Introduction and rationale
Mathematics is a wide-ranging subject with many aspects. Most people are familiar with the fact that mathematics is an intellectual discipline that deals with abstractions, logical arguments, deduction and calculation. But mathematics is also an expression of the human mind reflecting the active will, the contemplative reason and the desire for aesthetic perfection. It is also about pattern, the mathematics of which can be used to explain and control natural happenings and situations. Increasingly, mathematics is the key to opportunity. No longer simply the language of science, mathematics contributes in direct and fundamental ways to business, finance, health and defence. For students it opens doors to careers. For citizens it enables informed decisions. For nations it provides knowledge to compete in a technological community. Participating fully in the world of the future involves tapping into the power of mathematics. Mathematical knowledge and skills are held in high esteem and are seen to have a significant role to play in the development of the knowledge society and the culture of enterprise and innovation associated with it. Mathematics education should be appropriate to the abilities, needs and interests of learners and should reflect the broad nature of the subject and its potential for enhancing their development. The elementary aspects of mathematics, use of arithmetic and the display of information by means of a graph are an everyday occurrence. Advanced mathematics is also widely used, but often in an unseen and unadvertised way. The mathematics of error correcting codes is applied to CD players and to computers. The stunning pictures of far away planets and nebulae sent by Voyager II and Hubble could not have had their crispness and quality without such mathematics. In fact, Voyager’s journey to the planets could not have been planned without the mathematics of differential equations. In
ecology, mathematics is used when studying the laws of population change. Statistics not only provides the theory and methodology for the analysis of wide varieties of data but is essential in medicine, for analysing data on the causes of illness and on the utility of new drugs. Travel by aeroplane would not be possible without the mathematics of airflow and of control systems. Body scanners are the expression of subtle mathematics discovered in the 19th century, which makes it possible to construct an image of the inside of an object from information on a number of single X-ray views of it. Thus, mathematics is often involved in matters of life and death.
Leaving Certificate Mathematics aims to develop mathematical knowledge, skills and understanding needed for continuing education, life and work. By teaching mathematics in contexts that allow learners to see connections within mathematics, between mathematics and other subjects, and between mathematics and its applications to real life, it is envisaged that learners will develop a flexible, disciplined way of thinking and the enthusiasm to search for creative solutions.
The objectives of Leaving Certificate Mathematics are that learners develop mathematical proficiency, characterised as
•• conceptual understanding—comprehension of mathematical concepts, operations, and relations
•• procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
•• strategic competence—ability to formulate, represent, and solve mathematical problems in both familiar and unfamiliar contexts
•• adaptive reasoning—capacity for logical thought, reflection, explanation, justification and communication
•• productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence, perseverance and one’s own efficacy.
At Ordinary level and Higher level there are two assessment components
• Mathematics Paper 1
• Mathematics Paper 2
Each paper will contain two sections – A and B.
• Section A will address core mathematics topics, with a focus on concepts and skills.
• Section B will include questions that are context based applications of mathematics.
At Foundation level there is one assessment component, a written paper. Learners will be assessed by means of problems set in meaningful contexts.