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American Interdisciplinary Journal of Business 

and Economics 
ISSN: 2837-1909| Impact Factor : 4.6 

Volume. 9, Number 1; January-March, 2022; 

Published By: Scientific and Academic Development Institute (SADI) 

8933 Willis Ave Los Angeles, California 

https://sadipub.com/Journals/index.php/aijbe 

 

 

  

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MATHEMATICS TEACHERS’ VIEWS ON TEACHING AND LEARNING 

CALCULUS IN SECONDARY SCHOOLS 

 

 

Collins S. 

The Copperbelt University, School of Graduate Studies 

 

Abstract: This study aimed to investigate the perceptions and attitudes of mathematics teachers towards the 

teaching of calculus in secondary schools in the Mporokoso district of Zambia. A total of 16 mathematics 

teachers participated in the study, which employed a mixed-methods research design of structured interview 

questionnaires and data analysis using SPSS v20. The results indicated that teachers held positive attitudes 

towards the teaching of calculus, perceiving it as an essential foundation for other disciplines such as 

engineering. The study found that years of service in teaching and teacher qualifications influenced teachers' 

perceptions and attitudes towards teaching calculus. The study highlights the need to assess teachers' 

perceptions and attitudes towards teaching calculus, as they play a crucial role in determining the quality and 

effectiveness of mathematics education. Working on learners' perceptions and attitudes towards calculus can 

enhance their confidence and improve their understanding of the subject. The mastering of calculus is essential 

in learning, but many students consider it to be a difficult branch of mathematics. Assessing and addressing 

teachers' and learners' perceptions and attitudes towards calculus can lead to improved performance and 

outcomes in mathematics education. 

Keywords: calculus; perception; attitude; teaching; secondary school; mathematics education; Zambia.  

 

Introduction and Literature review  

In relation to teaching and learning mathematics, teachers’ perceptions and attitudes play an important role. 

According to Oktaviyanthi and Supriano (2015), learning mathematics is closely related to visualization and 

representation of mathematical objects and procedures; In relation to learning mathematics, teachers’ 

perceptions and attitudes play an important role in teaching mathematics (Mills, 2007), and Calculus is part 

of mathematics. Calculus is a branch of mathematics that includes limits, derivatives, integration, and infinite 

series. Calculus which has general applications in science and engineering is used to help solve the complex 

problems that are not sufficiently solved by basic algebra techniques. Oktaviyanthi and Supriano (2015) 

contends that most of the weaknesses of students is that they are only able to perform simple calculations. 

Mathematics is made up of many branches that include Calculus. Calculus is a branch of mathematics that 

includes limits, derivatives, integration, and infinite series. Calculus has general applications in science and 

engineering and is used to help solve complex problems that are not sufficiently solved using basic algebraic 

techniques. Calculus is important in the curriculum of almost all disciplines, such as engineering, science, 

business, economics, computer science and information system. Its concepts are arranged in a systematic, 

logical, and hierarchical pattern transitioning from the simplest to the most complex. Therefore, the mastering 

of calculus is essential in learning. However, many learners consider calculus to be a difficult branch of 

mathematics in their learning process. Calculus as part of mathematics has an abstract concept that most 

learners are not able to conceptualise. Consequently, working on their perceptions and attitudes towards the 



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learning of calculus can greatly enhance their confidence and hence result in an improved understanding of 

the concepts surrounding calculus.  

Gibson in 1966 and Gregory in 1970 propounded theories on perceptions called ‘bottom-up’ and ‘top-down’ 

theories. These theories posit that between sensations and our conscious perception of the real world there 

must be intermediate processes. For example, these processes would be ‘inferential thinking’. This kind of 

thinking allows us to go beyond the evidence of the senses (these inferences are at an unconscious level). 

Gibson and Gregory believed that perception is more than direct registration of feelings, but that other events 

intervene between stimulation and experience. They further claim that perception is an activity of forming 

hypotheses and testing them. Signals received by the sensory receptors trigger neural events, and appropriate 

knowledge interacts with these inputs to enable us to make sense of where we stay or live or what we should 

and why we do it. Perception allows behaviour to be generally appropriate.  

Perception and attitude deals with someone’s cognitive, affective, and emotional abilities. This is in support 

with Ajzen (1993) who argues that perceptions and attitudes have a predictive validity in that they help us to 

explain social behaviour. It is argued that there is a relationship between perception and attitude and behaviour 

Ajzen (1993). This kind of correlation needs to be assessed among Mathematics teachers and learners 

regarding their views on Calculus. Gibson and Gregory further indicate that perceptions and attitudes develop 

because of salient beliefs formed about the attitude object. Based on this theory, Mathematics teachers’ and 

learners’ perceptions and attitudes could be considered as their disposition to react with a certain degree of 

favorableness or unfavorableness towards the teaching and learning of Calculus. Gibson and Gregory contend 

that perceptions and attitudes are hypothetical constructs, implying that they may not be accessible to direct 

observation but must be inferred from measurable reactions to the attitude object, in this which is Calculus.  

This theory is fundamental to guide the proposed study, for instance, the cognitive component of Mathematics 

teachers could be viewed as those perceptions of and information about Calculus. The cognitive indicators 

of Mathematics teachers’ and learners’ perceptions and attitudes could therefore involve verbal expressions 

of beliefs, opinions and knowledge or non-verbal perceptual reactions towards the teaching and learning of 

Calculus in secondary schools of Mporokoso district. The effective indicators of teachers could include verbal 

expressions of feelings, physiological reactions, facial expressions, and non- verbal indicators of positive or 

negative sensations towards Calculus among teachers.  

Studies report that perceptions and attitudes are part of the mindset that affect how a person thinks and acts 

(Tsanwani et al., 2014). These can influence a person’s performance positively or negatively. For example, a 

positive perception and attitude towards Calculus could result in a positive performance. Conversely, 

perception and attitude could also influence how well a teacher plans and prepares his/her lessons in Calculus. 

In their study entitled ‘student’s attitude towards mathematics, Farooq and Shah (2008), argued that attitude 

and perception towards mathematics plays a crucial role in the teaching and learning processes of 

mathematics as it influences students’ achievement in mathematics. They further stated that the teaching 

methodology, the support structure of the school, the family and students’ perception and attitude towards 

mathematics affects the teaching and learning mathematics. It has been determined that teachers’ attitudes 

highly affect students’ interest in learning (Tsanwani et al., 2014). This is also supported by Nachiyunde et 

al. (2021) who posits that personality traits of the mathematics teachers are more powerful and influential 

than the course content or instructional strategies used in a classroom of mathematics. Breiteig & Grevholm 

(2005) also supports the preceding notion put forward by others that learning outcomes of students are 

strongly related to their beliefs and attitudes about mathematics.  

The perceptions and attitudes of teachers, their motives for teaching Calculus and the feelings they have of 

themselves may influence how well they will eventually teach the subject in secondary schools. Mohammed 

and Ja’ashan (2015) posits that positive perceptions and attitudes are very critical when it comes to learning, 

and the factors related to attitudes include confidence, experience, satisfaction, usefulness, and motivation. 

These factors could be considered as a drive to push the teaching process in schools. A study on ‘Outcomes 



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of Schooling: Mathematics Achievement and Attitudes Towards Mathematics Learning in Hong Kong’ by 

Cheung (1990), showed highly positive perceptions and attitudes towards teaching of mathematics because 

of the many benefits that both teachers experienced.  

Considering that perceptions and attitudes towards teaching can be related to motivation, Covington and Dray 

(2002) argue that decrease in attitudes towards mathematics can be associated with overall decrease in 

intrinsic motivation, competence-related beliefs, interest, and task values that occur during learning. The 

opposite is the same, when there is an increase in attitudes towards mathematics, generally, there is also an 

increase in learners’ intrinsic motivation and competence-related beliefs. Teacher motivation are a very 

critical aspect of determining positive or negative attitude towards mathematics among teachers. A teacher 

with a positive attitude towards teaching mathematics could ensure that there is adequate preparation in terms 

of teaching strategy and other resources. A good teaching strategy requires full interest and support from 

administrators and learners. A teacher with a negative attitude tends not to appear interested or does not foster 

a supportive learning environment (Masaiti & Naluyele, 2011). In addition to that, teachers with negative 

attitudes may not be as approachable as teachers who are positively motivated. Learners could also find it 

difficult asking such a teacher question on the grey areas of the subject he/she teaches. This implies that 

teachers’ attitude towards their students and teaching in general is very important for students’ success. In the 

same vein, teachers need to be highly interested in the subjects and topics they teach.  

Cheung (1990) argues that while many perception and attitude studies have generally focused on 

mathematics, little attention has been given to the specific topics like Calculus. Similarly, in a review article 

on attitudes towards mathematics, Covington and Dray (2002) concluded that perceptions and attitudes 

studies towards mathematics were very limited and hence the need to carry out an investigation of these 

perceptions and attitudes in teaching mathematics. Perceptions and attitudes towards mathematics become 

especially noticeable when studies that aim at evaluating and documenting them are implemented fully. 

Teachers’ perception and attitude helps to determine how well teachers teach the subject. Therefore, the need 

to assess their perception and attitudes towards teaching Calculus should not be overemphasized.  

To meet the needs of society or citizens, many countries in Africa reformed their educational curricula shortly 

after attaining political independence (MoE, 1996). For Zambia, in order to respond to developmental needs 

of the country and those of individual learners, the government, through the Ministry of Education (MoE) in 

1996 developed a national policy on education called ‘Educating Our Future’. For some time now this policy 

has become a backbone or guide for all educational strategies and programmes in the country (MoE, 1996). 

The countries, Zambia inclusive, believed that educational provision was the key that could nurture the 

holistic development of all individuals. The education policy resulted in the development of the Zambia 

Education Curriculum Framework (ZECF) in 2013.  

This development affected the school subjects including mathematics. Ordinary level mathematics syllabus 

underwent changes so that it could suit the trend in the Zambian education (ECZ, 2016). The changes resulted 

in the introduction of Calculus in the O-level mathematics syllabus in secondary schools (Nachiyunde et al., 

2021). According to ECZ (2016), Calculus was only introduced for the first time in the Zambian secondary 

school mathematics syllabus in 2013. Before 2013, at secondary school level Calculus was only offered to 

learners taking Additional Mathematics and such learners were not many because few schools were offering 

the subject at that time (MESVTEE, 2013). It is argued that Calculus was introduced at the Zambian 

secondary school level in order to create a bridge for further education especially in tertiary mathematics 

courses where there is demand for such (Nachiyunde et al., 2021).  

The following Calculus concepts were incorporated in the O-level Mathematics syllabus: calculating 

equations of tangents and normals, differentiating functions from first principles, using the formular for 

differentiation, explaining integration, evaluating simple definite integrals, finding the area under the curve, 

and finding indefinite integrals. Other topics included are composite functions, inverse functions, computer 



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and calculator, arithmetic and geometric progressions, graphs of cubic functions, standard deviation in 

statistics and trigonometric equations.  

With the integration of Calculus in the O-level Mathematics syllabus, teaching and learning Calculus in 

schools appears to be a difficult process. This may be attributed to the fact that understanding Calculus has 

posed a challenge for most Mathematics students. Since the incorporation of Calculus in O-level mathematics 

syllabus, the general observation by stakeholders in Zambia particularly in Mporokoso secondary schools is 

that learners are underperforming in this topic. For instance, the Examination Council of Zambia examiner’s 

report for 2016 revealed that some candidates of Mporokoso district that took part in the O-level mathematics 

syllabus performed poorly in Calculus topics. At Mukanga Secondary school, Grade 12 performance in 

Mathematics in 2016 was at 41%; 2017 at 42%; 2018 at 38.4% and 2019 at 42.1%. The underperformance 

of the learners in mathematics with reference to Calculus topics is generally becoming a major source of 

concern in Zambia at large.  

It is against this background that the study sought to assess teachers’ perceptions and attitudes towards the 

teaching and learning of Calculus topics in secondary schools of Mporokoso district. Specifically, the study 

was guided by the following questions:  

1. What are the perceptions and attitudes of mathematics teachers towards teaching of Calculus in 

secondary schools?  

2. What are the factors that influence mathematics teachers’ perceptions and attitudes in teaching 

Calculus  

Addressing these questions is important to the study for answers will indicate whether teachers appreciate 

the inclusion of the topic in senior secondary school Mathematics. How teachers respond to the questions 

may be an indication of how the topic is being taught. Consequently, it may be an indication of whether the 

topic is taught positively or negatively. The way the topic is taught may affect effect learners’ performance, 

positively or negatively. Therefore, the study was necessary so as to determine perceptions and attitudes held 

by teachers towards teaching of Calculus at this level of the education system.  

Methodology  

The following methods and procedures were adopted to conduct this study.  

Research design  

The study adopted both a descriptive and analytical research design. Consequently, two distinct data 

collection approaches were incooperated resulting in a mixed approach to data collection. The quantitative 

approach enabled the researchers to analyse yielded data and develop a statistical representation of the trend 

or connection regarding attitudes and perceptions of both teachers towards teaching of calculus. On the other 

hand, the qualitative approach, helped the study to learn from gathered data, details of participants of the 

study, such that conclusion was drawn by compiling, comparing and evaluating the informants’ feedback and 

input leading to the answer of the “why” behind the phenomenon or behaviour.  

Population and sample  

The population of the study comprised all mathematics secondary school teachers of Mporokoso district. 

Since Mporokoso district has a population of six (6) secondary schools, and 25 mathematics teachers, the 

study population then comprised six (6) secondary schools, and 25 mathematics teachers from the six (6) 

mentioned schools. Mporokoso district was selected using purposive sampling because it has secondary 

schools that offer mathematics and the researchers were interested in teachers’ perceptions and attitudes 

towards the mathematics topic of Calculus. Purposive sampling technique was employed because it has the 

advantage of selecting participants based on assumptions regarding the population of interest. This is 

supported by Odhiambo et al. (2010) who categorically state that purposive sampling is any sampling method 

where some elements of the population have no chance of selection (these are sometimes referred to as out 

of coverage).  



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Research Instruments  

A structured interview data collection method was used and data collected was quantitative in nature. 

Structured interviews were employed to gather data from Mathematics teachers. These interview schedules 

guaranteed a high response rate and allowed control of the interview situation (Odhiambo et al., 2010). The 

researchers were able to gain full insight into the participant’s beliefs or perceptions (opinions) regarding 

teaching Calculus.  

Validation of research instruments  

To ensure validity, research instruments were discussed by the researchers and also given to other research 

experts to reveal and sort out ambiguities. The meaning of every term in the interview schedule was defined 

to have the same meaning for all respondents. Reliability concerns were addressed or countered by ensuring 

that respondents gave consistent responses.  

2.5 Data Analysis Procedures  

Analysis of data was based on research questions, and was made possible by using a software package called 

SPSS version 20.0 (IBM) for generating descriptive statistical data tables, and correlation tables. An 

inferential statistical test to indicate relationship or correlation between perceptions and attitudes and 

performance was done. This enabled us to understand whether perceptions and attitudes of teachers predict 

performance.  

Results and Findings  

The analysis of results of the data set obtained are presented starting with those to do with perceptions and 

attitudes of mathematics teachers. Data were analyzed for trends using the SPSS version 20.  

Mathematics teachers’ perceptions and attitudes towards teaching Calculus  

The perceptions and attitudes questionnaire were administered to teachers in order to assess teachers’ 

perceptions and attitudes towards teaching of calculus. The results of analyzing the teacher’ perceptions and 

attitude towards teaching calculus are shown in Table 3.1.  

Table 3.1 Perceptions and attitudes of mathematics teachers towards teaching calculus (n=12)  

 
Going by the results of the study, teachers perceive calculus to be a subject that mainly deals with rate of 

change with a minority (16.7%) of teacher respondents pointing out that it is about concept combinations. 

Additionally, Table 3.1 shows that teachers consider the teaching of calculus to learners important since it is 

viewed as the mathematical backbone of other disciplines more especially engineering. In pursuing the 

undertaking, teacher respondents also report that the most ideal teaching strategy to use when teaching 

calculus is group work followed by class discussion while home work is deemed the least preferred teaching 



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strategy. Teacher respondents argue that the aforementioned teaching strategies are ideal since they enable 

learners to participate fully during lessons. With these said teaching strategies, learners are able to reciprocate 

and hence give positive feedback. However, it goes without not mentioning that while implementing the 

aforementioned teaching strategies, there existed some challenges such as learners failing to use their 

algebraic skills, coupled with the slow pace to comprehend concepts. Going forward, the teacher respondents 

indicate that emphasizing the basics of calculus to learners is the most viable way of overcoming the 

challenges, that is also in conformity with encouraging more study groups among the learners.  

Table 3.2: Mathematics teachers’ perceptions, attitudes, qualification and experience teaching Calculus 

(n=12)  

 
There is a mixed set of views regarding teaching of calculus among teachers. Those with diploma 

qualifications feel that teaching of calculus is a challenge for learners especially those that struggle in other 

topics. On the other hand, teachers with degrees feel that teaching calculus is not a challenge; all that is 

needed is to use different teaching strategies depending on which learners are being taught at a particular 

moment. A large majority of teachers, however, perceive the introduction of calculus as well timed although 

more preparations could have been done in order to ensure that there is an enabling environment within 

schools the teacher to thrive in their teaching of calculus. Furthermore, the correlation results obtained from 

the study indicate a very week correlation between mathematics teachers’ perceptions and attitudes and years 

of teaching. This means that as one increases in the years of service, the challenges faced reduces.  

Table 3.3: Table Factors that influence mathematics teachers’ perceptions and attitudes in teaching 

Calculus (n=12)  

 
Data was analysed to determine factors influencing mathematics teachers’ perceptions and attitudes towards 

teaching calculus. The results indicate that teachers’ perceptions and attitudes towards teaching of calculus 

were mainly influenced by teachers’ qualifications and the number of years of teaching i.e., their teaching 

experience. It was observed from the results that teachers who had degrees and a considerable number of 

years in service had positive perceptions and attitudes towards teaching of Calculus as opposed to those with 

diploma qualifications even though they had many years in teaching.  



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Discussion and Conclusion  

Results from respondents’ responses to the questionnaires indicated that most teachers value the importance 

of teaching calculus. This is because teachers in this study viewed Calculus as a foundation for many 

disciplines, especially engineering and natural sciences. Thus, in general respondents revealed perceiving the 

introduction and teaching of Calculus in secondary schools positively. This could be attributed to the many 

uses of Calculus. However, the study has established that teachers’ perceptions and attitudes towards teaching 

of Calculus were different depending on the qualifications of respondents. Respondents with degrees in 

mathematics exhibited positive attitudes and enthusiasm towards the teaching of Calculus in secondary 

schools. On the other hand, their diploma holding colleagues exhibited doubt and discomfort towards the 

teaching of Calculus as observed from their responses.  

Qualification of respondents, therefore, seemed to be one of the factors that influenced teachers’ perceptions 

and attitudes towards teaching Calculus in secondary schools. Apart from teachers’ qualifications, teachers’ 

years of experience in teaching mathematics were identified as one of the factors determining perceptions 

and attitudes of teachers towards the teaching of Calculus in secondary schools. Teachers who had more years 

of teaching exhibited positive perceptions and attitudes towards the teaching of Calculus. Such results reveal 

the confidence with which such teachers approach their teaching. The result is not just for Calculus but can 

be generalized to other topics (Mills, 2007). This group of teachers has over the years observed what works 

in their teaching and what does not work. As such they are able to arrange learning experiences which support 

learning for their pupils. Also, the teachers’ attitudes were influenced by availability of teaching materials for 

teaching Calculus. Teachers, in the study suggested that the presence of teaching materials especially 

textbooks on Calculus helped teachers develop positive attitudes towards the teaching of Calculus. It helped 

them have increased levels of confidence. This was true for all sets of teachers, whether degree holders or 

diploma holders. The importance of learning materials in a teaching and learning situation is echoed in other 

studies (e.g., Adalikwu & Iorkpilgh, 2012).  

Therefore, the researchers conclude that of the many factors determining teachers’ perceptions and attitudes 

towards teaching Calculus two stand out. The two factors are teachers’ qualifications and their teaching 

experience. Of the two, a teacher’s qualifications is the main influencing factor regarding teacher perceptions 

and attitudes towards teaching of Calculus. For this reason, the study asserts that those with degrees 

developed positive perceptions and attitudes towards teaching calculus, which in turn impacted the learners 

positively and resulted in improved learner achievement in Calculus and consequently in mathematics. The 

study by Yara (2009) is in agreement with this finding, that positive attitudes towards learning have positive 

effects on achievement. However, the fact that achievement in Calculus has not been as expected in schools 

under study, the conclusion may be that schools do not have sufficient numbers of degree holding teachers. 

This may be true but it is recognized that other factors affecting learners’ achievement in mathematics might 

be at play. Factors, such as learners’ mathematical background, teaching materials available, methods of 

teaching and others.   

Based on study findings, the conclusion is that teachers are of the view that teaching Calculus in secondary 

schools is a welcome development. Therefore, teachers in general are said to have positive attitudes towards 

teaching Calculus. Specifically, it has been established that a number of teachers exhibited differing levels of 

perceptions and attitudes and this depended mainly on two factors: teachers’ qualifications and teacher’s 

years of teaching mathematics. Consequently, it is recommended that further studies be conducted in future 

to determine what other factors influence teaching of Calculus in secondary schools.  

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