id: 06617739
dt: j
an: 2016e.00580
au: Peck, Frederick; Matassa, Michael
ti: Reinventing fractions and division as they are used in algebra: the power
of preformal productions.
so: Educ. Stud. Math. 92, No. 2, 245-278 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht
la: EN
cc: F40 H30
ut: realistic mathematics education; fractions; division; algebra; preformal
productions
ci:
li: doi:10.1007/s10649-016-9690-y
ab: Summary: In this paper, we explore algebra studentsâ€™ mathematical
realities around fractions and division, and the ways in which students
reinvented mathematical productions involving fractions and division.
We find that algebra studentsâ€™ initial realities do not include the
fraction-as-quotient sub-construct. This can be problematic because in
algebra, quotients are almost always represented as fractions. In a
design experiment, students progressively reinvented the
fraction-as-quotient sub-construct. Analyzing this experiment, we find
that a particular type of mathematical production, which we call
preformal productions, played two meditational roles: (1) they mediated
mathematical activity, and (2) they mediated the reinvention of more
formal mathematical productions. We suggest that preformal productions
may emerge even when they are not designed for, and we show how
preformal productions embody historic classroom activity and social
interaction.
rv: