id: 02323027
dt: j
an: 1998d.02857
au: Ribeiro Baldino, Roberto; Büttner Ciani, Andréia; Roesler Luersen,
Anemarie; Lopes Vieira, Márcia Cristina de C. Trindade Cirino; Sandalo
Pereira, Patricia
ti: From the slope of a straight line to the differential: Critical remarks on
the current methodology and alternatives. (Do coeficiente angular da
reta ao conceito de diferencial: Crítica ao ensino atual e proposta
alternativa.)
so: Quadrante 6, No. 1, 29-50 (1997).
py: 1997
pu: Associação de Professores de Matemática (APM), Lisboa
la: PT
cc: I45
ut: lacan,j.; semantic fields
ci:
li:
ab: We start from a meeting report of a study group, produced by students who
are working towards their Master Degree in Mathematics Education at
UNESP, Rio Claro. The discussion has shown that difficulties faced by
these students in dealing with differential approximations in their
calculus courses, were due to the conceptions of slope of a straight
line that they had learned in high school analytic geometry. We arrived
at a didactical proposition to high school analytic geometry and
trigonometry, intended to prevent this difficulty. The proposition
includes suggestions for teaching derivatives in high school The slope
should be thought of not only as $Δy$ divided by $Δx$, but also as
the number that, when multiplied by $Δx$, leads to $Δy$. The slope
should be thought of as a multiplier. Similar remark holds for tan, sin
and cos. The meeting report is analysed from the perspective of
production of meaning under Lacan’s concepts. The didactical
proposition is based on the theory of semantic fields and its practical
feasibility is being tested in a freshmen calculus course. The paper
describes a first attempt of carrying out research in Mathematics
Education under a psychoanalytical approach. (Authors’ summary)
rv: