Implications for mathematics teaching

Situating RWEI in the mathematics lesson implies that the lesson should make references to real world contexts. Further, when working within the broader concepts of critical mathematics and social justice, the classroom should be an environment of democratic participation where pupils can engage in discussion and make choices (Skovsmose, 1996; Bishop, 2010). That is not to say that mathematics should not have periods of ‘consolidation’ and work on exercises in a purely mathematical context. Referring to the milieus of learning matrix, Skovsmose (2001) supports the movement of mathematics education between different milieus. Nevertheless, the conditions of democratic participation and reference to real life contexts seem to be necessary for RWEI to be situated in the classroom. I agree that these are the ideal conditions for issues such as critical mathematics, social justice and RWEI to take place. Indeed, there has been criticism when issues of social justice have taken place in the mathematics classroom without these conditions in place (Nolan, 2009). However, in Section 6.1, I discussed how, in certain circumstances, these conditions might be a barrier to critical mathematics and social justice. The educational landscape is constantly changing and RWEI may have to be situated in contexts where compromises have to be made.

Many new academies and schools hold beliefs which are strongly in line with the ‘absolutist’ philosophy of mathematics education.

Head Teacher Katherine Birbalsingh explains the style of teaching at Michaela school which involves ‘imparting’ knowledge:

‘We have the teacher standing at the front and imparting knowledge. We believe the teacher knows more than the children. Most teachers in Britain do not believe that. They believe that the children and teachers all know pretty much the same stuff, which is why the children just need to be guided by the teacher as opposed to being taught by the teacher’.

(The Guardian newspaper, 2016)

If issues such as critical mathematics, social justice and RWEI are to exist within this new order, they may have to do so with an element of compromise, otherwise they may remain as unrealisable ideals in mathematics education which we rarely see practiced in the classroom. The eight case studies in this research include examples of RWEI situated in a range of ways in the mathematics classroom by teachers with differing mathematical beliefs and from a range of academic backgrounds.

This study demonstrates how secondary school mathematics teachers can situate RWEI in their classroom. It also presents reasons as to why these teachers situate RWEI in their lessons from eight different perspectives. Through the eight case studies, there is clear evidence of several different ways in which RWEI can be situated in a secondary school mathematics lesson. In the ‘Introduction’ and ‘Literature Review’, I have discussed how education relating to morals and ethics, for the most part, does not feature in the mathematics classroom. Under pressure to perform in exams, schools sideline moral, social and cultural issues, so making it difficult for teachers to situate such practice in their classroom. The eight case studies in this research have demonstrated different ways in which it is possible to situate RWEI in the secondary mathematics classroom and why some teachers decide to do this. These case studies provide mathematics teachers examples and also inspiration in the area of teaching mathematics from a critical mathematics education perspective.

In Chapter 5 (the Literature Review) I discussed how mathematics teachers may be reluctant to take risks and encourage learning processes such as RWEI. Therefore, important to this study is the fact that the participants have an interest in RWEI, but are not experts in the area. Indeed, the study established that some of the participants had identified their difficulties in situating RWEI in lessons because of the demands of the curriculum or a lack of confidence in this particular area. In some cases, teachers might find it difficult to come up with specific examples of real life contexts, but still be able to teach an RWEI lesson.

Also important is the fact that the participants had different mathematical beliefs. These ranged from Minervia prioritising ‘socially aware’ beliefs to Rachel, describing mathematics as an ‘absolute’ subject. Hence, teachers need to realise that situating RWEI in mathematics lessons is not a pedagogical approach accessible exclusively to teachers who have ‘fallibilist’ or predominantly ‘socially aware’ beliefs.

In conclusion, the implications for mathematics teaching is that teachers understand that situating concepts of critical mathematics and social justice in the secondary mathematics classroom is a pedagogical approach which can be practised by teachers from wide ranging mathematical beliefs. RWEI applies to all the areas of the National Curriculum and can be taught without reference to real world contexts. Although conditions of democratic participation are desirable, there are environments where this may not initially be possible. That is not to say that situating RWEI in the classroom is reduced to referring to a set of examples taught, or even delivered, to pupils, hence treating critical pedagogy as nothing more than a teaching technique rather than a means to an end (Ernest, 2016).