id: 06512802
dt: j
an: 2016a.00786
au: Johnson, Heather Lynn
ti: Reasoning about quantities that change together.
so: Math. Teach. (Reston) 106, No. 9, 704-708 (2013).
py: 2013
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: I23 F73 F93
ut: quantitative reasoning; rate of change; propaedeutics; relations;
functional relationship; bottle filling; volume; height; research;
interviews; graph of a function; quantities; simultaneous-independent
reasoning; change-dependent reasoning; pre-calculus education
ci:
li: http://www.nctm.org/Publications/mathematics-teacher/2013/Vol106/Issue9/Connecting-Research-to-Teaching_-Reasoning-about-Quantities-That-Change-Together/
ab: From the text: Imagine a soda bottle being filled at a constant rate. How
might the volume of soda in the bottle change with respect to the
height of soda in the bottle? To respond, we need to consider how the
quantities of volume and height â€ścovary", or change together, in
relation to the shape of the bottle. That is, we need to engage in
quantitative reasoning that involves describing rates of change.
Although we usually associate thinking about rates of
change-particularly, varying rates of change-with calculus, the
foundation of these ideas begins much earlier. In this article, I share
data from interviews with secondary school mathematics students to
illustrate two different types of reasoning that can be observed in
such situations.
rv: