Higher Certificate in Mathematics for Engineering Technology

Purpose

The Higher Certificate in Mathematics for Engineering Technology has as primary focus to provide access to higher education, and specifically for access to engineering technology qualifications for deserving learners that do not meet entry requirements into relevant mainstream qualifications.

The qualification provides learners with the foundational basis that will enable mastering of the basic introductory knowledge, cognitive and conceptual tools for higher education studies in Mathematics for Engineering Technology, such as Diploma studies in Engineering Technology. The qualification emphasises selected general principles together with more specific procedures and their application in Mathematics as relevant to Engineering Technology.

Rationale

The qualification will assist learners with lower grades in Mathematics from National Senior Certificate (NSC) level to be able to access Engineering qualifications at higher education institutions. Some schools provide Mathematical Literacy to all learners, which does not allow them to pursue engineering qualifications.

The Higher Education Qualifications Framework (HEQSF) of 2014 allows for a Higher Certificate that is not vocational. Instead, it provides learners with basic introductory knowledge, cognitive and conceptual tools and practical techniques for higher education studies.

The qualification consists of modules that have basic concepts required in engineering-related qualifications at higher education institutions. The qualification also has advanced Mathematics concepts that lay a foundation in the requirements of STEM-related qualifications at higher education institutions.

The qualification targets those who will have completed their NSC level and will have access to STEM-related qualifications in higher education institutions.

The qualification holders will be able to be employed as research assistants and Mathematics teaching assistants.

Recognition of Prior Learning (RPL)

Learners who do not possess the level of qualification outlined may apply for recognition of prior learning (RPL) in the prescribed format. RPL is an important policy goal, which is signalled in the Education White Paper, and reaffirmed by the Council on Higher Education (CHE), and which suggests promotion of RPL initiatives to improve the intake of adult learners as an essential avenue of redress.

Recognition of credit for prior learning is the process whereby the institution makes a judgement about the extent to which they can accept Accredited Prior Learning (APL) or Accredited Prior Experience (APE), as partial fulfilment of the institution's requirements for a given academic award.

In exceptional circumstances, learners may gain exemption from part of a qualification based on previous studies. Specific departments may refuse to consider any learners for such exemption.

Entry Requirements

The minimum entry requirement for this qualification is

• Senior Certificate (SC), Level 4.

Or

• National Senior Certificate (NSC), NQF Level 4 granting access to Higher Certificate studies.

Or

• National Certificate (Vocational) (NCV), Level 4 granting access to Higher Certificate studies.

This qualification consists of the following compulsory modules at National Qualifications Framework Level 5 totalling 132 Credits.

Compulsory Modules, Level 5, 132 Credits

• Mathematics Literacy, 6 Credits.
• Mathematics Problem Solving, 6 Credits.
• Studying Mathematics, 6 Credits.
• Mathematics for Engineering Technology 1, 24 Credits.
• Mathematics for Engineering Technology 2, 24 Credits.
• Mathematics for Engineering Technology 3, 24 Credits.
• Mathematics for Engineering Technology 4, 24 Credits.
• Mathematics for Engineering Technology 5, 18 Credits.

1. Communicate appropriately by correctly making use of the language of Mathematics.
2. Use mathematical process skills to identify, investigate and solve problems creatively and critically.
3. Use effective study habits and study strategies to improve in areas such as time management, organisation, and test-taking skills.
4. Understand and apply basic key mathematical terms, concepts, facts, principles, rules, methods and procedures to solve well-defined engineering technology problems.

Associated Assessment Criteria for Exit Level Outcome 1

• Communicate effectively in English.
• Apply reading strategies to learn Mathematics, including writing style, vocabulary, symbols, key concepts, metacognition, pre-reading, reading, reflection.
• Write to learn Mathematics.
• Communicate mathematical thinking coherently and clearly.
• Analyse and evaluate the mathematical thinking and strategies of others.

Associated Assessment Criteria for Exit Level Outcome 2

• Exhibit critical thinking skills.
• Identify other people's positions, arguments and conclusions; evaluate the evidence for alternative points of view; weigh up opposing arguments and evidence fairly.
• Apply Polya's problem-solving techniques.
• Understand the problem, devise a plan to solve it; carry out the project; and reflect on the solution.

Associated Assessment Criteria for Exit Level Outcome 3

• Demonstrate what is needed to know to study Mathematics.
• Demonstrate an understanding why studying Mathematics is different from studying other subjects.
• Discover Mathematics learning strengths and weaknesses.
• Measure and reflect upon Mathematics study skills; reflect upon practical study skills and build upon it.
• Reduce Mathematics test anxiety.
• Recognise test anxiety and its causes.
• Apply relaxation techniques and minimise negative self-talk.
• Improve listening and note-taking skills.
• Apply learning styles and memory techniques to improve memory.
• Improve Mathematics test-taking skills.
• Apply the ten steps to better Mathematics test-taking; minimise the six types of test-taking errors.

Associated Assessment Criteria for Exit Level Outcome 4

• Do calculations in algebra, mensuration, trigonometry, introductory complex numbers, matrices and vectors, statistics, probability and introductory calculus.
• Convert between binary, octal and hexadecimal numbers.
• Apply the factor and remainder theorems.
• Express a rational function into its partial fractions.
• Solve linear and quadratic equations and inequalities.
• Solve simultaneous equations.
• Transpose simple engineering formulae.
• Apply the properties of the straight-line graph to engineering problems.
• Reduce a non-linear law to a linear form.
• Discuss the features of periodic functions, continuous and discontinuous functions, even and odd functions and inverse functions.
• Apply the properties of exponential and logarithmic functions to engineering situations.
• Expand a binomial expression by making use of the binomial theorem.
• Apply the properties of the sine and cosine waveforms to engineering problems.
• Convert between Cartesian and polar coordinates.
• Simplify/Solve trigonometric identities/equations.
• Perform addition, subtraction, multiplication and division with complex numbers in rectangular form.
• Convert between the square and polar shape of a complex number.
• Perform multiplication and division with complex numbers in polar form.
• Perform general arithmetic operations on 2X2 matrices.
• Evaluate 2X2 determinants.
• Solve simultaneous equations by using Cramer's rule.
• Apply vectors to engineering problems.
• Represent given data in a histogram, frequency polygon, frequency distribution table and bar chart.
• Apply the rules of probability.
• Evaluate permutations and combinations.
• Understand the derivative in terms of a limit of a function.
• Find the derivatives of some standard engineering functions.
• Differentiate successively.
• Apply differentiation to solve some simple engineering problems.
• Understand integration as the opposite of differentiation.

Integrated Assessment

The formative assessments are in the form of eight tutorial tests and two class tests. The tutorial sessions allow learners to interact with the lecturer and tutors on an individual basis. The content of each session covers the previous week's material. During these sessions, the lecturers guide learners to become appreciative, observant and skilled in focusing on which matters are of critical importance. After each session, learners write a 15 minutes tutorial test. This assessment enables the coordinator to identify any shortcomings that learners need to address. The results from the formative assessments are discussed in open classroom sessions to ensure that the assessment processes are understood.

The lectures constitute about 50% of the total notional hours. The other 50% is split amongst tutorials, study time and assessment time.