id: 06514432
dt: j
an: 2016a.00700
au: Hackenberg, Amy J.; Lee, Mi Yeon
ti: Relationships between studentsâ€™ fractional knowledge and equation
writing.
so: J. Res. Math. Educ. 46, No. 2, 196-243 (2015).
py: 2015
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: H33 F43 E53
ut: equations; skills; mathematical concepts; fractional knowledge; algebraic
reasoning; equation writing; multiplicative concepts; iterative
fraction scheme; middle-school students; quantitative reasoning;
unknowns
ci:
li: http://www.jstor.org/stable/10.5951/jresematheduc.46.2.0196
ab: Summary: To understand relationships between studentsâ€™ fractional
knowledge and algebraic reasoning in the domain of equation writing, an
interview study was conducted with 12 secondary school students, 6
students operating with each of 2 different multiplicative concepts.
These concepts are based on how students coordinate composite units.
Students participated in two 45-minute interviews and completed a
written fractions assessment. Students operating with the second
multiplicative concept had not constructed fractional numbers, but
students operating with the third multiplicative concept had; students
operating with the second multiplicative concept represented
multiplicatively related unknowns in qualitatively different ways than
students operating with the third multiplicative concept. A
facilitative link is proposed between the construction of fractional
numbers and how students represent multiplicatively related unknowns.
rv: