An investigation into the teaching and learning of applications of mathematics in senior-cycle schools in Ireland

Current practises in Irish mathematics classrooms generally fail to make the necessary connections between mathematics and its place in real-life, as documents from the NCCA and the Chief Examiners Report have shown (NCCA, 2005; State Examinations Commission, 2005). This study focuses on the problem of improving the teaching and learning of mathematics, particularly upper secondary level in Ireland, by making a provision for the e ective teaching of applications. The author anticipated the national focus on the use of applications in mathematics education with the inception of ‘Project Maths’. APOS theory was adapted for use in this study and the resultant approach has been field tested in a small scale intervention in Irish Senior-Cycle schools. APOS Theory is a purpose built theory for mathematics teaching which was developed by Dubinsky (1996) and his colleagues in the Research for Undergraduate Mathematics Education Community (RUMEC) for the purpose of mathematics education at third level. The author harnessed the three-stage approach employed by APOS Theory (Exploratory, Implementation and Reflective Phase) to develop, pilot, implement and evaluate the subsequent teaching intervention. Bajpai’s Integrated Approach (1975) and the Harvard Calculus Approach (1991) influence the research design in that they offer a perspective on introducing mathematical concepts through multiple approaches (numerical, analytical, graphical, verbal) as opposed to the over-emphasis on analytical techniques widely practised in schools. Their emphasis on applications, modelling and case studies allows the author to achieve the overall aims of the research project. Results of the intervention showed that students find mathematics more interesting when taught through applications. In addition, the intervention highlighted the issue of assessment in the teaching of applications and modelling, where the participating students and teachers called for a review of assessment procedures in senior-cycle mathematics here in Ireland