id: 06448881
dt: j
an: 2015d.00274
au: Ernest, Paul
ti: Forms of knowledge in mathematics and mathematics education: philosophical
and rhetorical perspectives.
so: Philos. Math. Educ. J. 26, 18 p., electronic only (2011).
py: 2011
pu: Professor Paul Ernest, University of Exeter, Graduate School of Education,
Exeter
la: EN
cc: D20 E20 C30 C50
ut: mathematics and philosophy; mathematical knowledge; tacit knowledge;
rhetoric; mathematics and language; sociology of science; mathematical
texts; proofs; epistemology
ci:
li: http://people.exeter.ac.uk/PErnest/pome26/Ernest%20%20Forms%20of%20Knowledge%20in%20Mathematics%20and%20Mathematics%20Education.doc
ab: Summary: New forms of mathematical knowledge are growing in importance for
mathematics and education, including tacit knowledge; knowledge of
particulars, language and rhetoric in mathematics. These developments
also include a recognition of the philosophical import of the social
context of mathematics, and are part of the diminished domination of
the field by absolutist philosophies. From an epistemological
perspective, all knowledge must have a warrant and it is argued in the
paper that tacit knowledge is validated by public performance and
demonstration. This enables a parallel to be drawn between the
justification of knowledge, and the assessment of learning. An
important factor in the warranting of knowledge is the means of
communicating it convincingly in written form, i.e., the rhetoric of
mathematics. Skemp’s concept of ‘logical understanding’
anticipates the significance of tacit rhetorical knowledge in school
mathematics. School mathematics has a range of rhetorical styles, and
when one is used appropriately it indicates to the teacher the level of
a student’s understanding. The paper highlights the import of
attending to rhetoric and the range of rhetorical styles in school
mathematics, and the need for explicit instruction in the area.
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