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Proofs and Refutations:
The Truth About Black Children and
Mathematics
Danny Bernard Martin
University of Illinois at Chicago
iMathination 2013 Conference
Q Center, St. Charles, IL
January 26
09-23-2009
Axiom I: Black children are brilliant.
a turning point
• Danny Martin: Black children are brilliant.
• Response: Prove it!
the making of children in mathematics
the exception
the rule
my arguments today
•
In the logic models of mainstream mathematics education
research, policy, and practice, the brilliance of Black children has
never been axiomatic.
•
The prevailing narratives about Black children are vested in
foregrounding mathematical illiteracy and inferiority as the
primary identities of these children.
•
Instances of Black children’s brilliance, no matter how many are
offered, will always be framed as exceptions to a general rule.
•
The logic models of mainstream research, policy, and practice
operate efficiently and convincingly to prove that Black children
are not brilliant. We must deconstruct and disrupt these logic
models, even if this means, for example, unsettling the sensibilities
of teachers.
axiom
An axiom is a logical statement that is assumed to be
true. Axioms are not proven or demonstrated, but
considered to be self-evident. Axioms serve as starting
points for deducing and inferring other truths.
conjecture
A conjecture is a proposition that is unproven but is
thought to be true and has not been disproven.
counterexample
A counterexample is an exception to a proposed
general rule. Counterexamples are used to show that
certain conjectures are false.
Why do conservatives, neoconservatives, and members
of the right wing seem to control the debate on
important social issues, to the degree that their
opponents willingly vote against their own interests?
Speech 101: Frame the issue on your terms, stick to
those terms, and utilize a logic that your opponents
cannot escape. Turn your arguments and talking points
into common sense.
burden of proof
Prevailing Conjecture: Black children are mathematically
illiterate and intellectually inferior to White and Asian
children.
• Knowledge production: Focused on the accumulation
of evidence to support and prove this conjecture.
Unreasonable challenge: To prove that Black children are
not mathematically illiterate and intellectually inferior to
White and Asian children.
• Knowledge production: Remains grounded in the
language and ideology of inferiority.
burden of proof
Alternative Conjecture: Black children are brilliant.
• Knowledge production: focused on the accumulation
of evidence and examples to support and prove the
conjecture that Black children are brilliant (and not
mathematically illiterate in relation to White and Asian
children).
Unreasonable challenge: Prove that Black children are not
brilliant.
• Knowledge production: Returns to the status quo, de
facto constructions of Black children.
language and logic games
• If all Black children are brilliant, then no Black
children are brilliant…
• If some Black children are brilliant, then…
• If some Black children are not brilliant, then…
• Some Black children don’t want to be seen as brilliant
or smart because…
• Saying Black children are brilliant doesn’t make it so…
• All children are brilliant, why focus on Black
children…
damaging effects
Research and Policy: The conversations about Black
children in mainstream mathematics education research,
policy, and practice contexts are often conversations
about how they differ from “white” children, “Asian”
children, and “middle-class” children.
the making of children in mathematics
Most U.S. children enter school with mathematics abilities that
provide a strong base for formal instruction….A number of
children, however, enter school with specific gaps in their
mathematical proficiency….Overall, the research shows that
poor and minority children entering school do possess some
informal mathematical abilities but many of these abilities have
developed at a slower rate than middle-class children. This
immaturity of their mathematical development may account
for the problems poor and minority children have
understanding the basis for simple arithmetic and solving word
problems. (Adding It Up, 2005, p. 172-173, in section titled
Equity and Remediation)
damaging effects
Practice: It is becoming increasingly rare to find folks in
school contexts who truly believe in the brilliance of
Black children. The logic that often flows through school
discourse and school practices speaks to this disbelief.
a high-stakes test
• Question 1: How many of you have heard of the racial
achievement gap?
• Question 2: How many of you have, or plan to, devote some
aspect of your teaching practice, research, or policy-oriented
efforts to help close the racial achievement gap?
• Question 3: How many of you truly believe in the brilliance of
Black children?
where go we go from here?
• We must accept, and insist on, the brilliance of Black
children as axiomatic.
• We must avoid the trap of having to prove that Black
children are brilliant.
• We must avoid generating arguments, logic models,
and counternarratives requiring proof that Black
children are not brilliant.
ubiquity of brilliance
• Seeing brilliance in the ordinary, everyday lives of Black
children and not seeing brilliance as the exception or
counterexample.
• Studying and building on the mathematical lives of Black
children in the places where they live, learn, and grow.
• Studying and teaching Black children as Black children
and as children of the world who develop multiple and
complex identities, including identities as doers of
mathematics.
Thank you!