In this research, students’ strategies for solving linear equations were
examined.

Of particular interest was the strategy referred to as “change of variable” or
CV. CV was

found when students rewrote terms such as 3(x+2) + 6(x+2) as 9(x+2). There are
very

few research studies which attempt to understand students’ strategies to solve
linear

equations (e.g., VanLehn and Ball, 1987; Pirie and Lyndon, 1997). In prior
research in

this area, researchers have not commented on the use of the CV strategy to solve
linear

equations.

157 students who had completed 6^{th} grade participated in five one-hour
problem-solving

sessions on linear equation solving. Students were given a pretest and then a

short lecture (20 minutes) in which the researcher introduced four different
steps for

solving equations (adding to both sides of equation, multiplying both sides of
the

equations by the same constant, distributing, and combining variables or
constants) to

solve linear equations. After that, students worked to solve a series of linear
equations for

three one-hour sessions.

25% of students used CV at least one question throughout pretest and
posttest. An

analysis of the time that students spent solving each problem indicated that
students who

used the CV strategy spent less time than students who did not use CV. For
example, the

average time for all CV users was 3 min 41 seconds to solve CV questions
throughout the

pretest and posttest, while the average time for non-CV users to solve the same
questions

is 4 min 53 seconds, a difference that is significant. Not only did students who
use CV

solve problems faster, but they also used fewer steps to solve each problem, on
average.

While CV users typically solved problems in 3-5 transformations, non-CV users
solved

the same problems in 4-7 steps. The use of CV enabled solvers to solve problems
both

quicker and in fewer steps. Finding shorter and quicker solution paths is not
only

important for solution efficiency but it reduces the chance of error (VanLehn
and Ball,

1987). Non-CV users had significantly higher rates of error on CV questions as
compared

to CV users.

CV is an example of an innovative strategy for solving linear equations, but
it has

received little attention in prior research on linear equation solving. This
study represents

an initial attempt to investigate the prevalence and use of CV among beginning
algebra

learners