Shifts of mathematical thinking in adolescence

Abstract

This theoretical paper relates key features of the mathematics adolescents are expected to learn in school to other aspects of adolescent development. Difficulties in mathematical learning at that age include changes in perspective and in the actions that are mathematically productive. Commonly-recommended methods of trying to engage adolescents in mathematics do not necessarily enable students to shift to new perceptions and new ways of constructing mathematical understandings, yet the shifts students need to make are in accord with other aspects of adolescent development.

Keywords:

• Learning secondary mathematics
• adolescence
• secondary maths curriculum

Acknowledgements

Grateful thanks to Liz Bills and anonymous reviewers for critical and supportive comments, to participants in discussions at the conferences of AAMT (2007), BSRLM (2008), and CMESG (2008) who engaged with these ideas.

Notes

1. This view of adolescence may be dependent on culture, but I adopt it here because it is relevant to the UK culture in which I work, and also to other Western European and North American dominant cultures.

2. 2007 TIMSS results show a 25 percentage point drop in enjoyment of the subject in the UK

3. What is meant by ‘enquiry’ is encapsulated in the italicised aspects below on which teachers were questioned for evaluative purposes.

4. Success in year 3 was positively correlated with use of ‘real contexts’ however. This could be because elementary mathematical ideas are often learnt as successful formalisations of informal ideas, whereas secondary school mathematical ideas are more often formal mathematical ideas which do not easily relate to experience and intuition (Nunes, Bryant and Watson, 2009).