Mathematical thinking: challenging prospective teachers to do more than ‘talk the talk’

Abstract

This paper reports on a research project which aims to improve prospective mathematics teachers' relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of the mathematics they are required to teach at second level. This paper describes a course designed by the authors to challenge such beliefs and encourage students to confront and possibly transform their ideas about teaching, while simultaneously improving their subject knowledge and relational understanding. Both content and pedagogical considerations for teaching second-level mathematics are integrated at all times. The course was originally optional and was piloted and implemented in a third-level Irish university. Apart from offering an insight into the design considerations when creating a course of this type, this paper also addresses some of the challenges faced when evaluating such a course. Overall participant feedback on the course is positive and both qualitative and quantitative results are provided to support this and also highlight the efficacy of the programme.

‘Ours is not to reason why, just invert and multiply’: an insight into Irish prospective secondary teachers' conceptual understanding of the division of fractions

“…Questions such as 'Why do we invert and multiply?,' 'What is pi?,' 'Why does the product of two negative numbers result in a positive number?,' etc., are explored in a constructivist manner. An evaluation (Prendergast et al 2014) of classes designed in this manner demonstrated an increase in the conceptual understanding of participants over a semester on core mathematical concepts.…”

European Study investigating Adult Numeracy Education

“…While Martinez and Martinez (1996) determine it to be a construct with multiple causes, many link its origins to negative classroom experiences from the past (Tobias, 1993;Klinger, 2011). Such experiences may include the use of traditional teaching methodologies, where mathematics involves the memorisation of formulae, and the following of rules and procedures (Prendergast et al, 2014). While many adults recognise the cultural and societal benefits of being numerate, they still report it to be a difficult and demanding skill that they often fear and dread (Swain et al 2005).…”

Curriculum reform in Irish secondary schools – a focus on algebra

“…This lack of confidence in using the functions based approach highlights the importance of professional development for teachers in any reform, but particularly in Ireland where, in a 2009 study, nearly half of all secondary mathematics teachers at that time were deemed not to be sufficiently qualified to teach the subject (Ni Riordain & Hannigan, 2011). The teaching approaches advocated by 'Project Maths' require a much firmer knowledge of mathematics as teachers are required to step away from the textbook and to make subtle connections between different elements of mathematics (Prendergast et al, 2014b). Mathematics teachers, qualified or unqualified, are unlikely to do this when they have only been schooled in narrow instrumental approaches to algebra and symbol manipulation techniques (Blanton & Kaput, 2008).…”