id: 05970980
dt: j
an: 2012a.00572
au: Caddle, Mary C.; Brizuela, Barbara M.
ti: Fifth gradersâ€™ additive and multiplicative reasoning: establishing
connections across conceptual fields using a graph.
so: J. Math. Behav. 30, No. 3, 224-234 (2011).
py: 2011
pu: Elsevier, New York, NY
la: EN
cc: I23 H23 F43
ut: grade 5; linear graphs; multiplication; addition
ci:
li: doi:10.1016/j.jmathb.2011.04.002
ab: Summary: This paper looks at 21 fifth grade students as they discuss a
linear graph in the Cartesian plane. The problem presented to students
depicted a graph showing distance as a function of elapsed time for a
person walking at a constant rate of 5 miles/h. The question asked
students to consider how many more hours, after having already walked 4
h, would be required to reach 35 miles. To answer this question, the
students needed to extend the graph that was presented, either mentally
or on paper, as the axes did not go up to 7 h or 35 miles. They also
needed to be able to consider not only the total number of hours to
reach 35 miles, but also the interval of time after 4 h. The purpose of
this paper is to consider the student responses from the viewpoint of
multiplicative and additive reasoning, and specifically within
Vergnaudâ€™s framework of multiplicative and additive conceptual fields
and scalar and functional approaches to linear relationships (Vergnaud,
1994). The analysis shows that: some student answers cannot be
classified as either scalar or functional; some students combined
several kinds of approaches in their explanations; and that the
representation of the problem using a graph may have facilitated
responses that are different from those typically found when the
representation presented is a function table.
rv: