Box 8-2 Table Completion Task from NAEP Give the values of y
when x=3 and when x=n. SOURCE: Carpenter, Corbitt, Kepner,
Lindquist, and Reys, 1981. Used by permission of the National
Council of Teachers of Mathematics. merical values and use it
when x=3 (with success rates of 69% and 81% for the two groups
of students, respectively). They were less successful, however,
when asked to derive from the same table the value of y when x=n
(correct response: y=n+7; success rates: 41% and 58%,
respectively). The next three sections of the chapter present
representative findings from the large body of research on
algebra learning and teaching for the three types of algebraic
activity sketched above. Since much of this research has been
carried out with students making the transition from arithmetic
to algebra, it casts light on the kinds of thinking that
students bring with them to algebra from the traditional
arithmetic curriculum centered on algorithmic computation that
has been predominant in U.S. schools.17 Indeed,