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Official programme of record · SWY-22

Professional Certificate in Mathematics Education & Spiral Didactics

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
600 h
Scheduled class / seminar
200 h
Guided study, lab & research
400 h
Credits
30 ECTS

Each module is 60 hours: 5 lessons × 4 h class = 20 h class + 40 h guided study, laboratory or fieldwork. Programme version 2026.10 · fingerprint 3E2E3F2E172F6033

Graded courses on the transcript · 10
CodeCourseHoursECTS
SWY-22-M01Number & Algebraic Foundations603
SWY-22-M02Functions & Graphs603
SWY-22-M03Geometry & Measurement603
SWY-22-M04Calculus603
SWY-22-M05Statistics & Probability603
SWY-22-M06Discrete Mathematics603
SWY-22-M07Spiral Didactics of Mathematics603
SWY-22-M08Technology in Mathematics Teaching603
SWY-22-M09Assessment & Mathematics Anxiety603
SWY-22-M10Capstone — Teaching Practicum & Scheme of Work603
M01 Number & Algebraic Foundations · Module 1 · 60 h

Number systems, algebraic structure and proof.

Unit 1.1Number & Algebraic Foundations20 h class + 40 h study = 60 h · 5 lessons
  1. 1.1.1Number systems — Integers, rationals, reals and number sense.4h
  2. 1.1.2Algebraic expressions — Manipulation, factorisation and identities.4h
  3. 1.1.3Equations and inequalities — Linear, quadratic and simultaneous.4h
  4. 1.1.4Sequences and series — Arithmetic, geometric and induction.4h
  5. 1.1.5Reasoning and proof — Direct proof, contradiction and counter-examples.4h
M02 Functions & Graphs · Module 2 · 60 h

Functions, transformations and modelling.

Unit 2.1Functions & Graphs20 h class + 40 h study = 60 h · 5 lessons
  1. 2.1.1Function concepts — Domain, range, composition and inverse.4h
  2. 2.1.2Linear and quadratic functions — Graphs and applications.4h
  3. 2.1.3Exponential and logarithmic functions — Growth and decay.4h
  4. 2.1.4Trigonometric functions — Graphs, identities and equations.4h
  5. 2.1.5Transformations — Translating, stretching and reflecting graphs.4h
M03 Geometry & Measurement · Module 3 · 60 h

Euclidean geometry, coordinate geometry and mensuration.

Unit 3.1Geometry & Measurement20 h class + 40 h study = 60 h · 5 lessons
  1. 3.1.1Euclidean geometry — Angles, triangles, congruence and similarity.4h
  2. 3.1.2Circle theorems — Proofs and applications.4h
  3. 3.1.3Coordinate geometry — Lines, circles and distance.4h
  4. 3.1.4Mensuration — Area, surface area and volume.4h
  5. 3.1.5Vectors and transformations — Vector geometry and matrices.4h
M04 Calculus · Module 4 · 60 h

Limits, differentiation and integration.

Unit 4.1Calculus20 h class + 40 h study = 60 h · 5 lessons
  1. 4.1.1Limits and continuity — Intuitive and formal ideas.4h
  2. 4.1.2Differentiation — Rules, rates of change and tangents.4h
  3. 4.1.3Applications of differentiation — Optimisation and curve sketching.4h
  4. 4.1.4Integration — Antiderivatives, definite integrals and area.4h
  5. 4.1.5Differential equations — First-order models.4h
M05 Statistics & Probability · Module 5 · 60 h

Data handling, probability and inference.

Unit 5.1Statistics & Probability20 h class + 40 h study = 60 h · 5 lessons
  1. 5.1.1Data collection and display — Sampling and charts.4h
  2. 5.1.2Descriptive statistics — Averages, spread and box plots.4h
  3. 5.1.3Probability — Rules, tree diagrams and conditional probability.4h
  4. 5.1.4Distributions — Binomial and normal distributions.4h
  5. 5.1.5Inference — Confidence and simple hypothesis tests.4h
M06 Discrete Mathematics · Module 6 · 60 h

Logic, sets, combinatorics and graph theory.

Unit 6.1Discrete Mathematics20 h class + 40 h study = 60 h · 5 lessons
  1. 6.1.1Logic and sets — Propositions, truth tables and Venn diagrams.4h
  2. 6.1.2Combinatorics — Permutations and combinations.4h
  3. 6.1.3Graph theory — Networks, paths and trees.4h
  4. 6.1.4Algorithms — Sorting, searching and flowcharts.4h
  5. 6.1.5Number theory — Divisibility, primes and modular arithmetic.4h
M07 Spiral Didactics of Mathematics · Module 7 · 60 h

Concrete-pictorial-abstract, spiral sequencing and misconceptions.

Unit 7.1Spiral Didactics of Mathematics20 h class + 40 h study = 60 h · 5 lessons
  1. 7.1.1Spiral curriculum — Bruner and revisiting concepts at greater depth.4h
  2. 7.1.2Concrete-pictorial-abstract — Manipulatives and representations.4h
  3. 7.1.3Common misconceptions — Diagnosis and remediation.4h
  4. 7.1.4Problem solving — Pólya's method and rich tasks.4h
  5. 7.1.5Mathematical discourse — Questioning and classroom talk.4h
M08 Technology in Mathematics Teaching · Module 8 · 60 h

GeoGebra, spreadsheets and Python for the classroom.

Unit 8.1Technology in Mathematics Teaching20 h class + 40 h study = 60 h · 5 lessons
  1. 8.1.1GeoGebra — Dynamic geometry and graphing.4h
  2. 8.1.2Spreadsheets — Data, sequences and modelling.4h
  3. 8.1.3Python for mathematics — Simple programs and simulations.4h
  4. 8.1.4Online resources — Open textbooks and practice platforms.4h
  5. 8.1.5Responsible AI — Using AI tools without replacing reasoning.4h
M09 Assessment & Mathematics Anxiety · Module 9 · 60 h

Formative assessment, exam preparation and learner confidence.

Unit 9.1Assessment & Mathematics Anxiety20 h class + 40 h study = 60 h · 5 lessons
  1. 9.1.1Formative assessment — Hinge questions and exit tickets.4h
  2. 9.1.2Summative assessment — Test design and marking schemes.4h
  3. 9.1.3Exam preparation — Past papers and exam technique.4h
  4. 9.1.4Mathematics anxiety — Causes and confidence-building.4h
  5. 9.1.5Differentiation — Supporting low and high attainers.4h
M10 Capstone — Teaching Practicum & Scheme of Work · Module 10 · 60 h

Observed teaching and a complete scheme of work.

Unit 10.1Capstone — Teaching Practicum & Scheme of Work20 h class + 40 h study = 60 h · 5 lessons
  1. 10.1.1Scheme of work — Term plan mapped to the national syllabus.4h
  2. 10.1.2Lesson planning — Five detailed lesson plans.4h
  3. 10.1.3Observed teaching — Supervised practicum lessons.4h
  4. 10.1.4Learner evidence — Analysing learner work.4h
  5. 10.1.5Defence — Portfolio presentation before a review panel.4h
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