
06499067
j
2016a.00550
Johnson, Heather Lynn
Predicting amounts of change in quantities.
Math. Teach. Middle Sch. 19, No. 5, 260264 (2013).
2013
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
F93
G33
I23
mathematics of change
covariation perspective
elementary algebra
rectanglearea problem
rectangleresizing problem
lower secondary
quantitative reasoning
relationships between quantities
change in quantities
covariational reasoning
rectangles
area
height
length
noninteger amounts of change
diagrams
linear functions
propaedeutics
From the text: Analyzing relationships between quantities can support middlegrades students' reasoning about algebra and function. When students focus on relationships between quantities in a function, they are reasoning covariationally. A student taking a covariation perspective might think about a function as a special relationship between quantities in which change in one quantity depends on change in another quantity. Students often have to wait until calculus to study the mathematics of change. A focus on relationships between quantities is one way to introduce middlegrades students to the mathematics of change. My intent with this article is to illustrate how predicting amounts of change in quantities can promote students' covariation perspectives. I provide examples of their work to illustrate different ways in which students have viewed relationships between quantities to make sense of a linear situation.