Mathematics as Logical Thinking and a Teaching Resource
The IPA's Master's in Mathematics Teaching trains expert educators in mathematics didactics and the development of critical thinking, able to transform mathematics teaching in contexts where logical reasoning and problem solving are fundamental. The programme rests on four inseparable pillars that structure every semester and every academic project.
The first pillar concerns in-depth mastery of mathematics in its theoretical and applied dimensions. Students develop excellent mathematical expertise in algebra, geometry, analysis and applied mathematics, while gaining a critical understanding of mathematical structures, methods of proof and contemporary applications.
The second pillar concerns the didactics of mathematics as the science of reasoning and problem solving. Students master modern teaching approaches based on concept building, problem solving and mathematical modelling, critically assess their relative effectiveness, and develop the ability to design innovative learning sequences rooted in the Burundian and African context.
The third pillar concerns the in-depth study of mathematical thinking and its real-life applications. The IPA emphasises mathematics as a lever for understanding phenomena: how the study of mathematical structures develops critical thinking, logical reasoning and the ability to model complex real-world problems.
The fourth pillar emphasises continuing professional development and the ability to innovate in teaching practice. Graduates are not trained to reproduce existing practices, but to question them, adapt them and create innovative solutions to the real educational problems of Burundian and African schools.
Three Principles of Mathematics Teaching
This programme rests on three principles that shape every course, project and academic interaction.
Principle 1: From conceptualisation to mathematical proof
Recognising that mathematics is taught as a gradual construction of concepts, in which intuition and exploration come before formalism and proof. Students learn to teach mathematics by creating environments in which learners explore concepts, make conjectures, test their hypotheses and develop deep mathematical sense. This approach roots mathematics teaching in logical reasoning and guided discovery.
Principle 2: Supporting change in teaching practice
Training not only qualified teachers, but also professionals able to develop mathematical and educational practice in their institutions. Our graduates develop the skills to motivate colleagues, implement educational change, and contribute to debates on the quality of mathematics teaching and the development of critical reasoning at institutional and national level.
Principle 3: Contextual roots and African relevance
Effective mathematics teaching in Africa must respect the economic, technological and professional realities of the continent. Students develop a teaching practice that addresses real mathematical applications in Burundi and Africa, uses local contexts as teaching resources, and prepares citizens to take part in debates on technological development and innovation.
Curriculum Architecture of the Master's
This Master's programme spans two academic years, i.e. four semesters. It totals 120 ECTS credits (European Credit Transfer System), corresponding to about 1,800 hours of academic work combining theoretical courses, seminars, supervised practical work, research projects and classroom placements. Each semester is worth 30 ECTS credits.
The balance between theoretical teaching, problem-solving practicals, mathematics projects, research projects and professional placements ensures well-rounded and genuinely professional training. To complete the Master's, students must pass all modules, submit an original research thesis on a question of mathematics didactics or mathematical thinking, and defend this work publicly before an academic panel.
Fundamentals and Practice
Students take core courses in advanced algebra, geometry, mathematical analysis and applied mathematics. They study mathematics didactics, the cognitive psychology of mathematical learning, and research methodologies in mathematics and education. Supervised practical work allows systematic classroom observation and the delivery of lessons under the close supervision of a trainer. Students also complete optional modules: discrete mathematics, mathematical modelling, digital technologies and mathematics teaching.
Research and Educational Innovation
The focus shifts to applied research and independent teaching design. Students carry out a substantial research project (thesis) on a concrete question related to mathematics teaching or the development of mathematical thinking in the Burundian or regional context. Examples: how can the understanding of abstract concepts be improved? How can a problem-solving mindset be developed? How can mathematical modelling be integrated? Specialised seminars allow for in-depth study of themes. Students continue their classroom placements, gradually taking on greater teaching responsibility.
| MASTER 1 SEMESTER 1 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| UE | ECUE | Codes | Hours | Credits | |||||
| VHP | CM | TD/TT | TP | TPE | TGE | ||||
| UE1: Support Courses | Scientific Text Editors | MSEM1101 | 45 | 15 | 15 | 15 | 30 | 75 | 3 |
| Scientific English | MSEM1102 | 45 | 30 | 15 | 0 | 30 | 75 | 3 | |
| UE2: Fundamental Mathematics I | Group Theory | MSEM1103 | 60 | 30 | 30 | 0 | 40 | 100 | 4 |
| Riemannian Geometry | MSEM1104 | 60 | 30 | 30 | 0 | 40 | 100 | 4 | |
| UE3: Mathematics and Applications I | Operations Research and Optimisation | MSEM1105 | 60 | 30 | 30 | 0 | 40 | 100 | 4 |
| Wavelet Theory and Applications | MSEM1106 | 60 | 30 | 30 | 0 | 40 | 100 | 4 | |
| UE4: Mathematics and Applications II | Survey Theory and Practice | MSEM1107 | 60 | 45 | 15 | 0 | 40 | 100 | 4 |
| Statistical Software | MSEM1108 | 60 | 30 | 15 | 15 | 40 | 100 | 4 | |
| TOTAL M1-S1 | 450 | 240 | 180 | 30 | 300 | 750 | 30 | ||
| MASTER I SEMESTER II | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| UE | ECUE | Codes | Hours | Credits | |||||
| VHP | CM | TD/TT | TP | TPE | TGE | ||||
| UE5: Fundamental Mathematics II | Natural Operators in Differential Geometry | MSEM1201 | 60 | 30 | 30 | 0 | 40 | 100 | 4 |
| Fibre Bundle Theory | MSEM1202 | 60 | 30 | 30 | 0 | 40 | 100 | 4 | |
| UE6: Fundamental Mathematics III | Multilinear Algebra | MSEM1203 | 60 | 30 | 30 | 0 | 40 | 100 | 4 |
| Advanced Functional Analysis | MSEM1204 | 60 | 30 | 30 | 0 | 40 | 100 | 4 | |
| UE7: Fundamental Mathematics | Calculus of Variations | MSEM1205 | 45 | 30 | 15 | 0 | 30 | 75 | 3 |
| Martingale Space Theory | MSEM1206 | 45 | 30 | 15 | 0 | 30 | 75 | 3 | |
| UE8: Pedagogy | Curriculum Design and Evaluation | MSEM1207 | 30 | 20 | 10 | 0 | 20 | 50 | 2 |
| Inspection and Pedagogical Support | MSEM1208 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| UE9: Research 1 | Experimental Pedagogy | MSEM1209 | 30 | 20 | 10 | 0 | 20 | 50 | 2 |
| Research Methods and Techniques in Didactics | MSEM1210 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| TOTAL M1-S2 | 450 | 260 | 190 | 0 | 300 | 750 | 30 | ||
| ANNUAL TOTAL | 900 | 500 | 370 | 30 | 600 | 1500 | 60 | ||
| MASTER II SEMESTER III | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| UE | ECUE | Codes | Hours | Credits | |||||
| VHP | CM | TD | TP | TPE | TGE | ||||
| UE1: Mathematics and Applications III | Programming through Practice | MSEM2301 | 45 | 30 | 15 | 0 | 30 | 75 | 3 |
| Causal Analysis Theory | MSEM2302 | 45 | 30 | 15 | 0 | 30 | 75 | 3 | |
| UE2: Mathematics and Applications IV | Symplectic Geometry | MSEM2303 | 60 | 30 | 30 | 0 | 40 | 100 | 4 |
| Graph Theory | MSEM2304 | 60 | 30 | 30 | 0 | 40 | 100 | 4 | |
| UE3: Special Didactics | Pedagogy of Integration in Mathematics Teaching | MSEM2305 | 30 | 20 | 10 | 0 | 20 | 50 | 2 |
| Teaching Large Groups in Mathematics | MSEM2306 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| Mathematical Epistemology | MSEM2307 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| UE4: Differential Pedagogy | Elements of Differential Pedagogy | MSEM2308 | 30 | 20 | 10 | 0 | 20 | 50 | 2 |
| School Inclusion | MSEM2309 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| UE5: Seminars | Mathematics Seminars | MSEM2310 | 60 | 30 | 30 | 0 | 40 | 100 | 4 |
| Techniques for Writing Mathematics Papers | MSEM2311 | 30 | 20 | 10 | 0 | 20 | 50 | 2 | |
| TOTAL M2-S3 | 450 | 270 | 180 | 0 | 300 | 750 | 30 | ||
Professional Impact and Careers in Mathematics
Graduates of the IPA's Master's in Mathematics Teaching go on to diverse careers in the public and private sectors. Many become senior teachers in secondary and higher education institutions, directly applying the innovative approaches they have learned and helping to raise the overall quality of mathematics teaching. Others move into initial or in-service teacher training, working as trainers in teacher training colleges or professional development programmes.
Some graduates take up posts as education officers, curriculum managers or advisers to education ministries and technology institutions. A few graduates go on to doctoral studies to contribute to fundamental and applied research in mathematics and mathematics didactics. The professional impact extends beyond individual careers: our graduates transform educational practice, create more effective and conceptually rigorous learning environments, and contribute to improving mathematical literacy and critical thinking in Africa.
Admission Criteria and Procedure
The Master's in Mathematics Teaching is aimed at experienced mathematics teachers and science professionals who wish to deepen their subject and teaching expertise.
Admission to the IPA's Master's in Mathematics Teaching is based on the three official conditions set by the University of Burundi:
- Hold a first-cycle degree. Applicants must hold one of the following qualifications: a Licence or Bachelor's degree awarded by the University of Burundi, or a university degree recognised as equivalent by the National Commission for the Equivalence of Diplomas.
- Hold a degree compatible with the chosen specialisation. The degree submitted must correspond to the field of the Master's in Mathematics Teaching applied for, demonstrating adequate prior training in mathematics teaching or related fields (sciences, engineering).
- Pass the entrance examination or admission selection. The University of Burundi generally organises a Master's entrance examination according to an academic calendar published each year. The admissions committee assesses applicants on the basis of their academic record, their examination results and their fit with the objectives of the Master's programme.