id: 02331894
dt: j
an: 2000d.02279
au: Graeber, Anna O.
ti: Forms of knowing mathematics: what preservice teachers should learn.
so: Educ. Stud. Math. 38, No. 1-3, 189-208 (1999).
py: 1999
pu: Springer Netherlands, Dordrecht
la: EN
cc: B50
ut:
ci:
li: doi:10.1023/A:1003624216201
ab: What important ideas about forms of knowing mathematics should be included
in mathematics methods courses for preservice teachers? Ideas are
proposed that are related to categories in Shulman’s (1986) framework
of teacher knowledge. There is a brief discussion of the implications
each idea holds for teaching mathematics, and some suggestions are
given about experiences that may help preservice teachers appreciate
these notions. One portion of Shulman’s pedagogical content knowledge
construct is knowing what makes a subject difficult and what
preconceptions students are apt to bring. Three of the ideas offered
for inclusion in a methods course are related to this aspect of
pedagogical content knowledge: (1) Understanding students’
understanding is important, (2) Students knowing in one way do not
necessarily know in the other(s), and (3) intuitive understanding is
both an asset and a liability. The last two ideas, are related to the
other portion of pedagogical content knowledge, knowing how to make the
subject comprehensible to learners. These ideas are (4) certain
characteristics of instruction appear to promote retention, and (5)
providing alternative representations and recognizing and analyzing
alternative methods are important. Readers are asked to consider if the
suggestions offered are appropriate and how they might best be taught.
(Abstract)
rv: