Change

Educated citizens need to grasp the meaning of growth in order to understand financial contracts (e.g. credit card payments) and make sense of statements such as “the jobless rate is increasing at a lower pace than last year.” Scientists and technicians need to understand and model growth to represent processes in physical, social, and biological domains. Doubling the width of a shoebox has a very different effect on volume or surface area from doubling the radius of a ball. If we compare two populations, one twice as large as the first but both with same birth rate, or two populations of the same size but one of them with twice the birth rate of the other, the difference in the populations’ sizes over a number of years is even more dramatic. Course 3 will deal with various aspects of change, from the effects of positive or negative change on equations and inequalities, comparison of different types of functions for representing change, (e.g., things that go around in circles) to the meaning of rate of change. Studies of students’ understanding of various kinds of change over time (e.g. change in displacement, height, wages) and their interpretation of graphs are considered.