# MSc / Postgraduate Diploma in Mathematics Education

## Objectives

The M.Sc. / Postgraduate Diploma in Mathematics Education program prepares students to teach Mathematics at the middle school through secondary school level. It has a strong emphasis on Mathematics content and the role of mathematical ways of thinking in the teaching and learning of mathematics. It is designed to provide necessary skills, including the use of manipulatives and ICT in the classroom, and content knowledge for Mathematics teachers who are in service as well as recent graduates who wish to embark on a rewarding career teaching Mathematics here or abroad. It provides opportunities for in service teachers to reflect on their existing practice and engage in extended academic study to support their practice and their continuing professional development.

## Eligibility and Admission Criteria

Bachelor of Science degree (B.Sc.) from a recognized university with Pure Mathematics or Applied Mathematics as a subject or any other equivalent qualification acceptable to the senate of the University of Colombo. The candidates will be selected based on an interview and/or examination.

## Programme Structure and Duration

The MSc program consists of coursework (24C) and guided independent study (6C). The Faculty of Education of the University of Colombo will provide some of the modules. The duration of the entire program is 02 years (4 semesters). The earlier program, for 2010 and 2011 batches, has been revised to make the current program a course masters which can be completed in 2 years. One of the reasons for this revision is the new UGC Sri Lanka Qualifications Framework. After successfully finishing the course masters one can do a research of one year duration to obtain a master’s degree with research. The details of this option will be available soon.

COURSE MODULE | NAME | DETAILS |
---|---|---|

PART I FIRST SEMESTER CORE MODULES |
||

MME 5001 | Foundations of Education | 15L, 1C |

MME 5002 | Curriculum and Instruction | 15L, 1C |

MPM 5005 | Introduction to Abstract Mathematics | 30L, 2C |

MPM 5002 | Perspectives in Geometry and Vectors | 30L, 2C |

MME 5007* | Laboratory on Mathematical Software and Manipulatives | 60P, 2C |

SECOND SEMESTER CORE MODULES |
||

MPM 5001 | Perspectives in Algebra | 30L, 2C |

MME 5005 | Methodology of Teaching and Learning Mathematics | 30L, 2C |

MAM 5001 | Perspectives in Classical Mechanics | 30L, 2C |

MME 5007* | Laboratory on Mathematical Software and Manipulatives | 60P, 2C |

THIRD SEMESTER CORE MODULES |
||

MPM 5007 | Perspectives in Analysis | 45L, 3C |

MAM 5002 | Statistical Methods | 15L, 1C |

MPM 5004 | History of Mathematics | 30L, 2C |

MPM 5006 | Complex Algebra | 15L, 1C |

MPM 5003 | Problem Solving in Mathematics | 15L, 1C |

MME 5003 | Mathematics Education Seminar | 1C |

ONE OF THE FOLLOWING OPTIONAL MODULES | ||

MAM 5003 | Mathematical Modelling | 30L, 2C |

MAM 5004 | Mathematical Methods | 30L, 2C |

MAM 5005 | Combinatorics and Probability | 30L, 2C |

MME 5006 | Use of Information Technology and Manipulatives in Mathematics Education | 15L 30P, 2C |

PART II FORTH SEMESTER CORE MODULES |
||

MME 5009 | Contemporary Theories and Methodologies in Mathematics Education | 2C |

MME 5010 | Literature Review | 3C |

*This is a course conducted in two semesters.

Syllabuses are given below

## Evaluation Criteria

All the theory course modules will be evaluated by written examinations and/or assignments where appropriate. Laboratory course modules will be evaluated by a continuous assessment and/or end of the semester examination. Guided independent study course modules (MME 5003, MME 5009, and MME 5010) will be evaluated though written assignments and/or presentations.

## Degree Awarding Criteria

Students are required to offer 30 credits consisting of all the core modules and one of the optional modules with 2 credits. Those who obtain a GPA of not less than 2.5 for Part I of the program will be allowed to proceed to Part II of the program. Students who fail to obtain a GPA of 2.5 but maintain a GPA of not less than 2.00 in Part I will be eligible for the award of the Postgraduate Diploma in Mathematics Education.

The students who proceed to Part II are eligible for the award of M.Sc. in Mathematics Education if they obtain a GPA of 2.5 or above for the whole program. In addition to this, the general guidelines of the Faculty of Science are applicable to the award of the M.Sc. and the Postgraduate Diploma in Mathematics Education.

## Course Fee

Application Fee | 600 LKR |

Registration Fee | 3000 LKR |

Course Fee | 112 500 LKR |

Examination Fee | 12 500 LKR |

Library Fee | 2000 LKR |

Total (without the application fee) | 130 000 LKR |

The course fee can be paid in three interest free installments. The first installment of course fee (Rs. 62,500), the registration fee, the library fee and the examination fee must be paid upon registration. The second installment of the course fee (Rs. 40,000) may be paid at the beginning of the second semester. The third installment of the course fee (Rs. 10,000) must be paid at the beginning of the Part II.

Applicants from SAARC countries have to pay four times the normal fees except the application fee. For applicants from other countries it is eight times.

## Application Procedure

The application form can be obtained in person or by sending a self-addressed stamped envelope to the Senior Assistant Registrar, Academic and Publications Branch, University of Colombo, College House, Colombo 03. Application form can also be downloaded below. You can also download the brochure for the 2015 program below.

The duly completed application form together with the deposit slip after paying Rs. 600 to the University of Colombo, Account No. 314071500005 at any People’s Bank branch should be returned to the Senior Assistant Registrar, Faculty of Science, University of Colombo, Colombo 03, on or before 20th December 2014.

Application Form

MSc-PG Diploma in Mathematics Education 2015 Brochure

## Further Information

Further information regarding the program can be obtained from the coordinator of the program:

Chanakya J. Wijeratne

Senior Lecturer and Former Head

Department of Mathematics

PO Box 1490

University of Colombo

Colombo 03

Tel: 0770466731

Email: chanakya.wijeratne@gmail.com

## Syllabuses

**MME 5001: Foundations of Education (15L, 1C)**

Psychological aspects of learning and teaching: Intellectual development, Concept development, Learning theories, Sociological philosophical aspects of teaching and learning, Education and society, Socio-economic and cultural determinants of education, Education and human development, New trends in education.

**MME 5002: Curriculum and Instruction (15L, 1C)**

Designing curricula, Goals, Aims and objectives, Curriculum theory, Curriculum development models and curriculum patterns, Curriculum evaluation, Educational technology, Technology in education.

**MME 5003: Mathematics Education Seminar (1C)**

This module focuses on improving self-learning and presentation skills. Candidates are guided to study a specific process in the area of Mathematical Education (e.g. Problem based teaching in Mathematics, Small class teaching, Student-centered method, Teaching through home-work problems, Mathematics for day to day life) and present their work at a seminar.

**MME 5005: Methodology of Teaching and Learning Mathematics (30L, 2C)**

Instructional Design: Meaningful learning, Discovery learning, Advance organization of learning, Process-based teaching, Beyond process Mathematics teaching, Problem-based learning, Constructivists learning design, Various teaching methods, Using audio visuals, Unit and lesson planning, Class management, Practical works in relation to Mathematics, Evaluation achievement, Formative evaluation, Summative evaluation, Assessing cognitive skills, Assessing attitudes, Mathematics and co-curricular activities in school.

**MME 5006: Use of Information Technology and Manipulatives in Mathematics Education (15L & 30P, 2C)**

The history and development of the use of technology to support learning, especially by those who find learning difficult, Developing theories and policies related to the use of such technology, Central issues related to new and wider definitions of literacy in the light of recent developments in Information and Communication Technology (ICT) for Mathematics education. Teaching and education through the Internet – including email, chat and the World Wide Web.

**MME 5007: Laboratory on Mathematical Software and Manipulative (60P, 2C)**

Computer software packages (MATLAB / MAPLE /MATHEMATICA) for the Mathematics class room. Graphics that will be dealt with include various algebraic , geometric, and trigonometric relations. Problem solving and demonstrating using the software packages.

**MME 5009: Contemporary Theories and Methodologies in Mathematics Education (2C)**

The course will introduce students, through assigned readings, to the evolution of research in mathematics education, where “contemporary” is roughly taken to embrace the past 30 years. Each student is required to select and carefully read three research articles in the same area of study (for example: they might all be related to affect, or to learning functions or to teaching with technology) that use different theoretical frameworks and methodologies, and write a report that contains the following: (i) a synopsis and critique of each paper, and (ii) a comparison of the theoretical framings and methodologies of each paper.

**MME 5010: Literature Review (3C)**

Students will conduct a literature review on a topic of their choice, in mathematics or mathematics education, under the guidance of a supervisor and write a report.** **

**MPM 5001: Perspectives in Algebra (30L, 2C)**

Divisibility Theory in the Integers: The Division Algorithm, The Greatest Common Divisor, The Euclidean Algorithm, The Fundamental Theorem of Arithmetic, The Theory of Congruences.Linear Algebra: Matrices, Special Matrices, Matrix Operations, Inverse of Non-singular Matrices, Determinants, System of Linear Equations.Algebraic Structures: Groups, Rings, Vector Spaces; Definitions, Examples, Sub-structures and Mappings that preserve the Structure.

**MPM 5002: Perspectives in Geometry and Vectors (30L, 2C)**

Definition of a vector and a scalar, Equality of vectors, Geometric representation of a vector, Modulus of a vector, Unit vector, Vector algebra, Ratio theorem and related topics, Resolution of vectors, Basis vectors, Scalar, Vector and Triple products and their properties, Equation of a straight line, Equation of a plane, Applications of vectors in geometrical problems, Euclidean geometry and Axiomatic systems, Further developments of Euclidean geometry, e.g. analytical geometry, projective geometry, non-Euclidean geometry, etc. Basic ideas and structures of modern geometries, e.g. topology, algebraic geometry, etc.

**MPM 5003: Problem Solving in Mathematics (15L, 1C)**

Various kinds of methods to tackle mathematical problems. Problem relevant teaching methods in Mathematics, Problem based teaching methods in Mathematics.

**MPM 5005: Introduction to Abstract Mathematics (30L, 2C)**

Sets, Set operations, Relations, Functions, System of Real numbers. Mathematical InductionLogic : Truth Tables, Tautologies and Contradictions, Proof by Contradiction, Logical Equivalence, Proof using the Contrapositive, Arguments, Predicates and Quantifiers.

**MPM 5006: Complex Algebra (15L, 1C)**

The complex number system – Fundamental operations and properties, Graphical representation, Polar form, De Moivre’s Theorem and Solving complex equations.

**MPM 5007: Perspectives in Analysis (45L, 3C)**

Inequalities and absolute value, Sequences, Limit of a sequence, Real functions, Composition, One-to-one functions and Inverses, Limits, Continuity, Trigonometric limits, Intermediate value theorem, Absolute extrema for continuous functions (without proofs). Idea of rate of change, Derivatives, Chain rule, Product and Quotient rules, Differentiating inverses, Differentiating trigonometric functions. Implicit differentiation, Mean Value theorem (without proof). Monotonic functions. Extrema, Concavity, Curve Sketching, Asymptotes, Area problem, Definite integral, Fundamental theorem of Calculus, Anti derivatives. Techniques of integration (derived from Chain rule and Product rule for differentiation) Logarithmic and exponential functions, Series, Convergence, Geometric Series, Test for convergence, Power Series, Improper integrals, Indeterminant forms of limits, L’Hospital Rule.

**MPM 5008: History of Mathematics (30L, 2C)**

Origin of numbers, Role of numbers in the society, Euclidean geometry with original proofs, Cubic and quadratic equations, Historical approach to calculus, Eighteenth century work: B. Taylor, C. Maclaurin, J. D’alembert, A.L. Cauchy, E.F. Gauss, J. Jacobi, Riemann, Lebesgue, K. Weiestrass, G. Cantor and Albert Einstein.

**MAM 5001: Perspectives in Classical Mechanics (30L, 2C)**

Historical Perspective of Classical Mechanics: Developments due to Galileo, Newton , Lagrange, Hamilton , Maxwell, Einstein.Newtonean Mechanics: Space and time, inertial frame, particle dynamics in one, two and three dimensions. Dynamics of a system of particles, Motion of rigid bodies, Central force problem, Motion relative to rotating frames.Lagrangean formulation: De Alembert’s principle, Holomonic constraints generalized coordinates, Euler-Lagrange equations, Applications.Hamiltonean formulation: Principle of least action, Hamilton’s principle, Hamilton’s Equations, Elements of Special Relativity: Space-time concept of Einstein, Postulates of Special Relativity, Lorentz transformations, Invariant properties of Lorentz transformations, Length and time contraction, Mass energy equivalency.

**MAM 5002: Statistical Methods (15L, 1C)**

Introductions (what is statistics, importance of statistics, misleading statistics)Sampling (Simple random sampling, Cluster sampling, stratified sampling),Data presentation (graphs, charts, tables), Interpretation of basic statistics –mean, median, variance, SD, CV, 5-number summary. Applications in Statistics (Time series, Regression, Quality Control). Practice with real problems

**MAM 5003: Mathematical Modelling (Deterministic and Stochastic) (30L, 2C)**

Linear Programming, Data envelopment analysis and goal programming, Decision theory and game theory, Real life applications of the above topics.

**MAM 5004: Mathematical Methods (30L, 2C)**

Ordinary Differential Equations with examples: Particular solution, general solution, singular solution, complete primitive; Remark on existence of solution; Mathematical preliminaries for numerical analysis: Taylor’s theorem and its various forms; Orders of convergence; Big O and small o; Sources of errors; Algorithms and convergence. Solutions to non-linear equations:

**MAM 5005: Combinatorics and Probability (30L, 2C)**

Fundamental counting principles, Multiplication and addition principles, Permutations, Combinations and the Binomial theorem. Introduction to graph theory – planar graphs and colouring problems (chromatic polynomials, polya counting).Elementary probability theory, Discrete and continuous random variables and their distributions, Bivariate distributions