Commentary on Theories of Mathematics Education

642 K. Yasukawa
treatments that the same doctor gave to other patients in other parts of their practice
within the national health system, and compared with the treatments made by other
professionals working in the system. How do they compare? Which practitioner is
worthmoretothesystem?
This leads me to considering the last of Sriraman, Roscoe and English’s questions:
What does the future bear for mathematics as a field, when viewed through
the lens of equity and culture? If we are concerned to see a role for mathematics and
mathematics education in building a fairer, equitable and inclusive culture, then a
priority in mathematics education is to examine the cultures that are antagonistic to
these goals of social justice in which mathematics is playing a part. Mathematical or
qualculative thinking plays a big part in shaping the dominant thinking about what
is fair, equitable, inclusive. In ‘The Sociology of Critical Capacity’, Boltanski and
Thevenót (1999) observe that in moments of dispute, people operate in a ‘regime of
justification’ that deals with the establishment of ‘equivalence’ (p. 361). They illustrate
that in different spheres of our lives—the ‘world of inspiration’, ‘the domestic
world’, ‘the world of renown (opinion)’, ‘the civic world’, ‘the market world’, and
‘the industrial world’, different modes of evaluation are used to establish ‘worth’
that could then be used to establish or dispute ‘equivalence’. For example, the market
uses the ‘price’ of something, whereas, industry might use indicators of productivity
and efficiency, and in the civic world the level of collective interest might
be used (p. 368). They also identify the format of relevant information and the elementary
relation that are used in valuation in these different spheres: ‘emotional’
information that is relayed as ‘passion’ in the world of inspiration; orally, exemplary
or anecdotal information that establishes ‘trust’ in the domestic world; formal and
official information that is expressed as ‘solidarity’ in the civic world; semiotic tools
used to gain recognition in the world of the renown; monetary resources to facilitate
‘exchange’ in the market; and measurable resources such as criteria and statistics to
describe ‘functional link(s)’ in the industrial world (p. 368).
How are equity and inclusiveness evaluated and established in the world; in the
world of mathematics education? How is mathematical thinking, invisibly or visibly,
implicated in the way they are evaluated and established now? Which cultural
spheres are influencing what equity, fairness and inclusiveness mean? What
are these principles based on: passion; trust; solidarity; exchange value; industrial
functionality? Are these principles also reduced by qualculations to something that
can be easily tabulated and ranked?
The vision of all learners engaging enthusiastically in a multi-cultural history of
mathematical theories, and developing a passion for learning more mathematics for
mathematics’ sake is an attractive one. But will this necessarily lead to a more equitable
world; or just a more equitable and inclusive mathematics classroom (which I
recognise as a highly admirable if it could be achieved)? What mathematics is really
needed to be learned for people to become active citizens? What knowledge (including
mathematical knowledge) and critical thinking skills are needed for students to
interrogate the practices of qualculations that are defining principles of equity and
fairness in particular ways, and not other ways?
Sriraman, Roscoe and English take a social constructivist stance about the nature
of mathematics and say that what counts as mathematics is influenced by the