158 ◆ Assessment
- Which method do you use to get your answer? (This checks for
Transformation Errors.) (Record a T if there are problems here.)
A transformation error is when the student can read the prob-
lem, and comprehends what to do, but doesn’t know how to do
it. The student doesn’t know what operation(s) to use. They get
stuck. For example, they don’t know if it is a multiplication or a
division problem. - Show me how you get your answer, and “talk aloud” as you do it
so that I can understand how you are thinking. (This checks for Pro-
cess Errors.) (Put a P if there are errors here.) A process error is when
the student can read the problem, comprehend it, knows what
to do but can’t do it. It is when they don’t know how to do it. For
example, they know they need to multiply but they don’t know how. - Now, write down your actual answer. (This checks for Encod-
ing Errors—defined as an inability to express the answer in
an acceptable form.) Ask the student to tell you the answer and
to explain the answer. (Record an E if there are errors here.) An
Encoding Error is when the student finds the answer but can’t
write it out as the actual solution to the problem. They don’t
know how to express it as the answer.
Remember that if the student self-corrects it could be classified as a Care-
less Error and coded with an X. Newman (1977, 1983) also said that
students make errors due to a lack of motivation. Researchers have also
found that 70 percent of word problem errors were at the comprehension
and transformation levels (Marinas & Clements; Singhatat; Clements &
Ellerton; cited in White, 2005).
Willis and Fuson (1988) provide another lens through which to look
at student word problem errors. They give us four things to think about.
- Can the students represent the problem? I would also ask, “What
do they use?” Do they have a large repertoire of strategies for
solving problems ranging from concrete materials to pictorial rep-
resentations through abstract representations such as equations?
Do they know how to use pictures, bar diagrams and the open
number lines? - Do students understand the specific relations among the three
problem quantities? In other words, can they put the numbers in
the right place? Do they know what they know and what they
don’t know? Are they certain about what they are looking for?
I find this to be especially interesting when I ask students, what
does that number mean? What does it represent? What are you