In light of this statement, discuss and evaluate a range of approaches impacting on the teaching and learning of mathematical skills with reference to: * At least two current appropriate theories of mathematical skills acquisition, knowledge and learning * Current research and specialist publications
* At least two learners with whom you work
‘Numbers saturate the news, politics, life. For good or ill, they are today’s pre-eminent public language – and those who speak it rule. Blastland & Dilnot, 2008
For the purposes of this essay:
Learner A: a 22 year old female ESOL learner with ESOL reading and writing skills to Level 2, working towards her Level 2 OCR numeracy exam. She aspires to start her Access to Nursing course in September 2012. Learner B: a 40 year old female, Plymouth-born learner with low self-esteem and maths anxiety. She has been bringing up her children and now wants to gain a numeracy qualification so she can have more options when she returns to work. She is progressing towards an Entry 3 qualification.
1.2 The origins and status of mathematical knowledge on mathematics curriculum development: Gardener (1989) postulated that all humans possess differing degrees of innate mathematical ability which he termed, ‘logical mathematical intelligence.’ It gives individuals the capacity to investigate problems scientifically, analyse results logically, detect patterns and reason deductively. In ancient civilizations mathematical intelligence was used to develop systems which regulated commerce. Maths skills were taught in ‘schools’ and the academic discipline of mathematics was born, Ernest (1986). Ancient civilisations distinguished between maths for scholars (Relational Understanding) and maths for vocational trades (Instrumental Understanding) Hilton 1980. This division is reflected in our culture today: - * Numeracy for functional use, ‘equips students for life beyond school in providing access to further study or training, to personal pursuits, and to participation in the world of work and in the wider community’ Booker (1997). * Matheracy in academic study, involves more than counting and measuring for everyday life. Ubiratan d’Ambrosio, (2006), describes it as being concerned with a deeper reflection. It draws conclusions from data to propose hypotheses. How the designers of maths curriculums combine the two disciplines of mathematics defines the society in which we live. The content of the maths curriculum in the UK over the past twenty years has been highly contended by five distinct groups with differing values, interests and ideologies categorised by Ernest in Appendix 1. Consequently, the curriculum targets adopted are a hodgepodge of principles encompassing basic skills, problem solving for practical problems at work and some pure maths. Targets aimed at using and applying mathematics processes are included to a lesser degree. The aims of the democratic socialist and radical reformers concerned with social justice who proposed the empowerment of learners as mathematically literate citizens in society were largely ignored. Furthermore, the past twenty years has seen a widening social inequality as educational policies have not only failed in their objective to make learners more functionally numerate but also reduced the critical thinking skills encouraged in matheracy. In a Radio 4 broadcast, ‘Things ain’t what they used to be’, (May 2012), Aaronovitch examines the paradox that the more society becomes reliant on the functionality of maths, the more rapid the decline of individual’s ability to think logically. Individuals are exploited by statistics and number-based systems which are understood by few but which invade and control every aspect of everyday life in Postmodern Western materialistic societies. In my evaluation of teaching approaches in the skills for Life Sector I am considering the following: * What mathematical skills need to be...