id: 05179780
dt: j
an: 2007b.00070
au: Hartmann, George W.
ti: Gestalt psychology and mathematical insight.
so: Math. Teach. (Reston) 100, Spec. Iss., 16-21 (2007).
py: 2007
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: C30 A30
ut: abstract reasoning; holistic approach; history of mathematics education;
cognitive psychology; transpositions; mathematical ability
ci:
li:
ab: Summary: In this reprint of his 1937 article, George W. Hartmann challenges
the commonly held notion that the best way to teach mathematics was by
breaking down learning into discrete parts. This view, he felt, could
not account for the many instances of learning mathematics that
involved creativity, insight, and seeing the “big picture”. In
Gestalt psychology, thinking and reasoning are dependent upon the
processes of perceiving; applying this idea to mathematics education,
Hartmann explains that the way in which one comes to understand a
mathematical object or idea changes with time and that what a
mathematical object “is” is not the same as what one
“perceives”. Therefore, student or novice thinking should not be
seen as copying adult or expert thinking; rather, mathematical ideas
must mature with experience and be “created de novo by every
learner”. Although Hartmann wrote this article seventy years ago, his
ideas on the contribution of Gestalt psychology to mathematics
education still resonate today.
rv: