Teaching Relevant Mathematics Topics to Prepare Technical and Vocational Education Training College Students for Workforce: Lecturers’ Perspective

Abstract

The emphasis of this chapter is on the lecturers’ perspective on teaching relevant mathematics topic to prepare Technical and Vocational Education Training (TVET). This chapter focused on the National Certificate Vocational [NC(V)] programmes in one of the provinces in South Africa. A qualitative method was used, and data was collected through an open-ended questionnaire. Convenient and purposive sampling was used to select the participants. The chapter sampled three lecturers from one TVET college. Data from the open-ended questionnaire were analyzed through the process of thematic. The findings of the study revealed that relevant mathematics topics taught in TVET colleges. The main resources for teaching mathematics are textbooks, which are the recommended textbooks. The lecturers’ conceptual understanding of TVET mathematics was also discovered. The study suggests that TVET colleges should teach pertinent mathematics topics and use educational materials that connect mathematical ideas to practical situations.

1. Introduction

Vocational education has a big role to play in preparing the students for workforce. To answer the student’s question, “what do I need mathematics for?” according to [1], mathematics is efficiently unescapable in the future workplace. Therefore, lecturers must prepare the students by exploring mathematics applications to various situations in the workforce that are collecting the concept with the real world. Furthermore, in preparing students to learn mathematics, exercises that are designed to examine the benefits of learning mathematics as a social rather than individual activity should be incorporated into the teaching. In addition, lecturers must include activities that will involve critical thinking and problem solving to enhance students’ abilities in communication [2]. In this regard, lecturer will be able to perform the role of academic instructor as well as vocational instructor. Caron [3] asserted that lectures must give students context for decision-making and solving problems. The reason is that jobs in the contemporary workplace involve the application of mathematics which requires innovation, creativity, and the ability to look at a task and not only see the outcome but also imagine different ways to achieve it. The author [3] further explains that schools need to go beyond the “three R’s” to improve college and career readiness with technical skills since important skills such as teamwork are frequently absent among students entering the workforce. Therefore, lecturers must prepare and involve students in learning relevant mathematics topics to understand how to work well with others with cooperative learning and working in groups in mathematics class. Furthermore, students need to be taught relevant consumer mathematics skills, such as balancing a chequebook, filling out a tax return, and budgeting, so that they will be able to manage their lives and function as responsible members of society, especially in managing finances [3].

When preparing the TVET college students for workforce through learning mathematics, the author [4] emphasized that TVET college’s mathematics curriculum requirements need to be reviewed in the light of what has been learned and what students need to know, which are relevant topics about mathematics to be effective in their careers. In addition, TVET students need to be taught and competent in some areas of mathematics that are not frequently taught in elementary and secondary schools but relevant to the TVET mathematics curriculum such as schematics (diagrams, graphics, plans, representation, and charts), geometric visualization and complex applications of measurement to be effective and prepare for workforce. Furthermore, a high priority should be given to the improvement of the teaching of relevant topics in mathematics such as proportional relationships including percent, graphical representations, functions, and expressions and equations in TVET colleges, and their application to concrete practical problems to prepare students for workforce [4].

National Certificate Vocational [NC(V)] programmes lead to well-paying careers which require relevant mathematics application and are not included in the typical TVET college mathematics [4]. For instance, mathematical modeling, that is, how to frame a real-world problem in mathematical terms, statistics and probability; data analysis; and applied geometry are relevant TVET mathematics topics. Some of these topics are considered as optional and been avoided by the students. Therefore, the purpose of this study is to investigate the perspective of the lecturers on teaching relevant mathematics topics to prepare Technical and Vocational Education Training (TVET) college students for the workforce. The research questions of this study are:

• To what extent do the lecturers teach mathematics that fit the requirement occupation in TVET colleges?

• To what extent do the lecturers teach relevant mathematics topic to prepare students for workforce at TVET college?

• What is the lecturer’s conceptual understanding of TVET mathematics?

• What are the challenges of lecturers face in effect changes in TVET mathematics?

2. Literature review

Technical and Vocational Education Training (TVET) colleges play a crucial role in preparing students for the workforce, equipping them with practical skills and knowledge. Mathematics, being a fundamental subject, is essential for success in various vocational fields. This literature review explores the perspectives of lecturers regarding the teaching of relevant mathematics topics in TVET colleges to adequately prepare students for the demands of the workforce. By examining existing literature, this review aims to identify key mathematics topics considered essential by lecturers, challenges encountered in teaching these topics, and effective strategies for enhancing mathematics education in TVET colleges.

2.1 Teaching mathematics with appropriate resources in TVET colleges

Globally, mathematics classrooms are perceived as having the ability to effect change through the use of mathematics textbooks [5, 6]. For implementing mathematics teaching and learning, mathematics textbooks provided supporting materials [6, 7]. In the past, mathematics textbooks were intentionally created and employed as change agents in the teaching and learning of mathematics. History claims that the twentieth century saw a progressive recognition of the supportive and mediating function that mathematics textbooks played [6, 7]. In addition, there are a number of well-known school mathematics textbook series from the period when the US mathematics reform movement first started, as well as from the twentieth-century mathematics movements in the United Kingdom, France, and many other nations. The US-based School Mathematics Study Group (SMSG) and the UK-based School Mathematics Project (SMP) are the publishers of these textbooks. Reformed school mathematics was designed and put into practice with an emphasis on the subject’s techniques, organization, and content [6, 8]. [9] states that textbooks developed in the late 1970s were based on pedagogical techniques, such as student-centred learning, technology utilization, and cooperative learning. In contrast to traditional textbooks, these reform ideas are simply referred to as “reform textbooks” or “reform-oriented textbooks”. Textbooks, as teaching tools for mathematics, will thus always be viewed and utilized as intermediaries of reform and change in mathematics classrooms [6].

The authors [10] claim that there are many kinds of teaching resources that can be employed in the mathematics learning process, but not all of them are appropriate for accomplishing learning objectives. Textbooks are thought to be superior in encouraging self-directed learning, letting students’ study alone at their own speed, and providing exercises to help students become more proficient in their subjects. Students have the chance to participate in an activity that requires a deeper degree of comprehension of the material in the textbooks. As a result, learners who utilize textbooks have better mathematical learning capacities. Furthermore, according to the authors in [10], effective teaching resources enable students to learn activities to reach objectives and maximize their ability when solving mathematical problems.

According to [11, 12], mathematics textbooks are the common resources that TVET lecturers use in teaching mathematics in TVET colleges in South Africa.

2.2 Understanding TVET colleges mathematics

Technical and Vocational Education and Training (TVET) is the term for educational programmes that place a strong emphasis on imparting the competencies, knowledge, and practical skills needed for sectors and jobs [13]. The authors also point out that TVET colleges are widely recognized in South Africa as organizations that help students develop their practical engineering abilities and become ready to become artisans. The authors [13] state that the National Certificate Vocational (NC(V)), which is offered by South African public TVET colleges from Level 2 to Level 4, lasts 1 year for each level, and the National Accredited Technical Education Diploma (NATED), which is divided into two parts: the business and engineering components. Semesters are used for the business component, and trimesters are used for the engineering component.

One of the foundational courses for NCV programmes and one of the four N1–N3 engineering disciplines in NATED programmes is mathematics, as mentioned by the author in [13]. The authors [14] express a similar opinion, stating that all engineering degrees should require prospective artisans to study mathematics as a foundational topic. According to the author in [14], mathematics is a subject that teaches people how to solve problems and make decisions by using reason and methodical thinking. Research studies indicate that in Technical and Vocational Education and Training (TVET), mathematics is important for improving students’ skills [15, 16, 17]. According to the author in [18], mathematics is the cornerstone and essential discipline for technical and engineering domains. The authors [14] explain further that mathematics is an important topic for developing critical thinking abilities in addition to imparting the fundamental knowledge required in these fields.

According to the author in [18], mathematics-oriented thinking skills include the capacity to accurately apply mathematics to gather data and solve issues as well as the interpretation of information presented in a mathematical style. The author [19] states that a student who is mathematically literate is aware of the importance of mathematics in the real world and is therefore able to make the kind of well-informed decisions that are required for active, constructive, and thoughtful citizenship. Furthermore, according to [20], the main goal of vocational mathematics education is to prepare students for future employment prospects or to improve the abilities of competent workers, hence raising their competency.

The authors in [21] assert that mathematics is a foundational science that contributes significantly to the advancement of knowledge and technology through both its theoretical and practical parts. Essentially, mathematics is an academic discipline that deals with abstract ideas that need to be understood before they can be applied to real-world situations. This allows for a more profound comprehension of a variety of occurrences.

2.3 Teaching appropriate mathematics topics to prepare TVET students for workforce development

Teaching is the process of imparting to students the skills, information and understanding that they have gained via a combination of professional training and real-world experience [22]. The process of teaching and learning, according to the author in [23], involves several difficulties since teaching requires teachers to make sure that students learn effectively. Varieties of instructional strategies can be used to promote successful learning, including both conventional and cutting-edge approaches, individual and group techniques, and teacher- and learner-centred strategies [23]. In addition, teachers have a duty to establish a conducive learning environment and use efficient teaching strategies to pique students’ sincere curiosity and motivate them to take an active role in their education.

According to the author in [18], the themes in the mathematics curriculum are designed to aid students in comprehending mathematical ideas and techniques for solving problems. In contrast to other courses, mathematical concepts are frequently more abstract and call for students to work with symbols that have little to no real significance [18]. Furthermore, the author in [24] contend that the goal of the mathematics curriculum is to give students the knowledge and abilities they need to succeed in the rapidly changing technological environment. According to the author in [17], mathematics curricula and instructional strategies, especially for career education, must be thoughtfully planned to give students information and critical thinking abilities.

The authors in [25] say that mathematics education should give students the tools they need to apply mathematical ideas in a variety of job and everyday life contexts. The main goals of teaching mathematics in various nations and to all age groups are to develop students’ understanding of mathematical structures and their capacity for mathematical thought [26]. The author in [26] contends that instruction ought to support the growth of students’ mathematical cognition and provide them with a foundational understanding of mathematical ideas and concepts. Students’ ability to manage information and solve issues is bolstered by this foundation. In a similar vein, the author in [27] contends that the goal of mathematics education for engineering students is to grasp and master mathematical concepts and abilities so they may effectively solve problems in their coursework and in their future professional endeavors. This suggests that a grasp of mathematical ideas is necessary for engineering courses.

Nonetheless, the contemporary work environment is experiencing swift changes that affect the mathematical instruments needed to simulate its most significant obstacles [28]. The changes require new characteristics and unique features, which forces educational systems to give learners and students the skills and competencies necessary for promoting innovation, managing change, and carrying out ideas with initiative and flexibility. These attributes, often known as twenty-first-century talents, are considered necessary for successfully negotiating the complexity and unpredictability of the contemporary world [28]. As stated by [29], it is imperative that teachers recognize the basic changes that are taking place in twenty-first-century education and, more importantly, comprehend how these changes affect the way that mathematics is taught.

The authors in [30] point out that technological advancements and the accessibility of digital resources have created new opportunities for engineering work. For example, computer assistance is now used to solve complex mathematical problems, and simulations and visualizations are now essential tools in the engineering process. [26], who contend that teachers can actively engage students in challenging mathematical problems that promote the development of strategic thinking and provide credence to the idea that twenty-first-century abilities can be learned and taught through mathematics. Additionally, the authors in [25] posit that teaching mathematics appears to be a perfect fit for developing twenty-first-century abilities like communication, cooperation, problem-posing and solving, and critical thinking.

These abilities are seen as essential in problem-solving-based teaching approaches, which recognize that knowledge is not only transferred but rather concentrates on helping students build their mathematical understanding. In keeping with this line of reasoning, the author in [31] asserts that all students must achieve a conceptual understanding, show skill mastery, and retain a good attitude toward mathematics in order to succeed in the demands of the twenty-first century.

The authors in [25] state that using a mathematical lens to engage with the environment entails identifying, interpreting, and creating links, patterns, and functions. Therefore, using a variety of tools, such as tables, graphs, symbols, and spoken explanations, is frequently necessary for mathematical lens procedure. Furthermore, a basic understanding of economic, political, and social studies depends especially on an understanding of functions and interactions between variables. Additionally, [17] identified seven skills—critical thinking and problem solving, collaboration across networks and leading by influence which are agility and adaptability, initiative and entrepreneurialism, effective oral and written communication, accessing and analyzing information, and curiosity and imagination—that TVET students can acquire when they exhibit strong proficiency in mathematics.

The author in [17] also contends that mastery of all these abilities requires a solid foundation in mathematics for students. [27] argue that engineering students should broaden their knowledge in a variety of mathematical fields as part of their undergraduate education. These include mathematical optimization, potential and approximation theory, applied analysis, and numerical analysis, among many others. According to [32], calculus is one of the key subjects in advanced mathematics with a wide range of applications in fields like engineering and physics. Therefore, it is essential that students gain a thorough understanding of calculus ideas and be able to apply them in a variety of circumstances and contexts.

The 21st-century skills that are needed in mathematics, according to the author in [31], include investigative, learning, communication, information and communication technology (ICT), and reasoning capabilities. Extending these competences, the author in [29] identified the six Cs of twenty-first-century education: computational thinking, creativity, collaboration, communication, and compassion. These researchers also stress that by combining the six Cs with Integrative Mathematics Skills (IMS), students can benefit from integrated learning that promotes the development of critical twenty-first-century skills in addition to improving their mathematical ability. With the help of this integrated approach, teachers may support students’ growth in the areas of mathematical competency and the six critical skills that are vital to modern education.

In forming students’ mathematical identities, teachers are the most significant resource [33]. This requires thinking about the differences between canonical and noncanonical forms of mathematics, learning how to grasp the rigorous foundations of mathematics while also developing a general understanding of it, and balancing the formal and contextual aspects of mathematics [33]. The important mathematics themes, such as statistical literacy, space-geometry, measurement, data collecting, variables and co-variation, reading and interpreting data, graphs, and charts, are thought to be crucial in preparing students for job growth.

According to the author in [34], a number of mathematics specialists highlight the importance of algebraic knowledge and abilities for both scholastic success and developing a skilled workforce in scientific and technical fields.

2.4 Challenges encountered in teaching relevant mathematics topics

Research studies indicate that there are difficulties in the instruction and acquisition of mathematical concepts. For example, the author in [24] identify a number of factors that affect mathematics education, including connecting mathematics to real-world applications, making effective use of instructional materials, teachers’ personalities, their subject-matter expertise, ineffective instructional practices, and difficulties with classroom management brought on by a lack of commitment on the part of both teachers and students. According to the author in [16], students learn mathematics in schools mostly by having teachers explain concepts in front of them, after which they take notes and work on given sample problems. This method of instruction is known as inductive; while pupils perform mathematical computations, their capacity for problem solving and analytical reasoning appears to be restricted.

The author in [31] noted similarly that teaching and studying mathematics in Nepalese schools tends to focus more on students reproducing the methods their teachers use, with less attention paid to developing conceptual knowledge or practical problem-solving abilities. For students in the twenty-first century, [31] contends, this method of teaching and learning presents difficulties.

According to the author in [35], one of the reasons why students perform poorly in mathematics includes a dearth of mathematical texts that closely follow established curricula and teachers who lack the expertise and abilities to explain subjects clearly. Furthermore, some teachers are not completely aware of the cognitive processes that students use to learn mathematics. Moreover, a lot of South African students speak English as a second language, which can make it difficult for them to learn mathematics when taught in English.

3. Theoretical framework

The theoretical framework that underpinned this chapter is the theory of Constructivist Theory of Learning. Constructivism is the concept that learners construct their own knowledge from experience.

The continuum constructivism theory is divided into three broad categories: cognitive constructivism [36], social [37, 38], and radical constructivism [39, 40]. Cognitive constructivists emphasize accurate mental constructions of reality. Meanwhile, radical constructivists emphasize the construction of a coherent experiential reality. In addition, social constructivists emphasize the construction of an agreed-upon, socially constructed reality [41]. The essential core of constructivism is that learners actively construct their own knowledge and meaning from their experiences [41, 42, 43]. The essential epistemological views of constructivism are firstly, knowledge is not passively accumulated, but rather, is the result of active cognizing by the individual. Secondly, cognition is an adaptive process that functions to make an individual’s behavior more viable given a particular environment. Thirdly, cognition organizes and makes sense of one’s experience, and it is not a process to render an accurate representation of reality. Fourthly, knowing has roots both in biological or neurological construction and in social, cultural, and language-based interactions [44, 45, 46, 47].

According to [48] constructivist theories, knowledge results from a continual process in which it is constructed and continually tested. Constructivists are nevertheless not free to construct just any knowledge; therefore, the knowledge constructed must be viable and work. From this perspective, knowledge should not be judged on whether it is true or false but rather in terms of whether it works or not. Therefore, what we call the stakeholders (educators, policymakers and curriculum developers) should emphasize that the knowledge constructed in TVET functions satisfactorily in the contexts in which it is constructed and applied.

In the article “The radical constructivist view on Science” by Von Glasersfeld [40] where, he argues that the knowledge constructed must fit reality the way the key fits a lock, which means that is different from looking for a match between knowledge and reality because many keys with slightly different shapes can open the same lock. The implication is that knowledge should not be looked at as being true or false; it should be judged on the fact that it works or it does not. Therefore, knowledge that counts in TVET is knowledge that works in the contexts in which it is applied.

In vocational education, knowledge cannot be viewed in the same way as verbalizing explanations of what a vocation consists; instead, it should be viewed as being an integration of contextual, theoretical (conceptual, procedural, and propositional), practical and indigenous everyday knowledge. This is because to be a competent craftsman, and a person needs to put to use all forms of knowledge that relate to his or her vocation in the context in which it is applied.

According to [49], social constructivism offers a viewpoint for comprehending how students are learning within their surroundings. As with constructivism and socially critical collaborative learning, social constructivism is expected to see learning as a process of creating meaning in order to make sense of events [50]. TVET lecturers are supposed to be aware of their students in accordance with this expectation [51]. As a result, social constructivism promotes an atmosphere in which students actively participate in the construction of their knowledge, much like constructivism and socially critical collaborative learning do [52]. It is recommended that lecturers establish a classroom climate in which students feel free to express ideas, ask questions, pose difficulties, and set goals. Thus, it is important to promote active learning in students by exposing them to a range of teaching strategies [49].

4. Methods

The study employs qualitative research method, and the instrument was an open-ended questionnaire for lecturer. A descriptive approach on teaching relevant mathematics topics in TVET colleges to prepare students for future workforce The research paradigm is epistemological constructivism. This indicates that knowledge of mathematics is created by human perception and social experience. Data were collected through open-ended questionnaires from three (3) TVET mathematics lecturers. All the participants are lecturing in one of the TVET colleges doing National Certificate Vocational [NC(V)] programmes in one of the Provinces in South Africa. These mathematics lecturers were purposively selected to participate by providing pertinent information on the teaching of relevant topics in mathematics. The open-ended questionnaire was administered to each lecturer and collected back after 2 weeks. The open-ended questionnaire questions focused on teaching relevant topics in mathematics. The instrument meets the trustworthiness criteria. This is the questionnaire that can be transferred and dependable, credible, and confirmed. The lecturers were able to express themselves about their teaching methods as well as relevant topics in mathematics. The questionnaire was collected and analyzed descriptively. Themes were generated from the responses of the participants. The participants voluntarily participated in the study. The informed consent form was signed by the participants, and all ethical conditions were met. Data were analyzed inductively.

5. Results

The open-ended questionnaire was collected from the participants and analyzed descriptively. Three lecturers participated in the study from one TVET college in one province in South Africa. Two females and one male were the respondents who participated in the study. The two females are mathematics teachers for NC(V) levels 2–4 while the male participant teaches NC(V) levels 2 and 3. The findings of the study are categorized into four parts: which are resources used to teach mathematics, conceptual understanding of TVET mathematics lecturers, relevant mathematics topics taught in TVET colleges and challenges encountered in teaching the relevant mathematics topics.

5.1 Resources used to teach mathematics in TVET colleges

All the participants responded that the main resource they used to teach mathematics was textbooks. The three respondents mentioned the name of the textbook they are using to teach mathematics. The responses were:

NCVL1: “I use basic manual textbooks, reference textbooks. Additional to that the students also use workbook”.

NCVL2: “I use Handson- training mathematics – future managers. Hands on training mathematics literacy”.

NCVL3: “I use TVET 1^st and 3^rd Edition mathematics”.

These are recommended resources for teaching mathematics in the TVET colleges.

A further question on the resources used to teach mathematics asked if the resources (textbooks) are appropriate for the students to acquire mathematics skills and prepare them for the workforce. The responses of all the lecturers are as follows:

NCVL1: “They provide organised units of work. Textbooks contain series of balance chorological exercises to equip students with necessary skills to prepare them for workplace”.

NCVL2: “Yes, the knowledge the comprehend through textbooks is appropriate for them as it gives knowledge and skills that are required by the workforce”.

NCVL3: “The textbook contains balanced units of work”.

All the respondents acknowledged that the textbooks they are using to teach mathematics are appropriate for the students, and through these textbooks, students will be able to acquire mathematics skills that can be demonstrated in workforce.

5.2 Understanding of TVET mathematics

The participants acknowledged that they have a conceptual understanding of the subject (Mathematics) when teaching it in the classroom. These are their responses:

NCVL1: “Lecturers are qualified mathematics teachers with sound knowledge in mathematics and mathematical frameworks. They have necessary skills to facilitate students understanding of concepts and support the habit of thought or patterns conceptual learning encourages future learning therefore planning and seeing the bigger picture is always necessary”.

NCVL2: “Firstly one needs to have majored in mathematics- of FET level. Secondly thorough knowledge of the subject. The passion, enthusiasm, and interest in unfolding the world of mathematics”.

NCVL3: “Lecturers have the necessary skills to facilitate students”.

All the respondents are qualified and have a conceptual understanding of the mathematics they are teaching.

5.3 Relevant mathematics topics taught in TVET colleges

The respondents stated the aspect of mathematics they are teaching. Their responses are as follows:

NCVL1: “Algebra analysis, arithmetic analysis, game theory, geometrics analysis, number theory, numerical analysis, optimization, probability theory etc.”.

NCVL2: “All aspect of mathematics from traditional instruments”.

NCVL3: “Probabilities theory, numerical analysis, geometry, algebra, arithmetic, optimization game theory”.

Further questions are needed to probe if the topics they teach fit the required occupation in society. All the participants responded by enumerating some topics that required occupation in the society as:

NCVL1: “Numbers – Numbers are all round us”.

Space and shape and orientation—measurements of perimeter, are and calculation of volume of different objects and scenarios in real contexts.

Finances—Equipping them with budgeting, spending and consequences of reckless spending.

Data handling—collecting and analyzing information in different situations.

NCVL2: “Algebra, statistics, geometry, trigonometry, financial math, linear programming, calculus, space, shapes and measurements, probability”.

NCVL3: “Measurements of perimeter, calculation of different objects and different situations”.

The participants stated the topics that fit the requirements of occupation in society. The NCVL1 gave examples of where these topics can be useful in the world of work.

The participants gave the reasons why these topics are relevant to be taught in TVET colleges and how they can equip students for their future vocation when related to the procedure of concrete practical problems in real life. These are their responses:

NCVL1: “The topics are very much relevant because they equip the students with better problem-solving skills, analytical and logical reasoning. … also, by using real life experiences and doing practical examples using known”.

NCVL2: “they can be able to estimate expenses, understand financial statements-, be able to determine the best route to take. In calculating distances between 2 points time, they will take to have a certain distance. How to do conversions between measuring units (e.g. from km to m), map readings, whether focus (probability). …”.

NCVL3: “Yes, they are relevant as they equip learners with better problem-solving skills. … also, by using practical examples of real-life experiences”.

All the participants acknowledged that all the topics are relevant to equip the students and to prepare them for the workforce in the future by using examples from real-life experiences.

5.4 Challenges encountered in teaching relevant mathematics topics

Two of the participants responded to the type of challenges the encountered when teaching these topics. Their responses are as follows:

NCVL1: “The most challenges part is to make students relate whatever thought to real-life situations. Students need to master the skills of breaking barriers wall between theory gained and the application of that theory in their daily lives”.

NCVL2: “I encountered challenges when I focus on knowledge of mathematical facts, rules, formulae methods to approaches in real life applications”.

These participants acknowledged that relating these topics to real-life situations and their applications is difficult for them to explain or demonstrate in the classroom. Also, for students to understand the applications is problematic.

6. Discussions and conclusions

The findings of this study revealed that lecturers used textbooks to teach mathematics as the main resources. The responses of the lecturers indicated that the lecturers are using textbooks to teach mathematics in the TVET college and that these are the recommended textbooks and appropriate to teach the subject. This result concurred with [11, 12, 53, 54], where these researchers concluded that textbooks are the main resources that lecturers use to teach mathematics in TVET colleges. Furthermore, the findings of the study also revealed that the lecturers are skilled and qualified and have a conceptual understanding of the mathematics concepts to teach the subject. Moreover, the results of the study revealed the relevant topics that are fit for the requirements profession in the industries and society. These topics are relevant and can be applied in fields and disciplines such as computer science, engineering, natural sciences, medical science, economics, and accounting. In addition, the findings show the challenges lecturers encountered during the implementation of change in mathematics. The lecturers encountered challenges when relating and applying the topics to real-life situations, which is also a challenge for the students to comprehend. These results agreed with [13], wherein mathematics professors are encouraged to pursue professional development opportunities to enhance their pedagogical abilities, mathematical topic understanding, and capacity to apply cutting-edge teaching methodologies. According to the authors in [55], lecturers are confident in their abilities to fully impart skills to students. The findings of the study also corresponded with the studies of [22, 29, 32] where these researchers discovered that the most pertinent topics are statistics, space-geometry, and calculus, and all mentioned by the respondents grow the teaching mathematics in TVET colleges to help students to decode and interpret information, structure and conceptualize the problem situation, make inferences and assumptions, formulate a model, and access data and information in society. These results also coincided with the author in [24], who determined the various factors that impact mathematics education, such as relating mathematics to real-world applications, utilizing instructional materials effectively, teachers’ personalities, subject-matter expertise, ineffective instructional practices, and challenges with classroom management resulting from a lack of commitment from both teachers and students.

In conclusion, this study revealed that relevant mathematics topics have been taught in the TVET colleges, which can prepare students for the application in the workforce. TVET mathematics lecturers were skilled and knowledgeable in teaching mathematics. The lecturers possessed a conceptual understanding of the mathematics concept. In addition, the challenges the lecturers faced when teaching these concepts were discovered in this study.

The implication of the findings of this study is that poor performance in mathematics and inadequate quality education might result from using textbooks as the primary teaching resource for mathematics in Technical and Vocational Education (TVET) courses. Students’ preference for memorization of key components of mathematical accomplishments and rote learning are the causes. Furthermore, there will not be enough real-world instances.

7. Recommendations

This study suggests that TVET colleges should teach pertinent mathematics topics. The country’s Higher Education Department ought to suggest topics that are pertinent and help students apply their learning to the actual world. TVET lecturers must try to ascertain what prior knowledge their students possess and cultivate a solid rapport with them as students. Additional educational materials that connect mathematical ideas to practical situations should be available.

8. Conclusions

The sections of this chapter are numbered one through seven. The introductions provided an overview of the study’s contents about the teaching and learning of mathematics in TVET colleges and how to get students ready for the workforce at the beginning of the chapter. The chapter’s second section, the literature review, summarizes several research on teaching pertinent mathematics at TVET colleges. Teaching mathematics with appropriate resources in TVET colleges; Understanding TVET colleges mathematics; Teaching appropriate mathematics topics to prepare TVET students for workforce development; and Challenges encountered in teaching relevant mathematics topics are the subheadings into which the literature review was divided. The theoretical underpinning that directed the research was constructivism. This chapter employs a qualitative approach using the epistemological constructivism research paradigm. Thematic analysis was used to analyze the data. The chapter’s discussion and conclusions were appropriate and well-supported by pertinent material. The chapter recommended that pertinent subjects be taught in TVET mathematics and that these subjects be connected to actual circumstances.

Acknowledgments

My acknowledgement goes to the research committee of Walter Sisulu University, which approves the project to be carried out. My appreciation also goes to the Department of Research and Innovation of the institution for the funding of the publication. Furthermore, I want to express gratitude to all the participants who participated in this study for their contribution to making the article a reality.

Conflict of interest

The authors declare no conflict of interest.

Notes/thanks/other declarations.

There is no declaration.

Appendices and nomenclature

Lecturers’ interview questions

Gender		LECTURER’S POSITION
Male		NCV 2
Female		NCV 3
		NCV 4

1. What type of textbooks do the students/lecturers use to study/teach mathematics?

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2. In what way do the textbooks appropriate for students to acquire mathematics skills and prepare them for the workforce?

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3. What are the admission requirements for students for TVET? Do the admission to TVET colleges require high/medium/least grades in mathematics?

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4. What is the sound conceptual understanding of the mathematics do the lecturers have for their teaching?

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5. What aspect of mathematics are you teaching in TVET colleges? What challenges do you encounter teaching them?

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6. What are the mathematics topics do you teach that fits the requirement occupation in the society?

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7. In what way do these topics relevant to the student’s vocation in the future?

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