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Official programme of record · SWY-25
Professional Master of Education in Mathematics Pedagogy, Spiral Didactics & STEM Leadership
This page is the single official record of this programme. Transcripts, syllabus PDFs, the learner workspace and the public verification page are all generated from it, and each printed syllabus carries the version and fingerprint shown below so evaluators can compare them line by line.
Total learning hours
1800 h
Scheduled class / seminar
540 h
Guided study, lab & research
1260 h
Credits
60 ECTS
30 learning hours per ECTS credit. Taught units: 20 h seminar + 30 h guided study. Research stages: 20% supervision, 80% independent research. Programme version 2026.10 · fingerprint 7E186494675CE211
Graded courses on the transcript · 7
| Code | Course | Hours | ECTS |
|---|---|---|---|
| SWY-25-S1 | Spiral 1 — Mathematical Reasoning & Proof | 150 | 5 |
| SWY-25-S2 | Spiral 2 — Didactics of Algebra, Calculus & Discrete Mathematics | 150 | 5 |
| SWY-25-S3 | Spiral 3 — Technology in Mathematics Teaching | 150 | 5 |
| SWY-25-S4 | Spiral 4 — Assessment & Mathematics Anxiety | 150 | 5 |
| SWY-25-S5 | Spiral 5 — STEM Curriculum & Mathematical Modelling | 150 | 5 |
| SWY-25-S6 | Spiral 6 — Quantitative Research & STEM Leadership | 150 | 5 |
| SWY-25-CRP | Capstone Research Project (Months 7–12) | 900 | 30 |
S1 Spiral 1 — Mathematical Reasoning & Proof · Month 1 · 150 h
From 'solving problems' to 'teaching mathematical reasoning'.
Unit 1.1Proof and mathematical structure20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — algebra & proof
- Content
- Axiomatic thinking, proof techniques and structure.
- Required output
- Proof portfolio with commentary.
Unit 1.2Cognition in mathematics learning20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — didactics
- Content
- Tall & Vinner, Sfard and APOS theory.
- Required output
- Learner-thinking case study.
Unit 1.3Mathematics curriculum standards20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — curriculum
- Content
- Cambridge, IB, NCTM and national curricula compared.
- Required output
- Curriculum comparison report.
S2 Spiral 2 — Didactics of Algebra, Calculus & Discrete Mathematics · Month 2 · 150 h
From 'teaching procedures' to 'teaching concepts'.
Unit 2.1Didactics of algebra20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — algebra
- Content
- Early algebra, generalisation and symbolism.
- Required output
- Algebra unit with misconception tasks.
Unit 2.2Didactics of calculus20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — calculus
- Content
- Rate of change, limits and accumulation concepts.
- Required output
- Calculus concept lesson sequence.
Unit 2.3Discrete mathematics in schools20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — discrete maths
- Content
- Graphs, algorithms and computational thinking.
- Required output
- Discrete mathematics enrichment unit.
S3 Spiral 3 — Technology in Mathematics Teaching · Month 3 · 150 h
From 'using software' to 'designing technology-rich tasks'.
Unit 3.1Dynamic geometry & graphing20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — GeoGebra
- Content
- Task design with GeoGebra.
- Required output
- Three GeoGebra tasks with evaluation.
Unit 3.2Programming and simulation20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — Python
- Content
- Python and symbolic computation for mathematics.
- Required output
- Simulation-based lesson.
Unit 3.3AI and mathematics learning20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — digital tools
- Content
- Responsible AI use and reasoning integrity.
- Required output
- Classroom AI-use policy.
S4 Spiral 4 — Assessment & Mathematics Anxiety · Month 4 · 150 h
From 'testing' to 'diagnosing and remediating'.
Unit 4.1Diagnostic assessment20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — assessment
- Content
- Diagnostic tests and error analysis.
- Required output
- Diagnostic test with analysis.
Unit 4.2Mathematics anxiety research20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — learner confidence
- Content
- Measuring and reducing anxiety.
- Required output
- Anxiety-reduction intervention plan.
Unit 4.3Equity in mathematics20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — differentiation
- Content
- Gender, language and access in mathematics.
- Required output
- Equity audit of a mathematics department.
S5 Spiral 5 — STEM Curriculum & Mathematical Modelling · Month 5 · 150 h
From 'textbook problems' to 'real-world modelling'.
Unit 5.1Mathematical modelling20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — functions & statistics
- Content
- Modelling cycle and real data.
- Required output
- Modelling project with learners.
Unit 5.2Integrated STEM design20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — STEM
- Content
- Linking mathematics with science and technology.
- Required output
- STEM integrated unit.
Unit 5.3Syllabus evaluation20 h class + 30 h study = 50 h
- Builds on
- BSc foundation — curriculum
- Content
- Evaluating national mathematics syllabi.
- Required output
- Syllabus evaluation report.
S6 Spiral 6 — Quantitative Research & STEM Leadership · Month 6 · 150 h
From 'teacher' to 'research-led STEM leader'.
Unit 6.1Quantitative education research20 h class + 30 h study = 50 h
- Builds on
- Research methods
- Content
- Experimental designs and effect sizes.
- Required output
- Draft research design.
Unit 6.2STEM department leadership20 h class + 30 h study = 50 h
- Builds on
- Leadership
- Content
- Leading mathematics departments and teacher development.
- Required output
- Professional development plan.
Unit 6.3Research proposal defence20 h class + 30 h study = 50 h
- Builds on
- Research methods
- Content
- Proposal writing and peer review.
- Required output
- Defended research proposal.
R1 Research methods & proposal scoping · Month 7 · 150 h
Open the Capstone Research Project: method, question and ethics approval.
Unit 7.1Quantitative research in Mathematics education10 h class + 40 h study = 50 h
- Builds on
- Research methods
- Content
- Statistical analysis of learner-performance data with R or SPSS.
- Required output
- Quantitative pilot study on a chosen teaching intervention.
Unit 7.2Qualitative research in Mathematics education10 h class + 40 h study = 50 h
- Builds on
- Research methods
- Content
- Case studies, classroom observation and interview techniques.
- Required output
- Qualitative case study with coded interview transcripts.
Unit 7.3Proposal & ethics review10 h class + 40 h study = 50 h
- Builds on
- Research methods
- Content
- Full research proposal submitted to the internal ethics board.
- Required output
- Approved proposal with signed supervision and ethics record.
R2 Literature review & curriculum-design artefact · Month 8 · 150 h
Theoretical scaffolding and a publishable design artefact.
Unit 8.1Publication-ready literature review15 h class + 60 h study = 75 h
- Builds on
- Research methods
- Content
- Thesis structure, literature synthesis and citation management.
- Required output
- Publication-ready literature-review chapter.
Unit 8.2Modernised Mathematics curriculum artefact15 h class + 60 h study = 75 h
- Builds on
- Capstone design
- Content
- Integrates spiral didactics, modelling and technology into a national mathematics syllabus.
- Required output
- Full scheme of work, lesson plans and assessment rubrics.
R3 Fieldwork & data collection · Months 9–10 · 300 h
Run the study; collect, code and clean the evidence.
Unit 9.1Fieldwork execution30 h class + 120 h study = 150 h
- Builds on
- Capstone Research Project
- Content
- Interventions, surveys, interviews or observations in partner schools with informed consent.
- Required output
- Cleaned, anonymised dataset with audit trail.
Unit 9.2Mid-project review30 h class + 120 h study = 150 h
- Builds on
- Capstone Research Project
- Content
- Formal mid-point review with supervisor and one external assessor.
- Required output
- Signed mid-project review record.
R4 Analysis & writing · Month 11 · 150 h
Turn the dataset into defensible chapters.
Unit 11.1Analysis (quantitative or mixed)15 h class + 60 h study = 75 h
- Builds on
- Capstone Research Project
- Content
- Statistical or thematic analysis with stated limitations.
- Required output
- Analysis chapter with replicable methods appendix.
Unit 11.2Discussion, policy and pedagogy contribution15 h class + 60 h study = 75 h
- Builds on
- Capstone Research Project
- Content
- Actionable recommendations for schools and curriculum bodies.
- Required output
- Discussion chapter and one-page practice brief.
R5 Defence & professional portfolio · Month 12 · 150 h
Public defence and registry-anchored portfolio.
Unit 12.1Public oral defence15 h class + 60 h study = 75 h
- Builds on
- Defence
- Content
- Defence before supervisor, one academic external and one practice external.
- Required output
- Pass with distinction / pass / revise, recorded in the registry.
Unit 12.2Professional digital portfolio15 h class + 60 h study = 75 h
- Builds on
- Portfolio
- Content
- Curriculum designs, research papers and teaching evidence in one public portfolio.
- Required output
- Public, citeable portfolio anchored to the SWY registry.
Assessment weighting (every course)
- • Written examination — 30% of the course mark
- • Laboratory / practical portfolio — 40% of the course mark
- • Project defence — 20% of the course mark
- • Professional conduct & participation — 10% of the course mark