id: 06498180
dt: j
an: 2015f.00532
au: Tabach, Michal; Nachlieli, Talli
ti: Classroom engagement towards using definitions for developing mathematical
objects: the case of function.
so: Educ. Stud. Math. 90, No. 2, 163-187 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: E49 C39 I29
ut: discourse analysis; sociocultural approach; mathematics definitions;
learning processes; commognitive conflict
ci:
li: doi:10.1007/s10649-015-9624-0
ab: Summary: For mathematicians, definitions are the ultimate tool for reaching
agreement about the nature and properties of mathematical objects. As
research in school mathematics has revealed, however, mathematics
learners are often reluctant, perhaps even unable, to help themselves
with definitions while categorizing mathematical objects. In the
research from which we take the data presented in this article, we have
been following a group of prospective mathematics teachers studying
functions. In the course of learning, the students gradually accepted
the definition as the ultimate criterion to identify examples of
function. And yet, this use was hindered by the difficulty the students
experienced while trying to understand the logical structure of the
definition. Our close analysis has shown that the determiners “for
every” and “unique” constituted the main source of the
difficulty. We propose that a brief introduction to logic and, in
particular, to parsing complex mathematical sentences, may be a useful
addition to mathematics curriculum.
rv: