and interruptions caused by technology may also be a concern for some students. Words like badly, issues, and concentration refer to the problems faced by students in terms of technology.
Overall, the table suggests that technology and online learning play a significant role in student learning perception in the studied environment but that there may also be concerns related to the use of technology, such as connectivity issues and potential distractions.

Group Discussion
Technology Q02: What do you think about technology in online classes? Physical classes were preferred over online classes, but use of technology was considered as an important element. Some of the respondents viewed technology as a useful tool for online learning and thought it is good only as an alternate. Some respondent's thoughts identified the role of technology as a useful self-learning mechanism. Some responses indicated that technology has limitations, and it needs improvement in THE learning environment.

Interview Questions:
Opinion about Technology Q11: What is your opinion about role of technology in an online learning setting?
Students responded by referring to technology as a blessing and important tool in the learning environment especially during lockdown conditions. Some responses highlighted that technology reduces time-wasting and it is a useful alternative if physical classes are not possible.

Q12: Use of technology-based tools is preferred in an online setting or in physical classes?
Interviews concluded that technology-based tools are good only in online settings. Some responses indicated that technology-based tools might increase understanding even in physical learning environments.

Crucial Elements of Online Learning
Q13: What are the most crucial elements in an online learning environment? Student responses highlighted that in an online learning environment, most crucial elements include communication, participation, interaction, keeping track of the things, and clarity of audio and video. These are the most crucial elements regarding online learning environment mentioned by students in an online learning environment.

Assessment
Assessment-related responses were recorded from questionnaire-based interviews and group discussions. Question numbers 14-15 targeted technology in an online learning environment, whereas question number 04 from the group discussion was about assessment. Results were generated using analysis of all the responses. It indicates the association of assessment with other elements and responses, Figure 7. Linkage of assessment indicates association with the communication, but it also works as an independent theme. Effective communication is a crucial part in terms of assessment in any learning environment. Therefore, this linkage falls in line with expected results. Table 4 displays the results from word frequency analysis for the interview questions 14-15 and group discussion open-ended question # 04. Results indicate that assessment is linked to student learning in an online learning environment. The table shows the importance of assessment in an online learning environment.
The table showed that the word "assignment" occurs 16 times in the table with a weighted percentage of 4.88%. The term "assignment" can be interpreted as an assessment of how students perceive their learning. Students may see assignments as a method for their teachers to assess their knowledge of the course material and offer constructive criticism.
Assignments can assist students in applying what they have learned in class and in the development of critical thinking abilities. Words like better, concept indicates that assessments are one crucial part of the learning environment. Words like cheat and copied indicate that students think that online assessments are not at par with physical assessments due to better performance of maybe invigilator. The word frequency table indicates assessment and data patterns related to student perception of difficulty in an online learning environment regarding concepts, copying, and cheating.

Group Discussion
Assessment Q04: Do online assessments play an important role in online learning environment or physical ones are better?

Figure 7. Caption -Assessment Responses Linkage.
Physical evaluations and assessment were considered better over online assessments. Some of the respondents viewed assessments made by teachers as unfair or sometimes not according to their expectations. It was also highlighted that these assessments do not serve the purpose as some students copy and paste. Some students stated that physical invigilators perform better than online protocols. Students responded by referring to the importance of practical application of mathematics concepts rather than through online learning. It was mentioned that online assessments have problems related to copying and pasting of content and reduce the effectiveness of learning environment through assessments.

Q15: How does online assessment influence your learning about Mathematics?
There was a mixed response from students about how assessment influences their learning about mathematics. Some highlighted the influence as bad or letting them feel insecure about their preparation towards exams. The only point highlighted about utility was that it enables them to keep pace with studies.

Conclusion
From the empirical findings obtained through node analysis, it was confirmed that the main themes of our research question fall in line with most important elements in line with student learning perception in an online learning environment. Communication and assessment had an association, but the result obtained from linkage graphs using NVivo code indicates that these are separate themes or crucial elements interlinked. Technology is an independent and a crucial element in building student perception. Communication is considered the most crucial element in an online learning environment. Student responses through group discussion and individual interviews indicated that physical classes for mathematics are preferable to the online environment. Word frequency tables and interviews indicated a positive sentiment towards improved learning through physical classes rather than online classes. Central point was student perception that effective communication is established in physical classes more than online learning environment. Technological improvement has made online learning relatively effective. Still, it lacks the development of effective communication due to problems like disruptions, interactions, connectivity, cross-questioning, and lack of individual interactions and focus of students. It can be concluded through research work that communication is the main driver behind learning in an online environment, and technology, with its limitations, is still unable to meet the requirements. Physical classes remain the best possible way to learn in the case of mathematics classes while incorporating technological tools for assessment, tracking, and noting down lectures can enhance learning in such environments. This research work highlights problems associated with reliance on technology for learning. Technology is not preferable as it still lags with multiple problems. Word frequency table, questionnaire, interviews, focus group survey and sentiment analysis indicated inability of technology in an online learning environment. There were concerns related to the use of technology, such as connectivity issues, concentration loss, cheating, inability to develop concepts, and potential distractions. Future research may include extensive research on tools and areas where technology is proving effective compared to physical classes. The inability to interact with the instructor was argued as one central problem, which gets sorted in physical classes with utmost focus and attention.

Communication, Technology and Assessment:
Q16: What do you think about the role of communication, technology and assessment in online environment?
Student responses highlighted that in an online learning environment, the most crucial element was communication. Technology was considered as a way to enhance learning only in the time when physical classes option ceases to exist. Assessment and learning in online environment considered to be bad for learning mathematics.
Technology was considered with communication as the most essential element in an online learning environment. However, assessment role in enhancing understanding of mathematics was questioned. Students had reservations that it does not help in developing strong understanding of the subject. Technology was thought to be one of the most important elements, but limitations of technology were highlighted as disruptions, interactions, connectivity, cross-questioning, focus to details and teacher response. These elements of technology were asked to be improved to enhance online learning experience in the mathematics learning environment.
Finally, the shared perception was that communication is only effective in physical classes. Online classes can be used only where there is utmost requirement; otherwise, online learning cannot be preferred over physical classes even with all the technological support due to its limitation regarding technological glitches, interaction and flawed assessment mechanism.

Limitations of the study
This study had some limitations, which include sample data limitations, student response, hesitance about disclosure of information and others. Students were reluctant to share the information due to fear about personal information. Sampling proved to be a big challenge as only 27 students responded to emails for data collection. Out of the responses, only 12 agreed to become a part of the group discussion. This resulted in challenging situations for data collection. Therefore, study was limited to focused group-based research finding rather than a general result, which is applicable from a wider perspective. Another limitation was reluctance to share thoughts due to fear of disclosure of information. One possible effort made to reduce this effect was with the inclusion of open-ended questions for group discussion as well as using different modes of data collection.

Future recommendations
Although this study has identified that even with technological support and all other factors, effective communication is still missing in an online learning environment, which means it still needs more research studies to be done. This fact is further strengthened by the problems identified when it comes to assessment, which was identified by students as an area, which is not effective at all in an online environment. In addition, more studies are needed to help instructors understand the major problems faced by students when converting the content they teach from traditional way to online setting, especially when it comes to communication, technology and online assessment. Besides that, this study has raised several questions for future works, which include how to effectively communicate in an online setting when physical setting is not possible? How to use technology crucial elements to improve on the learning process? What type of assessment invigilator mechanism may be used for online assessments?

Questions Asked in the Group Discussion
Icebreaking Question: May I know something about your ability class experience online?

Hierarchy of Questions:
(1) Do you prefer online or physical classes of ability?
(2) What do you think about technology in online classes?
(3) Does communication in online classes help in learning or create problems?
(4) Are online assessments necessary in online learning environments, or are physical ones better?
Student 1: Sir, I prefer Physical classes. I feel there are some hurdles we face regarding communication during online classes. For me, Physical evaluation is better as compared to online.
Student 2: It's better to have online classes if there is no chance of physical, but again comes some cons with technology like disturbance, connection issues, electricity, etc. I prefer physical classes because, in physical classes, our attention and focus are on the point. In online classes, we can't pay so much attention; online classes are tiring and wasteful, and even continuous hours and hours spent on screens affect us so badly.
Student 3: In my personal experience, I don't think it plays a good role in online classes; while we can't focus and pay attention to a specific point, all things are wasted. I prefer physical classes. Technology is good as far as interview or test is concerned, but as far as online class, it is not fruitful. It creates a problem because he can't ask mid-class if someone has any queries. After all, the whole decorum will be disturbed. The physical one is better because it motivates the amygdala to attempt a test with whim and wisdom.
Student 4: If the teacher has expertise in the subject, it doesn't matter if it is online or physical. So I prefer Online classes as it saves time. Students and teachers should be familiar with the technology. Moreover, there are many user-friendly apps like Blackboard and others. I think online learning is creating more ways for students to learn, and they are going towards self-learning through different mediums, which is good as they don't depend on the teacher entirely. This is where I found some issues. As students copy-paste the assignment, all teachers are also not evaluating correctly.
Student 5: I prefer Physical classes. Technology is essential in developing skills like attentive listening and quick learning. Still, human nature catches or learns more in physical class because of collective behavior and environment. I've more experience with online classes, as I have completed three consecutive semesters in online classes. Yes, it helps; however, on the other hand, sometimes it creates numerous problems like network issues from the other side like the quality of Video, fluctuating voice, and sometimes lack resources for the poor and needy students who can't afford the gadgets. I'd instead go for physical ones. Student 6: I prefer Physical classes because we can concentrate better. Online courses cause disturbances if there are connection issues. Students can now use technology to shift to online mode. Teachers are good at using it as well. Habitual due to COVID-19 lockdowns, but some students cannot access good technology for better connection. Communication goes well, but students connecting and reconnecting can cause disturbances. Physical assessments are always better as better invigilation can take place.
Student 7: I must prefer physical classes. Technology in online classes offers students many opportunities, like chatting and using other social media apps that divert the student's minds. Resultantly he does not concentrate. Moreover, there is a connection problem; the power goes off suddenly, which causes hindrances in online learning. Physical assessments are better.
Student 8: Physical classes are better than virtual classes because if we have any issue we can ask at that moment and get it cleared. The concepts become more apparent when the discussion is done face-to-face rather than virtually. The interaction between students and teachers is comparatively less in online classes, so we prefer physical classes. The main reason for NO to online classes is a poor internet connection.
Student 9: I prefer physical classes because we can concentrate or understand better. Instead, of using technology, we should focus on physical classes because it is betterment, during in online classes, we can distract because of social media sides.
Student 10: I prefer physical classes over online classes as I feel in-person interaction and collaboration with classmates and teachers are more effective for learning. Technology in online classes is helpful but can also distract and cause technical difficulties, hindering the learning experience. Communication in online classes can be challenging, primarily if language barriers exist or students have trouble expressing themselves in writing. Physical assessments are better than online assessments as they allow for more personalized feedback and a better understanding of the material.
Student 11: I prefer online classes because they are more flexible and convenient, especially for students with other commitments like work or family. Technology in online classes is essential and enables students to participate in class discussions and assignments from anywhere with an internet connection. Communication in online classes can be effective, but it requires active participation from students to ensure they are engaged and receive the necessary instructor feedback. Online assessments are just as critical as physical assessments, objectively measuring a student's progress and understanding of the material.
Student 12: I prefer physical classes because face-to-face interaction with instructors and classmates is more beneficial for learning and retention. Technology in online classes is helpful, but it can also be distracting and difficult to manage, especially for students who are not as familiar with the technology. Communication in online classes can be challenging, especially if there are technical difficulties or students are uncomfortable expressing themselves in writing. Physical assessments are better than online assessments as they provide a more personalized learning experience and allow instructors to provide immediate feedback to students.