@@ contextIn secondary schools within the UK there are many teachers of mathematics who have arequalified teachers,but have not been trained to teach mathematics．There are various courses,some of which have been supported by government that‘retrain’these teachers SO that theyare‘specialist secondary mathematics teachers’(TDA 20 1 1,DIE 20 1 2a)and this paper drawson experience of providing several of such courses．This is not unique to the UK,for example,there are on—going investigations into a similar situation in Germany(Bosse and Tomer 20 1 2),but this paper is focussed on the situation in the London area．The teachers in question havebeen prepared to teach subjects that include physical education,art,modem languages,citizenship or they have been trmned as primary teachers fto teach children of ages 5-1 1years)．The central discussion concems design and delivery of courses that aim to tumqualified teachers into mathematics teachers and addresses issues of equity and quality．In thecontext of this paper,‘equity’is concerned with these teachers being trmned to offerequitable provision to their students and‘quality’refers to their mathematics teaching．