id: 06617746
dt: j
an: 2016e.00528
au: Ernest, Paul
ti: The problem of certainty in mathematics.
so: Educ. Stud. Math. 92, No. 3, 379-393 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht
la: EN
cc: E20 D20 C20 E50
ut: certainty; objectivity; mathematical knowledge; beliefs; proof; social
construction
ci:
li: doi:10.1007/s10649-015-9651-x
ab: Summary: Two questions about certainty in mathematics are asked. First, is
mathematical knowledge known with certainty? Second, why is the belief
in the certainty of mathematical knowledge so widespread and where does
it come from? This question is little addressed in the literature. In
explaining the reasons for these beliefs, both cultural-historical and
individual psychological factors are identified. The cultural
development of mathematics contributes four factors: (1) the invariance
and conservation of number and the reliability of calculation; (2) the
emergence of numbers as abstract entities with apparently independent
existence; (3) the emergence of proof with its goal of convincing
readers of certainty of mathematical results; (4) the engulfment of
historical contradictions and uncertainties and their incorporation
into the mathematical narrative of certainty. Individual learners of
mathematics internalize ideas of invariance, reliability and certainty
through their classroom experiences and exposure to such cultural
factors. Lastly, with regard to the first question, it is concluded
that mathematics can be known with a certainty circumscribed by the
limits of human knowing.
rv: