TY - JOUR

T1 - Reinventing fractions and division as they are used in algebra

T2 - the power of preformal productions

AU - Peck, Frederick

AU - Matassa, Michael

N1 - Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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 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.

AB - 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 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.

KW - Algebra

KW - Division

KW - Fractions

KW - Preformal productions

KW - RME

KW - Realistic mathematics education

UR - http://www.scopus.com/inward/record.url?scp=84959106707&partnerID=8YFLogxK

U2 - 10.1007/s10649-016-9690-y

DO - 10.1007/s10649-016-9690-y

M3 - Article

AN - SCOPUS:84959106707

SN - 0013-1954

VL - 92

SP - 245

EP - 278

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

IS - 2

ER -