For those engaged in educational "improvement," it is important to pause from time to time to ask the question: what is improving? If Bourdieu's thesis is correct, namely that education is a key site of social reproduction, does school improvement, and/or improvement of mathematics education, also enhance that capacity for the social reproduction of social class differences? Most teachers, leaders, researchers and politicians would not want this, and would not ordinarily recognise such a process or their contribution to it, but it is an important question nonetheless; one that my colleague Peter Gates and I recently explored in a chapter for teachers: School Mathematics as Social Classification. In this response, the author agrees with Williams and Choudry's opening statement that "mathematics education needs a better appreciation of the dominant power structures in the education field." Bourdieu has much to offer in this regard. In response to their article, the author will address five points briefly: (1) the usefulness of Bourdieu's theory of practice; (2) the problem of language; (3) forms of capital; (4) hope; and (5) going beyond Bourdieu.