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SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED QUALIFICATION: 

Advanced Diploma in Mathematics Education 
SAQA QUAL ID QUALIFICATION TITLE
101749  Advanced Diploma in Mathematics Education 
ORIGINATOR
University of Johannesburg 
PRIMARY OR DELEGATED QUALITY ASSURANCE FUNCTIONARY NQF SUB-FRAMEWORK
CHE - Council on Higher Education  HEQSF - Higher Education Qualifications Sub-framework 
QUALIFICATION TYPE FIELD SUBFIELD
Advanced Diploma  Field 05 - Education, Training and Development  Schooling 
ABET BAND MINIMUM CREDITS PRE-2009 NQF LEVEL NQF LEVEL QUAL CLASS
Undefined  120  Not Applicable  NQF Level 07  Regular-Provider-ELOAC 
REGISTRATION STATUS SAQA DECISION NUMBER REGISTRATION START DATE REGISTRATION END DATE
Reregistered  EXCO 0821/24  2021-07-01  2027-06-30 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2028-06-30   2031-06-30  

In all of the tables in this document, both the pre-2009 NQF Level and the NQF Level is shown. In the text (purpose statements, qualification rules, etc), any references to NQF Levels are to the pre-2009 levels unless specifically stated otherwise.  

This qualification does not replace any other qualification and is not replaced by any other qualification. 

PURPOSE AND RATIONALE OF THE QUALIFICATION 
Purpose:
The purpose of this qualification is to strengthen, supplement, upgrade and/or enrich Senior Phase Mathematics/Further Education and Training (FET) Mathematics/Mathematical Literacy teachers' knowledge, understanding and skills in their existing specialisation. The qualification offers intellectual enrichment and intensive, focused and applied specialisation in Mathematics/Mathematical Literacy. This qualification will provide a deep and systemic understanding of the current thinking, practice, theory and methodology in Mathematics/Mathematical Literacy. This qualification will also guide teachers in developing an understanding of the nature of the subject discipline and to acquire pedagogic content knowledge. The teacher will be able to teach Mathematics in the Senior/FET Phase or Mathematical Literacy. The curriculum covers theoretical and pedagogical components required in the teaching of Mathematics/Mathematical Literacy. This qualification comprises a knowledge mix consisting of four knowledge strands according to the Curriculum Assessment Policy Statements (CAPS), accompanied by four Pedagogical Content Knowledge (PCK) components, to break the predominant transmission mode that characterises many classrooms.

Therefore, the modules are broadly aligned to these knowledge strands to develop specialist skills of teachers in:
  • Using visual, symbolic and language skills in Mathematics/Mathematical Literacy using descriptions in words, graphs, symbols, tables and diagrams.
  • Collecting, analysing and organising quantitative data to evaluate and critique conclusions.
  • Using mathematical process skills to identify, investigate and solve problems creatively and critically.
  • Using spatial skills and properties of shapes and objects to identify, pose and solve problems creatively and critically.
  • Participating as responsible citizens in the life of local, national and global communities.

    Rationale:
    As Mathematics/Mathematical Literacy teachers develop in their practices and also become more experienced, they are expected to make greater contributions with regard to subject expertise, academic leadership and Continuing Professional Development (CPD). However, according to Miranda and Adler (2010, p. 15) "curriculum alone as a document cannot fulfil the current reform demands imposed onto teachers in order to help learners make meaning of the subject content they are supposed to learn". Furthermore, "poor trends in international Mathematics and Science Study (TIMMS) results and widespread disappointing mathematics results in South Africa necessitate more efficient professional development for in-service mathematics teachers" (Wessels and Nieuwoudt, 2011, p. 1). Therefore, there is a need among teachers for continuing professional development in terms of specialised knowledge of and skills in Mathematics/Mathematical Literacy teaching. Darling-Hammond (2008, p. 92) gives a very good description of what a good teacher needs to know:
  • Teachers need to understand subject matter deeply and flexibly, so that they can help students create useful cognitive maps, relate ideas to one another, and address misconceptions. Teachers need to see how ideas connect across fields to everyday life. This kind of understanding provides the foundation for pedagogical content knowledge (Shulman, 1987) which enables teachers to make ideas accessible to others.

    The rationale for Continous Professional Development (CPD) qualifications such as this qualification is to assist teachers to become such keystone teachers, and also to provide teachers with opportunities to strengthen or supplement their existing specialisation in either Senior Phase Mathematics, Further Education and Training (FET) Mathematics or Mathematical Literacy, in ways that will be meaningful to the lives of learners.

    The above needs are phase and subject specific. To address these, the teacher needs in the Senior Phase and FET Phase, an Advanced Diploma in Mathematics Education with an endorsement for Mathematics in the Senior Phase, an endorsement for Mathematics in the FET Phase and an endorsement for Mathematical Literacy has been designed. Teachers who enrol for this qualification will typically be practicing teachers in the Senior/FET Phase in schools, who wish to upgrade their qualifications or who want to enrich and supplement their existing knowledge and competence with regard to subject knowledge and methodology in Mathematics/Mathematical Literacy. This qualification is designed to address pedagogical content knowledge development of Mathematics/Mathematical Literacy teachers in the different knowledge strands. The school curriculum adequately captures the important knowledge strands in Mathematics/Mathematical Literacy as a subject, and this qualification capitalises on these identified knowledge strands.

    Teachers who complete this qualification will also benefit society and address the needs of stakeholders by being able to help provide in the urgent demand for specialised Mathematics/Mathematical Literacy teachers with sufficient content knowledge and Pedagogical Content Knowledge (PCK). The Centre for Development and Enterprise (CDE) report by Bernstein (September 2011, p. 23), made it clear that there is a need to incubate and retain good teachers, especially in scarce subjects such as Mathematics and Science for it is the key to economic growth, and the empowerment of more South African citizens to get jobs. Through this qualification teachers will be equipped to inspire and motivate their learners to pursue careers in Science, Technology, Engineering and Mathematics (STEM). 
    		•

    LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING 
    Recognition of Prior Learning (RPL):
    The Faculty accepts Recognition of Prior Learning (RPL) as an integral part of education and academic practice. It is acknowledged that all learning has value and the Faculty accepts the challenge to assess prior learning and award credit that is aligned to Faculty programmes to promote lifelong learning. The purpose of the institution's RPL policy is to Recognise Prior Learning in order to provide for admission to qualifications, grant advanced placement in qualifications and grant credits for modules using the principles and processes that serve as basis for Faculty-specific RPL practices.

    A panel of selected staff members will determine, on a one-on-one basis, the competence of prospective students who apply for RPL. In determining an applicant's competence against the relevant Exit Level Outcomes, this panel will do one or more of the following:
  • Verify the standard/quality of an applicant's prior qualifications.
  • Ask for and assess a portfolio containing examinationples of the applicant's work in the field of education, training and development.
  • Observe the applicant's performance in authentic and/or in situ teaching-learning situations and/or contexts.
  • Conduct one-on-one interviews with applicants to discuss the results of the evidence collection process.

    Learners will be supported mainly through monitoring of assessment results and provision of assistance through the tutor system:
  • The lecturer in conjunction with the tutor identifies at-risk students.
  • A support strategy is developed by the lecturer and discussed with the tutor.
  • Support includes: Individual tutor sessions with students, group work sessions, referral to the Academic Development Division for professional services.
  • The student's progress is then tracked and monitored.

    Entry Requirements:
    To gain admission into the Advanced Diploma in Education in Mathematics Education a potential student should possess:
  • A four-year Bachelor of Education Degree.
    Or
  • A pre-2009 NQF Degree, Level 6 or Diploma, plus an Advanced Diploma in Teaching, Level 7.
    Or
  • A pre-2009 NQF Postgraduate Certificate in Education, Level 6.
    Or
  • A pre-2009 NQF Higher Diploma in Education (Undergraduate).
    Or
  • A pre-2009 NQF Diploma in Education.
    Or
  • An Advanced Certificate in Education, Level 6.
    Or
  • An Advanced Certificate in Teaching, Level 6.
    Or
  • A pre-2009 NQF three-year College of Education Diploma or a National Professional Diploma in Education (NPDE) (360 Credits at Level 5) followed by an Advanced Certificate in Teaching. 
    		•

    RECOGNISE PREVIOUS LEARNING? 
    Y 

    QUALIFICATION RULES 
    This qualification comprises compulsory modules at Level 7 totalling 120 Credits.

    Compulsory Modules, Level 7,120 Credits:
  • Advance Mathematics for Education A, 10 Credits.
  • Pedagogical Content Knowledge (PCK) A, 10 Credits.
  • Advance Mathematics for Education B, 10 Credits.
  • Pedagogical Content Knowledge (PCK) B, 10 Credits.
  • Conceptual Change, 20 Credits.
  • Pedagogical Content Knowledge (PCK) C, 10 Credits.
  • Advance Mathematics for Education C, 10 Credits.
  • Pedagogical Content Knowledge (PCK) D, 10 Credits.
  • Advance Mathematics for Education D, 10 Credits.
  • Inquiry Methodology, 20 Credits. 
    		•

    EXIT LEVEL OUTCOMES 
    1. Interrogate practice by using theories and research findings in Mathematics Education.
    2. Analyse and use relevant Mathematics/Mathematical Literacy support materials, and demonstrate a sound grasp of the fundamental conceptual mathematical knowledge required for teaching Mathematics/Mathematical Literacy.
    3. Articulate and apply the different components of the Faculty's conceptual framework for teaching and learning, namely care, accountability, critical reflection and facilitating learning in diverse contexts.
    4. Commit to high ethical standards in the practice of Mathematics/Mathematical Literacy Education.
    5. Use a variety of teaching and learning approaches, such as inquiry-based learning in the classroom, in order to better address problem solving in Mathematics/Mathematical Literacy.
    6. Assist learners in their conceptual change and to address learner misconceptions effectively in the organising fields of learning.
    7. Function within a small online community of practice and to this effect use on-line technology, e.g. Blackboard (Ulink). 

    ASSOCIATED ASSESSMENT CRITERIA 
    Associated Assessment Criteria for Exit Level Outcome 1:
  • Use concepts and ideas about the nature of mathematics and of mathematical activity and thinking and what it means to learn and to teach mathematics.
  • Communicate learning theories in mathematics Education, including associationism (behaviourism), rationalism (naturism), constructivism, and sociocultural theory; and the work of Piaget and Vygotsky and their associates and followers.
  • Use examinationples of learners' activities and thinking and learning theories as lenses to explain situated learning.
  • Analyse research findings in Mathematics Education in published research on how current learning theories inform teaching and judge the coherence of the theory within which published research is framed.
  • Evaluate critically the consistency within theoretical arguments in the field of teaching and learning mathematics.
  • Organise theoretical arguments from different sources to synthesise new ideas especially in relation to students' own research goals.
  • Develop and gain a level of mastery of discussing, explaining, and critically evaluating and interpreting the theories of learning and teaching in the field of Mathematics Education.

    Associated Assessment Criteria for Exit Level Outcome 2:
  • Identify and solve problems involving number patterns and sequences, and to use simple and compound decay formulae and apply knowledge of geometric series to solve annuity and bond repayment problems.
  • Understand the working relationships between variables in terms of numerical, graphical, verbal and symbolic representations of functions, and Differentiate specified functions by using specified rules of differentiation.
  • Prove and use trigonometry within a two-dimensional Cartesian co-ordinate system to derive and apply.
  • Investigate and prove theorems of geometry.
  • Solve geometry problems and prove riders.
  • Collect, organise and interpret numerical data.
  • Compare the relative frequency of an experimental outcome with the theoretical probability of the outcome and doing probability problems.
  • Analyse resource materials in the Mathematics/Mathematical Literacy classroom with regard to fundamental and specialised knowledge in Mathematics.
  • Reflect critically on own practice and identify areas of growth in subject and pedagogical knowledge, and mapown professional development.

    Associated Assessment Criteria for Exit Level Outcome 3:
  • Demonstrate care, accountability, critical reflection and facility learning articulation in diverse contexts.
  • Apply by discussing and considering current issues in Mathematics including multilingualism and affective constructs in the teaching and learning of mathematics, e.g. beliefs, attitudes, emotions and values.

    Associated Assessment Criteria for Exit Level Outcome 4:
  • Address the sociocultural, economic and political questions that form the basis of the evaluation of performance of mathematics teaching.
  • Develop and integrate within own value system a consistent theory of learning and teaching mathematics by explaining and interpreting own research goals within their beliefs and value system.

    Associated Assessment Criteria for Exit Level Outcome 5:
  • Determine the relationship between approaches to teaching and teachers' perspectives on mathematics and on the learning of mathematics.
  • Use inquiry-based learning strategies and heuristic methods in the classroom, in order to better address the syntactical nature of mathematics learning.
  • Interrogate problem-solving models, creativity and teaching strategies.
  • Design, implement and report on lesson plans.

    Associated Assessment Criteria for Exit Level Outcome 6:
  • Foster conceptual change by establishing a sound understanding of the conceptual change theory, curriculum differentiation, and accompaniment of learners with learning difficulties or misconceptions.

    Associated Assessment Criteria for Exit Level Outcome 7:
  • Submit and evaluate assessments via Black Board.
  • Participate in on-line discussions.
  • Video-stream mathematics lessons.
  • Use on-line technology software, such as Geo Algebra, to teach Mathematics/Mathematical Literacy.

    Integrated Assessment:
    There is a minimum of three summative assessment opportunities per semester module and at least seven summative assessment opportunities per year module. One of these summative assessment opportunities, preferably towards the end of a module, should be substantial (such as a written examination, a portfolio or substantial assignment) to ensure that outcomes are assessed in an integrated manner. The weighting of the latter assessment opportunity must be at least 50% but not more than 60% of the final mark.
    Formative and summative assessment opportunities are available to students. Formative assessment supports teaching and learning, provides feedback to the student, diagnoses the students' strengths and weaknesses, assists in the planning of future learning and helps to make decisions on the readiness of the student to do a summative assessment. Summative assessments are conducted for the purpose of making a judgment about the level of competence of students in relation to the outcomes of a module. An assessment analysis is done for each assessment to ensure that all questions are on the correct cognitive level as well as to ensure an appropriate percentage of higher and lower cognitive questions.

    Methods, procedures and management of assessment:
    A range/variety of summative assessment opportunities is required and may include tests, assignments, portfolios, practical demonstrations, presentations, written and oral examination open book written examination "take-home" examinations, etc.

    Formative assessment opportunities may vary according to individual programme/module outcomes and the composition of these is at the discretion of the lecturer. The primary purpose of formative assessment is to support the learning process through constructive feedback to students. The following procedures apply to students who are enrolled for a programme in the Faculty of Education:
  • Access to and viewing of the final written assessment script/activity, etc.

    Assessment procedures for Advanced Diploma in Education (AdvDip (Ed)):
    The final mark in each module is cumulatively compiled. The final mark consists of at least three assessment opportunities in an approximately 14 week (semester) module in accordance with University's Academic Regulations. These may comprise of assignments, portfolios, practical work, oral presentations, formal, tests, examinations, etc.

    The final summative assessment opportunity, at the end of a module, must be substantial (such as a written examinationination, or a portfolio) to ensure that outcomes are assessed in an integrated manner. A minimum module year mark of 40% is required for admission to the final summative assessment opportunity. The assessment task that carries the greatest weight in each module must be externally moderated for quality assurance purposes.

    For the final summative assessment opportunity, students should obtain a mark of at least 40% and a final calculated promotion mark of at least 50%. Module lecturers must provide written, detailed and constructive feedback to students on continuous assessment tasks within fifteen working days after receiving these assessment tasks. Programme-specific assessment criteria rules and regulations must be communicated to students in all learning guides. 
    		•

    INTERNATIONAL COMPARABILITY 
    Cambridge University, England, United Kingdom:
    Qualification: Teaching Advanced Mathematics (TAM):
    The Teaching Advanced Mathematics (TAM) qualification has been designed to support teachers of GCSE Mathematics who wish to teach A level Mathematics for the first time. Students should be qualified teachers in state-funded schools and colleges in England. Teachers enrol for the qualification to deepen their subject knowledge and gain new ideas for teaching of Mathematics. The qualification is professional development focusing on developing the teaching skills and subject knowledge of teachers new to teaching A-level Mathematics.

    Content:
    The contents of the qualification includes a combination of subject knowledge where the purpose is to on deepen the teachers' understanding of mathematics; for example, lessons where the focus is on pedagogy; and facilitated reflections.
    Comparison:
    This qualification was compared against Teaching Advanced Mathematics (TAM) qualification of Cambridge University and it compares with its scope, which is to deepen their subject knowledge and gain new ideas for teaching of Mathematics. This qualification focuses primarily on strengthening, supplementing, upgrading and/or enriching teachers' knowledge, understanding and skills in Mathematics. Both qualifications are one year in duration and are geared for professional development. Similarities are as follows: current teaching approaches (pedagogical content knowledge), subject content and designing, implementing and reporting on lesson plans, and opportunities for critical reflection.

    Edge Hill University, Ormskirk, Lancashire, England:

    Qualification: Subject Knowledge Enhancement Mathematics Professional Development Programme.

    The Subject Knowledge Enhancement Mathematics Professional Development Programme is a flexible programme designed for non-Mathematics specialists who want to be retrained to teach Mathematics and/or want to enhance and extend their subject knowledge. The aim of the qualification is to develop teachers' subject knowledge in Mathematics so as to prepare them to teach the conceptual and applied aspects of the subject effectively.

    Content:
    Address gaps in subject knowledge; the Mathematics curriculum; develop enthusiasm for working mathematically; promote learning in Mathematics that is challenging and engaging for all students; identify and build upon prior learning and develop capacity for future; the use of Mathematics in society; an understanding of the connections that exist between topics in Mathematics; the use of appropriate technology in teaching and learning.

    Comparison:
    This qualification is also compared against Edge Hill qualification with the purpose of retraining teachers to teach Mathematics and this qualification focuses primarily on guiding teachers, who wish to upgrade their qualifications or who want to enrich and supplement their existing knowledge and competence, in developing an understanding of the nature of the subject discipline and to acquire pedagogic content knowledge. Both are one-year programmes, preparing students for Postgraduate studies. Similarities would cover content knowledge in Mathematics, learning in Mathematics that is challenging, thus problem solving, curriculum differentiation in order to engage all learners and the nature of Mathematics, including in society. This qualification differs in the sense that it also includes conceptual change theory, accompaniment of learners with learning difficulties or misconceptions and learning theories. 

    ARTICULATION OPTIONS 
    This qualification offers horizontal and vertical articulation opportunities.

    Horizontal Articulation:
  • Bachelor of Education (BEd), Level 7.

    Vertical Articulation:
  • Bachelor of Education Honours Degree
  • Honours Degree in another cognate field, Level 8
  • Postgraduate Diploma in Education in Mathematics Education, Level 8. 
    		•

    MODERATION OPTIONS 
    N/A 

    CRITERIA FOR THE REGISTRATION OF ASSESSORS 
    N/A 

    NOTES 
    N/A 

    LEARNING PROGRAMMES RECORDED AGAINST THIS QUALIFICATION: 
     
    NONE 


    PROVIDERS CURRENTLY ACCREDITED TO OFFER THIS QUALIFICATION: 
    This information shows the current accreditations (i.e. those not past their accreditation end dates), and is the most complete record available to SAQA as of today. Some Primary or Delegated Quality Assurance Functionaries have a lag in their recording systems for provider accreditation, in turn leading to a lag in notifying SAQA of all the providers that they have accredited to offer qualifications and unit standards, as well as any extensions to accreditation end dates. The relevant Primary or Delegated Quality Assurance Functionary should be notified if a record appears to be missing from here.
     
    1. University of Johannesburg 


    All qualifications and part qualifications registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.