**ANALYSING STUDENTS’ PERCEPTIONS ON ONLINE MATHEMATICS LEARNING USING FUZZY CONJOINT METHOD**
**Zurina Kasim 1\*, Nur Izza Hazwani Azali Azman 2**
1,2Faculty of Computer and Mathematical Sciences,
Universiti Teknologi MARA Perlis Branch, Arau Campus, 02600 Arau, Perlis, Malaysia
Corresponding Author: \*zkas@uitm.edu.my
Received Date: \*date
Accepted Date: \*date
Published Date: \*date
**HIGHLIGHTS**
- Fuzzy conjoint analysis is used in analysing students’ perceptions on online mathematics learning among degree in mathematics management major’s students at UiTM Perlis.
- Students rated neutral on all attributes except for one attribute in the students’ performance in the online learning aspect.
- Students were strongly disagreed that they are copied each other works during online test.
- Students viewed mathematics as a difficult subject to study online despite having flexible time for revision and detailed instruction from the lecturer on how to participate on online learning.
**ABSTRACT**
*Online distance learning is increasingly popular, especially since the pandemic Covid-19. All stages of learning from elementary to university level used online learning. Because students' learning abilities variety, it takes motivation and support from their surroundings to learn new things.* *It is important to understand students’ experiences, perspectives, and preferences toward online distance learning. This study analyzes the perceptions of online mathematics learning among 40 undergraduate mathematics majors' students at Faculty of Computer and Mathematical Sciences, UiTM Perlis. The perceptions were analyzed in 3 dimensions which are students’ opinion, students’ performance and lecturers’ roles on online mathematics learning using fuzzy conjoint method. Degree of Similarity is used to rank each attribute in each dimension. According to the findings, all attributes were rated “neutral” except for one attribute which rated “strongly disagreed”. Students were rated “strongly disagreed” that they sometimes copy each other works blindly during the online assessment (students’ performance). Students viewed mathematics as a hard subject to learn through online even though they have flexible time to study the feedback on tests/quizzes returned by the lecturers (students’ opinion). The lecturers had play their role well like always give feedback on student assessment and provide a detailed instruction on how to participate on online learning (lecturers’ role). This study helps teachers as well the university to understand students’ experiences, perspectives, and preferences. Hence, it helps find a way to improve the quality of online education.*
***Keywords:** online distance learning, fuzzy conjoint, perception, attribute*
# INTRODUCTION
Online learning refers to internet-based learning whereby the learning process is conducted in the virtual environment. It is also known as e-learning and first introduced as internet is created in 1990. Online learning has been used ever since in open distance learning for working adult as a way to develop equitable access to higher education for all. For the past two years the Covid - 19 pandemic has led to unprecedented challenges in all aspects of human well-being including education. Lock down due to the pandemic had significantly disrupted the education system worldwide. Students are unable to attend classes face-to-face and interact with friends as they used to. These factors will affect students emotionally and also their learning perception during the pandemic. During Movement Control Order (MCO) online distance learning was unavoidable. At all levels of education, from primary schools to universities all over the world, online learning is used to replace the face-to-face or so called traditional classroom learning.
There are many studies conducted in analysing the students’ perceptions towards e-learning during the ongoing COVID-19 pandemic at high school level as well as university level. Study by Khan et. al (2021), on university students of National Capital Territory (NCT) of Delhi, revealed the positive perception toward e-learning and the acceptance this new form of learning. It is because online distance learning provides them much freedom to connect with their teachers, fellow students and engage with their study materials at the comfort and flexibility of space and time. However, study at Liaquat College of Medicine and Dentistry, India found that during the lock down students preferred face-to-face teaching rather than online teaching (Abbasi et al., 2021). The sudden shift from face-to-face to online learning platforms during the pandemic posed challenges to students, teachers as well as parents. The dramatic change in the education process give the big impact on the students. People's ability to process information is limited and by using many learning modalities may lead to cognitive overload, which might limit the capability to learn new material effectively (Hodges et al., 2020). In addition, if students are not comfortable utilizing the technology, it might have a negative impact on their learning outcomes. Access to a device, the internet, a physical learning area, and a strong habit of learner autonomy are necessary before changing to an online learning platform. Device ownership is a recurring barrier to the successful implementation of online learning due to the digital divide. In developing nations, irregular internet access prevents successful online learning (Salac, 2016). In the case study of Western Michigan University, students reported negative experiences of distance learning such as lack of social interaction, time and location flexibility (Al-Mawee et al., 2021). Time management is the most important factor influencing students' academic performance in online distance learning beside learning environment, learning method and internet connection (Mohd Idris et al.,2022).
The student’s perception of online learning on mathematics course has become a great interest among the educators. It is because students often have a negative perception on mathematics since it is often difficult for students to master (Kasmin et al., 2019). Online learning requires motivation and encouragement from the surroundings as students have different learning capabilities. The quality of emotional life of the students had effect their attitude toward mathematics learning. Therefore, positive climate of emotions must be established by family’s members, teachers and learning institution to ensure that the students stay motivated, highly confident and less anxiety in learning mathematics (Colomeischi & Colomeishi, 2015). Mathematics self-concept is important to understand as it perceived students’ abilities in learning mathematics. Students had positive as well as negative mathematics self-concept in online learning (Bringula et al., 2021). Their study also identified challenges faced by the students such as technological, personal and test anxiety to name a few.
Blended learning or hybrid learning uses both face-to-face and online. This mode of learning is convenient and flexible, over more the uses of technology in online component really influence young generation to learn. However, the study found that students were preferred the face-to-face component compare to the online component in blended learning mode of mathematics course (Krishnan, 2016). Students were more comfortable communicating with teachers and peers face-to-face and its enable them in better understanding of the mathematics concept.
Meanwhile, high school students were mostly very positive toward online learning mathematics during the time of Covid-19 (Doly \&Ahmad, 2021). The result agreed with Nuril Huda et.al.(2020), which found that students have a good perception of online mathematics learning using youtube and there exist positive relationship between students’ perceptions and achievement. Study by Baya’a & Daher(2009) on students’ perception of mobile phone usage in mathematics learning suggested the positivity of the students acceptance. They were positively impressed by the potentialities and capabilities of mobile phone in the process of learning mathematics. This indicates that these new technological tools have benefit in mathematics education.
Conjoint analysis is a form of statistical analysis used in market research to understand how the customers value different features of the products or services. It was initially used in understanding how people make decisions based on attributes that impact users’ perceived value of the product or service. The main types of conjoint analysis is Choice-Based Conjoint and Adaptive Conjoint Analysis. However, over years there are various forms of conjoint analysis have been developed, such as the Fuzzy Conjoint Method (FCM) proposed by Burhan Turksen & Willson, (1994). There are many studies on perceptions conducted using FCM. For instance, Lazim & Osman, (2009) used FCM to analysed the data from 23 mathematics teacher from 4 secondary schools in Terengganu in order to measure teachers’ beliefs about mathematics. The study recorded ‘Drills and Practice’ is one of the best ways of learning mathematics’ with level of ‘strongly agree’. Abdullah et al. (2011) also used FCM in their study of describing students’ perceptions on computer algebra system learning environment which conducted in secondary school in Terengganu, Malaysia. FCM used by Kasim & Muhamad Sukri (2022) in measuring students’ perception on mathematics learning among undergraduate students at UiTM Perlis which found that in overall students had relatively good attitude toward mathematics learning. Abiyev et al. (2016) used FCM to measure job satisfaction among hotel employees in North Cyprus. Shahani & Rasmani (2020) used FCM with both continues and discrete fuzzy in evaluation job satisfaction. The finding showed that both discrete fuzzy sets and continuous fuzzy sets produce consistent results regardless of whether the fuzzy similarity measure was used.
# METHODOLOGY
The aims of this study is to analyse the students’ perceptions on mathematics online learning on three perspectives; opinion, performance and lecturers’ roles in online mathematics learning using Fuzzy Conjoint method.
**Data Collection**
The data for this study were collected by using a questionnaire distributed to 40 degree in management mathematics students from Faculty of Computer and Mathematical Sciences, UiTM Perlis Branch. These set of students were chosen due to their experience in taking online mathematics classes during the pandemic (2020 - 2022). All of them had taken at least three mathematics courses online. This study focuses students opinion on three perspectives of mathematics online learning namely students’ opinions, students’ performance and lecturer’s roles. Each factor consists of seven, five and five attributes respectively. This study used the criteria from Kasim & Muhamad Sukri, (2022) with some adjustment to suit with online learning. Table 1 below shows the lists of attributes for this survey.
> **Table 1:** The survey of attributes towards students’ opinion, students’ performance, and lecturers’ role.
| Attributes | Statement | |
| ------------------------------------------------- | ---------- | --------------------------------------------------------------------------------------------------------------- |
| Students’ Opinion on Online Distance Learning | \[A_{1}\] | Mathematics is hard to learn through online learning. |
| | \[A_{2}\] | Mathematics causes me stress, dizziness, and headache. |
| | \[A_{3}\] | I received mathematics notes provide by the lecturer clearly but easily forgot. |
| | \[A_{4}\] | Mathematical materials are interrelated between one topic to another. |
| | \[A_{5}\] | Mathematical knowledge is useful for problem solving in various field. |
| | \[A_{6}\] | Mathematics helps me to understand other subjects easier. |
| | \[A_{7}\] | I do not take exams seriously as I can refer to the notes and discuss with friends. |
| Students’ Performance in Online Distance Learning | \[A_{8}\] | I do assignments given by the lecturer independently. |
| | \[A_{9}\] | I am able to achieve a good grade learning through online. |
| | \[A_{10}\] | During online test, I sometimes copy my friend’s answers blindly. |
| | \[A_{11}\] | I managed to improve my analytical skills such as problem solving and decision making. |
| | \[A_{12}\] | I have flexible time to study all the test and quizzes returned by the lecturer. |
| Lecturers’ Roles in Online Distance Learning | \[A_{13}\] | The lecturer gave detailed instructions on how to participate in the course learning activities. |
| | \[A_{14}\] | The lecturers always give feedback on student assessment. |
| | \[A_{15}\] | The lecturers are always available when you need help. |
| | \[A_{16}\] | Face-to-face contact with my lecturer is better than online. |
| | \[A_{17}\] | The teaching platform (Zoom, Google Classroom, Google Meet, Microsoft Team etc) used is easy for you to access. |
**Likert Scale**
**This study applied the fuzzy sets to represent the linguistic term for the Likert Scale. It is defined as**
**{strongly disagree, disagree, neutral, agree, strongly agree}. Table 2 below shows the set of fuzzy for each where .**
**Table 2: The set of Fuzzy for each linguistic terms taken** **Yahaya & Mohamad (2011).**
| **Linguistic Term** | **Rating** | **Fuzzy Sets** |
| --------------------- | ---------- | ------------------------------------- |
| **Strongly Disagree** | **1** | **{1/1, 0.75/2, 0.5/3, 0/4, 0/5}** |
| **Disagree** | **2** | **{0.5/1, 1/2, 0.75/3, 0.25/4, 0/5}** |
| **Neutral** | **3** | **{0/1, 0.5/2, 1/3, 0.5/4, 0/5}** |
| **Agree** | **4** | **{0/1, 0.25/2, 0.75/3, 1/4, 0.5/5}** |
| **Strongly Agree** | **5** | **{0/1, 0/2, 0.5/3, 0.75/4, 1/5}** |
**Fuzzy Conjoint Method**
This study used FCM in analysing the students’ perception in online mathematics learning due to the fuzziness in perception. The hierarchy of all respondents against the specific attributes was presented in fuzzy set *F*. The approximate degree of membership for each element, in fuzzy set *F* is defined as
> **(1)**
where
- and indicates the element of the domain, **with *j* refer to number of linguistic terms which is 5.**
- **is the attribute used, *m* refer to the number of attribute; where in students’ opinion, in students’ performance and in lecturers’ role.**
- is the weighted for *i*-th respondent, as is the linguistic value given by *i*-th respondent.
> (2)
- is the membership degree for element**for attribute according to the linguistic term for each fuzzy set**
- ***n* is the number of respondents**
**Measuring Degree of Similarity**
Degree of similarity of the fuzzy set representing the whole respondents (*F*) and every fuzzy set represent by five linguistic values for each attribute was measured using the sum of a distance formula known as Euclidean distance. The formula for the similarity of two sets is given by,
, **(3)**
**where** is the fuzzy set defined for linguistic rating and is calculated from (1).
**Measurement Procedure**
There are 17 attributes that need to be considered in this study and the procedure for this method is detailed as shown in Figure 1:
**Figure 1:** Measuring Procedure of Fuzzy Conjoint Model
The preference of attributes is described by the similarity degree S. Therefore it can be used to determine the ranking of the attributes by selecting the maximum similarity which is denoted as Smax (Turksen & Willson , 1994).
**FINDINGS AND DISCUSSIONS**
The result obtained by running the data using Microsoft Excel and split according to categorization of attributes. Measurements and discussions for each attribute were presented in accordance with the respective category. Table 1 shows the frequency of students’ perceptions on each attribute.
**Table 3:** The frequency of students’ perceptions for each attribute
| | Attribute | L1 | L2 | L3 | L4 | L5 | Total |
| ------------------------------------------------- | --------- | -- | -- | -- | -- | -- | ----- |
| Students' Opinion on Online Distance Learning | A1 | 4 | 9 | 16 | 7 | 4 | 40 |
| | A2 | 2 | 9 | 6 | 16 | 7 | 40 |
| | A3 | 1 | 12 | 6 | 14 | 7 | 40 |
| | A4 | 3 | 7 | 7 | 15 | 8 | 40 |
| | A5 | 0 | 2 | 8 | 16 | 14 | 40 |
| | A6 | 0 | 10 | 13 | 15 | 2 | 40 |
| | A7 | 7 | 16 | 10 | 6 | 1 | 40 |
| Students’ Performance in Online Distance Learning | A8 | 0 | 4 | 13 | 18 | 5 | 40 |
| | A9 | 0 | 9 | 12 | 12 | 7 | 40 |
| | A10 | 10 | 13 | 7 | 7 | 3 | 40 |
| | A11 | 0 | 2 | 13 | 22 | 3 | 40 |
| | A12 | 4 | 7 | 14 | 9 | 6 | 40 |
| Lecturers' Roles in Online Distance Learning | A13 | 1 | 2 | 10 | 20 | 7 | 40 |
| | A14 | 1 | 4 | 9 | 19 | 7 | 40 |
| | A15 | 1 | 2 | 9 | 18 | 10 | 40 |
| | A16 | 1 | 2 | 6 | 14 | 17 | 40 |
| | A17 | 0 | 2 | 7 | 16 | 15 | 40 |
The weight of each attribute with respect to the linguistic value , was computed using equation (2), and the results are shown in Table 4.
**Table 4:** Weight of each attribute for relayed to linguistic values
| | Attribute | L1 | L2 | L3 | L4 | L5 |
| ------------------------------------------------- | --------- | ------ | ------ | ------ | ------ | ------ |
| Students' Opinion on Online Distance Learning | A1 | 0.1000 | 0.2250 | 0.4000 | 0.1750 | 0.1000 |
| | A2 | 0.0500 | 0.2250 | 0.1500 | 0.4000 | 0.1750 |
| | A3 | 0.0250 | 0.3000 | 0.1500 | 0.3500 | 0.1750 |
| | A4 | 0.0750 | 0.1750 | 0.1750 | 0.3750 | 0.2000 |
| | A5 | 0.0000 | 0.0500 | 0.2000 | 0.4000 | 0.3500 |
| | A6 | 0.0000 | 0.2500 | 0.3250 | 0.3750 | 0.0500 |
| | A7 | 0.1750 | 0.3500 | 0.2750 | 0.1750 | 0.0250 |
| Students’ Performance in Online Distance Learning | A8 | 0.0000 | 0.1000 | 0.3250 | 0.4500 | 0.1250 |
| | A9 | 0.0000 | 0.2250 | 0.3000 | 0.3000 | 0.1750 |
| | A10 | 0.2250 | 0.2750 | 0.2000 | 0.1750 | 0.1250 |
| | A11 | 0.0000 | 0.0500 | 0.3250 | 0.5500 | 0.0750 |
| | A12 | 0.1000 | 0.1750 | 0.3500 | 0.2250 | 0.1500 |
| Lecturers' Roles in Online Distance Learning | A13 | 0.0250 | 0.0500 | 0.2500 | 0.5000 | 0.1750 |
| | A14 | 0.0250 | 0.1000 | 0.2250 | 0.4750 | 0.1750 |
| | A15 | 0.0250 | 0.0500 | 0.2250 | 0.4500 | 0.2500 |
| | A16 | 0.0250 | 0.0500 | 0.1500 | 0.3500 | 0.4250 |
| | A17 | 0.0000 | 0.0500 | 0.1750 | 0.4000 | 0.3750 |
The next step it to calculate the membership degree for a fuzzy set *F* of students opinion to each linguistic value *k*, where using equation (1). The result for *L1* Strongly Disagree is shown in Table 5.
**Table 5:** Membership degree of each element of fuzzy set \(F\) correspond to linguistic value \(L_{1}\) for each attribute .
| | Attribute | L1 | L2 | L3 | L4 | L5 |
| ------------------------------------------------- | --------- | ------ | ------ | ------ | ------ | ------ |
| Students' Opinion on Online Distance Learning | A1 | 0.1000 | 0.1688 | 0.2000 | 0.0000 | 0.0000 |
| | A2 | 0.0500 | 0.1688 | 0.0750 | 0.0000 | 0.0000 |
| | A3 | 0.0250 | 0.2250 | 0.0750 | 0.0000 | 0.0000 |
| | A4 | 0.0750 | 0.1313 | 0.0875 | 0.0000 | 0.0000 |
| | A5 | 0.0000 | 0.0375 | 0.1000 | 0.0000 | 0.0000 |
| | A6 | 0.0000 | 0.1875 | 0.1625 | 0.0000 | 0.0000 |
| | A7 | 0.1750 | 0.2625 | 0.1375 | 0.0000 | 0.0000 |
| Students’ Performance in Online Distance Learning | A8 | 0.0000 | 0.0750 | 0.1625 | 0.0000 | 0.0000 |
| | A9 | 0.0000 | 0.1688 | 0.1500 | 0.0000 | 0.0000 |
| | A10 | 0.2250 | 0.2063 | 0.1000 | 0.0000 | 0.0000 |
| | A11 | 0.0000 | 0.0375 | 0.1625 | 0.0000 | 0.0000 |
| | A12 | 0.1000 | 0.1313 | 0.1750 | 0.0000 | 0.0000 |
| Lecturers' Roles in Online Distance Learning | A13 | 0.0250 | 0.0375 | 0.1250 | 0.0000 | 0.0000 |
| | A14 | 0.0250 | 0.0750 | 0.1125 | 0.0000 | 0.0000 |
| | A15 | 0.0250 | 0.0375 | 0.1125 | 0.0000 | 0.0000 |
| | A16 | 0.0250 | 0.0375 | 0.0750 | 0.0000 | 0.0000 |
| | A17 | 0.0000 | 0.0375 | 0.0875 | 0.0000 | 0.0000 |
**Students’ Opinions on Online Distance Learning**
**The** measurement outcome for students’ opinion about online learning is shown in Table 6. All attributes recorded level of agreement “neutral” with close value of degree of similarity. However, the top rank on students’ opinion is that mathematics is hard to learn online (F1) with maximum degree of similarity of 0.4988. Followed by the attribute that mathematics is helping them understand in other subject easier (F6) with maximum degree of similarity of 0.4940. Unfortunately, students do not take exams seriously as they can refer to the notes and discuss with friends (F7) ranked number 3 with the score of 0.4903. Students rank number 4 and 5 with maximum degree of similarity 0.4791 and 0.4754 respectively on the attribute received the notes clearly but easily forgotten (F3) and on the attribute that mathematics causes dizziness and headache during online learning (F2). The second lowest and the lowest degree of similarity registered “neutral” is F4 (Mathematical materials are interrelated between one topic to another) and F5 (Mathematical knowledge is useful for problem solving in various field) respectively. Overall, students’ opinion of online distance learning towards mathematics are not positive. Contrarily, with the outcome before online learning was implemented where students showed relatively good attitude in learning mathematics (Kasim & Muhamad Sukri, 2021).
**Table 6:** Degree of similarity between the fuzzy set *F* and linguistic variables *L* for Students’ Opinion.
| Fuzzy Set | L1 | L2 | L3 | L4 | L5 | S(max) | L(S(max)) | Rank |
| --------- | ------ | ------ | ------ | ------ | ------ | ------ | --------- | ---- |
| F1 | 0.4734 | 0.4756 | 0.4988 | 0.4439 | 0.4347 | 0.4988 | L3 | 1 |
| F2 | 0.4562 | 0.4570 | 0.4754 | 0.4330 | 0.4288 | 0.4754 | L3 | 5 |
| F3 | 0.4574 | 0.4631 | 0.4791 | 0.4336 | 0.4274 | 0.4791 | L3 | 4 |
| F4 | 0.4573 | 0.4548 | 0.4747 | 0.4334 | 0.4301 | 0.4747 | L3 | 6 |
| F5 | 0.4364 | 0.4369 | 0.4698 | 0.4328 | 0.4323 | 0.4698 | L3 | 7 |
| F6 | 0.4554 | 0.4656 | 0.4940 | 0.4416 | 0.4332 | 0.4940 | L3 | 2 |
| F7 | 0.4939 | 0.4896 | 0.4903 | 0.4373 | 0.4275 | 0.4903 | L3 | 3 |
**Students’ Performance in Online Distance Learning**
Table 7 shows the results of the attribute related to students’ performance in online mathematics distance learning. All attributes recorded level of agreement “neutral” except for attribute F10 which is students are “strongly disagree” that they sometimes copy their friend’s answers blindly during online test. The second highest maximum degree of similarity of 0.4932 is on having flexible time to study the tests and quizzes returned by the lecturer (F12). The third highest maximum degree of similarity with the score of 0.4901 with rated “neutral” is on the ability of getting good grade through online test (F 9). It is probably students were confident with open book exams they can answer the questions easily even though they admit that they do the assignment independently (F8, rank4). The lowest rank which also rated “neutral” is on the attribute of manage to improve analytical skill such as problem solving and decision making (F11). This shows that students were unsure the benefit of mathematics to them specifically in becoming a good decision maker. It is coherent with the fact that during online test students can refer notes or googling the answers. This resulted lack of confidence and unable to think on their own in which meant that they missed the actual opportunity in learning. The consequences can be seen on the performance of other mathematics courses in the semesters to come.
**Table 7:** Degree of similarity between the fuzzy set *F* and linguistic variables *L* for Students’ Performance.
| Fuzzy Set | L1 | L2 | L3 | L4 | L5 | S(max) | L(S(max)) | Rank |
| --------- | ------ | ------ | ------ | ------ | ------ | ------ | --------- | ---- |
| F8 | 0.4439 | 0.4484 | 0.4845 | 0.4395 | 0.4354 | 0.4845 | L3 | 4 |
| F9 | 0.4528 | 0.4613 | 0.4901 | 0.4402 | 0.4331 | 0.4901 | L3 | 3 |
| F10 | 0.4932 | 0.4782 | 0.4775 | 0.4323 | 0.4260 | 0.4932 | L1 | 1 |
| F11 | 0.4399 | 0.4428 | 0.4809 | 0.4385 | 0.4357 | 0.4809 | L3 | 5 |
| F12 | 0.4674 | 0.4665 | 0.4908 | 0.4412 | 0.4344 | 0.4908 | L3 | 2 |
**Lecturers' Roles in Online Distance Learning**
Table 8 shows the degree of similarity for lecturers’ roles in online distance learning. All attributes were registered “neutral” level of agreement. Lecturers always give feedback on student assessment (F14) had the highest maximum degree of similarity value of 0.4753. The second highest degree of similarity value (0.4741) is on attribute that the lecturers gave detailed instructions on how to participate in the course learning activities (F13). The lecturers are always available when students need help (F15) was registered at rank 3 with linguistic value in the range of “neutral”. The easy access of the teaching platform used (F17) and face-to-face contact with lecturer is better than online (F16) ranked number 4 and 5 respectively. According to the survey in this research the most popular teaching platform used by mathematics lecturers are Google Meet, followed by Google Classroom, WhatsApp and Telegram.
**Table 8:** Degree of similarity between the fuzzy set *F* and linguistic variables *L* for Lecturers’ Role.
| Fuzzy Set | L1 | L2 | L3 | L4 | L5 | S(max) | L(S(max)) | Rank |
| --------- | ------ | ------ | ------ | ------ | ------ | ------ | --------- | ---- |
| F13 | 0.4416 | 0.4411 | 0.4741 | 0.4350 | 0.4337 | 0.4741 | L3 | 2 |
| F14 | 0.4449 | 0.4454 | 0.4753 | 0.4350 | 0.4327 | 0.4753 | L3 | 1 |
| F15 | 0.4409 | 0.4399 | 0.4719 | 0.4339 | 0.4330 | 0.4719 | L3 | 3 |
| F16 | 0.4386 | 0.4362 | 0.4653 | 0.4304 | 0.4308 | 0.4653 | L3 | 5 |
| F17 | 0.4357 | 0.4357 | 0.4676 | 0.4316 | 0.4316 | 0.4676 | L3 | 4 |
**CONCLUSION AND RECOMMENDATIONS**
This study used fuzzy conjoint analysis in measuring the students’ perceptions toward learning mathematics in virtual classes. The respondents were 40 students of degree in Mathematics Management, UiTM Perlis who experienced at least 3 mathematics courses online during the pandemic. The study focuses on 3 components of perspectives with 17 attributes. The respondents were asked to rate their level of agreement in Likert Scale *L1 - L5* (Strongly Disagree – Strongly Agree). The overall outcome displayed by the similarity between fuzzy set *F* and linguistic variables.
The result shows “neutral” level of agreement in all attributes except for one attribute in which students are strongly disagree upon. Students admitted that they didn’t copy their friends’ answers blindly during the online test. In students’ opinion mathematics is a difficult course to study online despite having flexible time to study the tests and quizzes returned by the lecturer. In terms of mathematics performance, students ranked third place in the ability to achieve good grade through online test. This differ from Bringula et al. (2021) which found almost half of the students feel that they will get lower grades in the online test compare when if it is done in a face-to-face session. On the lecturers’ roles, various effort had been done in facilitating students learning activities such as gives feedback in the assignments as well as detail instructions on how to participate in online learning. In conclusion, result of this study shows that students do not show neither positive nor negative of the mathematics online learning as almost all attributes were rated “neutral”. The result is agreed to Bringula et al. (2021) where students had positive as well as negative mathematics online learning self-concepts. It supported by the study of Krishnan (2016) in the case of mathematics blended learning where students were preferred face-to-face learning mode as they find the face‐to‐face instruction is efficient in the learning process of mathematics concept.
Since this study is only limited to management mathematics degree students at UiTM Perlis and focuses on only17 attributes, the finding can’t be generalized to all system of UiTM. Therefore, a larger number of respondents from various faculties are needed. Further exploration of factors influencing students’ perceptions towards mathematics e-learning are needed in order to obtain more accurate and relevant conclusion of overall students’ perception towards mathematics online learning. The same study can be done on other courses also.
**REFERENCES**
> Abbasi, S., Ayoob, T., Malik, A., & Memon, S.I. (2020). Perceptions of students regarding E-learning
>
> during Covid-19 at a private medical college. *Pak J Med Sci*., *36*(COVID19-S4):COVID19-S57-S61. doi: https://doi.org/10.12669/pjms.36.COVID19-S4.2766.
Abdullah, L., Tap, A. O. M., & Abdullah, W. S. W. (2011). *Fuzzy Set Conjoint Model in Describing Students’ Perceptions on Computer Algebra System Learning Environment*. *8*(2), 92–97.Abiyev, R. H., Saner, T., Eyupoglu, S., & Sadikoglu, G. (2016). Measurement of Job Satisfaction Using Fuzzy Sets. *Procedia Computer Science*, *102*(August), 294–301. https://doi.org/10.1016/j.procs.2016.09.404Al-Mawee, W., Kwayu, K.M., & Gharaibeh, T. (2021). Student's perspective on distance learning during COVID-19 pandemic: A case study of Western Michigan University, United States. *International journal of educational research open*, *2*, 100080. https://doi.org/10.1016/j.ijedro.2021.100080.Baya'a. N., & Daher.W.(2009). Students' perceptions of mathematics learning using mobile phones*IMCL International Conference on Mobile and Computer aided Learning* - www.imcl-conference.org.Bringula, R., Reguyal, J. J., Tan, D. D., & Ulfa, S. (2021). Mathematics self-concept and challenges of learners in an online learning environment during COVID-19 pandemic. *Smart Learning Environments*, *8*(1). https://doi.org/10.1186/s40561-021-00168-5.Burhan Turksen, I., & Willson, I. A. (1994). A fuzzy set preference model for consumer choice. *Fuzzy Sets and Systems*, *68*( 3), 253–266. https://doi.org/10.1016/0165-0114(94)90182-1.Colomeischi. A.A. & Colomeischi.T. (2015). The Students\` Emotional Life and Their Attitude toward Mathematics Learning. *Procedia - Social and Behavioral Sciences* 180 ( 2015 ) 744 – 750. http://doi.org/10.1016/j.sbpro.2015.02.192.Doly. N.M. & Ahmad (2020)**.** Students’ perception on learning mathematic during the time of covid-19 J*ournal of Physics:* *Conference Series* 1778 (2021) 012036 IOP Publishing doi:10.1088/1742-6596/1778/1/012036. Hodges, C. B., & Fowler, D. J. (2020). The COVID-19 crisis and faculty members in higher education: from emergency remote teaching to better teaching through reflection. *International Journal of Multidisciplinary Perspectives in Higher Education*, *5*(1), 118-122.Huda. N., Wahyuni. T.S., Fauziya.F.D. (2020). Students' perceptions of online mathematics learning and its relationship towards their achievement. *Advances in Social Science, Education and Humanities Research, volume 522. http://doi.10.2991/assehr.k210421.77.*Kasim, Z., & Muhamad Sukri, N. L. (2022). Measuring Students’ Perception on Mathematics Learning Using Fuzzy Conjoint Analysis. *Journal of Computing Research and Innovation*, *7*(1), 79–88. https://doi.org/10.24191/jcrinn.v7i1.270.Kasmin, F., Othman, Z., & Syed Ahmad, S. S. (2019). Improving Students’ Perception Towards Learning Mathematics: Impact of Teaching Application of Mathematics. *EDUCATUM Journal of Science, Mathematics and Technology*, *6*(1), 29–34. https://doi.org/10.37134/ejsmt.vol6.1.4.2019.Khan, M.A., Vivek, Nabi, M.K., Khojah, M., Tahir, M. (2021). Students’ Perception towards E-Learning during COVID-19 Pandemic in India: An Empirical Study. *Sustainability*, 13, 57. https://dx.doi.org/10.3390/ su13010057.Krishnan, S. (2015). Student‐centered learning in a First Year Undergraduate Course. International Journal of Learning, Teaching and Educational Research, 11(2), 88‐95.Lazim, M. A., & Abu Osman, M. T. (2009). Measuring teachers’ beliefs about mathematics: A fuzzy set approach. *World Academy of Science, Engineering and Technology*, *33*, 1098–1102.Mohd Idris. M.F.I., Abd Aziz, L.A., Aminuddin, M.H., (2022) . Fuzzy logic to evaluate significant factors affecting students’ academic performance through online distance learning *Journal of Computing Research and Innovation*, *7*(1), 60–72. https://doi.org/10.24191/jcrinn.v7i1.267.Salac, R. A. (2016). *A Study on The Internet Connectivity in The Philippines*. *1*(August), 67–88.Shahari, N.,& Rasmani, K. A. (2020). Job satisfaction evaluation based on fuzzy conjoint method with continuous fuzzy sets. *Indonesian Journal of Electrical Engineering and Computer Science 19*(1) pp. 363\~370. DOI: 10.11591/ijeecs.v19.i1.pp363-370.