Effectiveness of the Change in Variable Strategy for Solving Linear Equations Mustafa F' Demir and J

1
Effectiveness of the Change in Variable
Strategy for Solving Linear EquationsMustafa F.
Demir and Jon R. Star, Michigan State University
Results 25 of students used CV at least one
question on the 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 on the pretest and posttest, while the
average time for non-CV users to solve the same
questions was 4 min 53 seconds, a difference that
is significant. CV users also used fewer steps to
solve each CV problem, on average. While CV users
typically solved CV problems using 3-5 steps,
non-CV users solved the same problems using 4-7
transformations. In addition, CV users solved CV
problems more accurately than students who did
not use CV, as shown in Table 1. In sum, our
results indicate that the use of CV enabled
solvers to solve CV problems quicker, more
accurately, and in fewer steps.
Table 1 Comparison of CV and Non-CV Students
Performance on CV Questions
Introduction 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 Ball, 1987). In these studies,
researchers pay little attention about students
practices of CV strategy to solve linear
equations and its effects on students solution
processes which is the focus of this paper.
Method 157 students who had completed 6th 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 equation by the same constant, distributing,
and combining variables or constants) to solve
linear equations. In this short lecture, students
did not take any information about using CV.
After that, students worked to solve a series of
linear equations for three one-hour sessions.
References VanLehn, K., Ball, W. (1987).
Understanding algebra equation solving strategies
(Technical Report PCG-2). Pittsburgh, PA Dept.
of Psychology, Carnegie-Mellon University.
Conclusion 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.
Further research is investigating the knowledge
that CV users developed that enabled them to
solve CV more accurately and efficiently and how
and whether this knowledge might transfer to
non-CV problems.
Contact Information Jon R. Star, jonstar_at_msu.edu
Mustafa F. Demir, demirmus_at_msu.edu. College of
Education, Michigan State University, East
Lansing, Michigan, 48824. This poster can be
downloaded at www.msu.edu/jonstar.