b.a. in mathematics & Education - year 1

History and Structure of Irish Education (5 ECTS): This module examines the history, culture and structure of Education and Mathematics Education in Ireland, with a focus on major policies and movements set in the context of international trends and theories of teaching and learning. It will integrate a series of lectures with individual and collaborative tasks designed to promote independent student learning.

Principles of Second-Level Mathematics (5 ECTS): This module examines concepts from Higher Level Junior Certificate and Leaving Certificate Mathematics with particular emphasis on depth of understanding and connections across topics. As part of the requirements for this course, students will attend tutorials offered by second-year students on topics in first-year undergraduate mathematics. These lectures will serve to help students draw connections between their current mathematical studies and principles underlying second-level mathematics, in an effort to support their transition to more advanced mathematical studies.

Practical Teaching Programme: Primary School Observations (5 ECTS): Students will conduct 10 hours of observation in primary schools. Assessment: Observation report and critical reflection in which students address how their experiences will inform their tutorial work with both primary and second-level students during the subsequent semester.

Semester 2:

Introduction to Educational Sciences (10 ECTS): This course will combine a series of lectures with a Problem Based Learning approach to examining issues in Psychology, Sociology, and the Learning Sciences. Students engage with general principles of Psychology and Sociology and apply them to the context of working with adolescents and the unique dynamics of a school environment. Special attention is given to contemporary issues in adolescence, cultural diversity and special educational needs. In addition, students will engage with a range of technological mediums through which they can create visual representations and valuable learning experiences for pupils.

Practical Teaching Programme: Service Learning (5 ECTS): After-school programme with St. Vincent de Paul in which students tutor primary and second-level students for mathematics remediation and/or enrichment. Weekly reflections and responses to classmates’ reflections posted on a blog are required.

Full-Year Modules:

Skills of Mathematics: Algebra and Analysis (15 ECTS)

Algebra: Introduction to linear algebra and matrix algebra, eigenvalues and eigenvectors, diagonalization, coordinate and vector geometry in two and three dimensions. Mathematics of the integers including: the Well-Ordering axiom, the principle of mathematical induction, modular arithmetic and the Chinese Remainder Theorem, Euler’s totient function. Introduction to Group Theory and Lagrange’s Theorem.

Analysis: Limits of functions, differential and integral calculus, continuity and differentiability, trigonometric, exponential and logarithmic functions, countable and uncountable sets, convergence of sequences and series.

Skills of Applied Mathematics: Introduction to Applied Mathematics (15 ECTS): Topics include Newton’s laws of motion, mechanics, simple harmonic motion, motion of rigid bodies, conservation laws, gravitational orbits.

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