id: 06261879
dt: j
an: 2014b.00560
au: Ramful, Ajay
ti: Reversible reasoning in fractional situations: theorems-in-action and
constraints.
so: J. Math. Behav. 33, 119-130 (2014).
py: 2014
pu: Elsevier, New York, NY
la: EN
cc: H33 F43 E53
ut: division; fraction; multiplicative reasoning; reversibility; units;
Vergnaud’s theory
ci:
li: doi:10.1016/j.jmathb.2013.11.002
ab: Summary: The aim of this study was to investigate, at a fine-grained level
of detail, the theorems-in-action deployed and the constraints
encountered by middle-school students in reasoning reversibly in the
multiplicative domain of fraction. A theorem-in-action [{\it G.
Vergnaud}, “Multiplicative structures”, in: J. Hiebert (ed.) and M.
Behr (ed.), Number concepts and operations in the middle grades. Vol.
2. Reston, VA: National Council of Teachers of Mathematics and Lawrence
Erlbaum Associates. 141‒161, (1988)] is a conceptual construct to
trace students’ reasoning in a problem solving situation. Two seventh
grade students were interviewed in a rural middle-school in the
southern part of the United States. The students’ strategies were
examined with respect to the numerical features of the problem
situations and the ways they viewed and operated on fractional units.
The results show that reversible reasoning is sensitive to the numeric
feature of problem parameters. Relatively prime numbers and fractional
quantities acted as inhibitors preventing the cueing of the
multiplication-division invariant, thereby constraining students from
reasoning reversibly. Among others, two key resources were identified
as being essential for reasoning reversibly in fractional contexts:
firstly, interpreting fractions in terms of units, which enabled the
students to access their whole number knowledge and secondly, the
unit-rate theorem-in-action. Failure to conceptualize multiplicative
relations in reverse constrained the students to use more primitive
strategies, leading them to solve problems non-deterministically and at
higher computational costs.
rv: