id: 06639313
dt: j
an: 2016f.00895
au: Hackenberg, Amy J.; Lee, Mi Yeon
ti: Studentsâ€™ distributive reasoning with fractions and unknowns.
so: Educ. Stud. Math. 93, No. 2, 245-263 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht
la: EN
cc: F40 H20 H30
ut: fractional knowledge; algebraic reasoning; distributive reasoning;
distributive property; distributive partitioning scheme; multiplicative
concepts; unknowns
ci:
li: doi:10.1007/s10649-016-9704-9
ab: Summary: To understand relationships between studentsâ€™ quantitative
reasoning with fractions and their algebraic reasoning, a clinical
interview study was conducted with 18 middle and high school students.
The study included six students with each of three different
multiplicative concepts, which are based on how students create and
coordinate composite units (units of units). Students participated in
two 45-min semi-structured interviews and completed a written fraction
assessment. This paper reports on how 12 students operating with the
second and third multiplicative concepts demonstrated distributive
reasoning in equal sharing problems and in taking fractions of
unknowns. Students operating with the second multiplicative concept who
demonstrated distributive reasoning appeared to lack awareness of the
results of their reasoning, while students operating with the third
multiplicative concept demonstrated this awareness and the construction
of more advanced distributive reasoning when they worked with unknowns.
Implications for relationships between studentsâ€™ fractional knowledge
and algebraic reasoning are explored.
rv: