Recent changes to the Teaching Council requirements means that every teacher on entry to the profession of teaching must study at least 5 credits of Geometry, either Euclidean or non-Euclidean. At present, no such module is available in the University of Limerick and so it is critical that we provide this option for students so that they can complete their entire undergraduate, pre - service mathematics programme in - house. Geometry is a core part of mathematics education and provides the basis for an introduction to rigorous mathematical reasoning. The study of geometry allows for student improvement in the area of logic, deductive reasoning and problem solving - all of which are skills that will benefit students in a range of other mathematical strands. Geometry is unlike pure mathematics modules in the sense that it has a wide range of practical applications. It is used, for example, in art, engineering, sport, construction, architecture, to name but a few. The literal translation of the word Geometry ("Earth Measure") serves to further highlight its applicability and this module will seek to highlight the relevance of the subject to all students undertaking it. As such, this module will share with students key mathematical concepts that underpin a lot of objects they see and use on a daily basis. Finally, Geometry and Trigonometry now makes up one - fifth of the junior and senior cycle mathematics curricula which the majority of students who study this module will end up teaching. As such, it is critical that they are equipped with the skills needed to teach this topic for understanding. IN order to do this they themselves need a solid grounding in the subject and need to understand the rationale behind the theorems and constructions that they will encounter in the mathematics classroom. This module seeks to provide them with this knowledge.

The syllabus will be broke up into 8 sections/chapter. These 8 sections are: Pythagoras Congruences and Similarity Circles and Angles Trigonometry Co-ordinates Vectors and Symmetry Spherical Trigonometry Non Euclidean Geometry

At the end of this module students will be able to: - Understand, express and use geometric results in a meaningful and logical manner. - Prove a range of key geometric theorems. - Demonstrate an ability to deduce corollaries and key geometric facts in a hierarchical fashion. - Determine certain geometric quantities using theorems and techniques of Euclidean geometry. - Explain the rationale for the procedures undertaken during a construction.

At the end of this module students will be able to: - Appreciate the applicability of many of the constructions that they carry out. - Work in groups to derive proofs and the rationale behind constructions, hence developing their communication skills. - Value the need for proof and logical reasoning in mathematics. - Appreciate the need for pre service teachers to develop a solid foundation in theorems, axioms, and constructions.

At the end of this module students will be able to: - Competently use a range of geometry equipment in the relevant situations. - Carry out a range of geometric constructions. - Use co-ordinates to solve geometric problems analytically.

The module will be taught over 36 lectures and 11 tutorials. The module will be taught in a hierarchical fashion and the syllabus is laid out with this in mind. A constructivist approach will be adopted during the lectures and teaching for understanding will be the key goal. Guided discovery will be used wherever possible in order to build on students' prior knowledge and to support them in discovering key theorems and the rationale behind key constructions for themselves. This is all in line with the research previously carried out into effective mathematics teaching (References). Teaching mathematics through the use of applications has also been put forward as the optimum approach for mathematics teaching (References). Geometry is very conducive to such an approach and this will also be a focus of the module. The relevance and applicability of a range of theorems and constructions will be integral to the course.