The influence of previous understanding and relative confidence on adult maths learning : building adult understanding on a brownfield site

Dodd, Mary Delene (2012). The influence of previous understanding and relative confidence on adult maths learning : building adult understanding on a brownfield site. EdD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000bfd7

Abstract

Expansion of Higher Education has resulted in increasing provision of Access and Foundation programmes, often aimed at mature learners. Adults returning to learn mathematics bring with them a wealth of prior understanding and expectations The two common teaching approaches, remedial 'fill in the gaps' or mythical 'start again', are popular with students but argued to be unrealistic because the teaching of adults is better likened to building on a brownfield site. The purpose of this research was to consider what understandings adults brought with them and explore how these understandings interacted with new learning.

203 foundation students were given questions, on proportional reasoning, percentage calculation and over-generalisations. Responses, and response hierarchies, were compared with those from children in the 1970's CSMS survey (Hart, 1981 a). Individual behaviours were then explored through interview using a framework developed from ideas of Schoenfeld (1992) and Leron and Hazzan (1997).

It emerged that multiple interactions and choices of behaviour were taking place, indicating final answers, right or wrong, represented only one possibility from a selection of outcomes. Method selection might be influenced by number and beliefs in non-conservation of operation (Greer, 1994) causing potential difficulties for building new learning by method extrapolation. The habit of selt-checkinq and testing for reasonableness might cause difficulties when reasonableness could not be recognised or was counter-intuitive. Other themes identified included: the false recall of certain number calculations with potential for interference with diagnostic practices and the belief in the 'one right method' based on perceived outcome requirements or confidence from previous success, causing reluctance to consider more efficient or appropriate methods.

This research highlights the benefits of making processes and choices explicit to teachers and students facilitating the integration of previous understandings with new ways of working without disempowerment and increasing the potential for new learning to be built.