
06617739
j
2016e.00580
Peck, Frederick
Matassa, Michael
Reinventing fractions and division as they are used in algebra: the power of preformal productions.
Educ. Stud. Math. 92, No. 2, 245278 (2016).
2016
Springer Netherlands, Dordrecht
EN
F40
H30
realistic mathematics education
fractions
division
algebra
preformal productions
doi:10.1007/s106490169690y
Summary: In this paper, we explore algebra students' mathematical realities around fractions and division, and the ways in which students reinvented mathematical productions involving fractions and division. We find that algebra students' initial realities do not include the fractionasquotient subconstruct. This can be problematic because in algebra, quotients are almost always represented as fractions. In a design experiment, students progressively reinvented the fractionasquotient subconstruct. 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.