The transition from the elementary word problems discussed in chapter 4
to the multistep problems discussed in chapter 5 was relatively straightfor-
ward. Multistep problems can be solved by formulating a plan for combining
the elementary schemas found in chapter 4. But the transition from arith-
metic word problems to algebra word problems is more complicated. Al-
though I have used algebra word problems in most of my research on
problem solving, I have never been very confident that I could distinguish
between algebra word problems and other kinds of problems. One reason
is that this distinction seems to depend more on the approach used to solve
the problem (whether or not the student uses algebra) than on the problem
itself. A better distinction therefore is to distinguish among the different
methods that students use to solve problems that we might typically classify
as algebra word problems.

According to the NCTM standards, the ability to represent situations with
algebraic quantities is a central skill that is a prerequisite to understanding
many areas of mathematics. The first section of this chapter looks at what
is involved in making this transition from arithmetic to algebra. The transi-
tion requires thinking differently about mathematical operations and about
the meaning of symbols such as the equals sign. It also requires under-
standing how letters are used in equations to represent variables. The
difficulty of representing relations between variables is illustrated in the
extensive research that has been done on variations of the student-profes-
sor problem. One consequence of student's difficulty with algebra is that
they often attempt to solve word problems by using nonalgebraic ap-
proaches. When this is possible, students typically do better by having
access to a variety of strategies.

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