80 ◆ The Language of Word Problems
worms?” Many of the children could not solve the problem. However,
when the problem was reworded, “How many birds won’t get a worm?”
many of the students could solve the problem. Riley, Greeno and Heller
(1983) said that rewording helps students to understand the problem, and
when students understand the problem they can solve it. Cummins (1991)
pointed out that “the data seem to indicate that the knowledge [to solve
problems] is there, but is simply is not accessed when problems are worded
in certain ways (p. 267).” She argues that students who fail do so because
they are “missing” or “have” inadequate mappings of verbal expressions
to part-whole structures. She maintains that “rewording enhances
performance.”
I really find this to be true. When students know what they are look-
ing for, they are much more likely to find it. For example: The teacher
says: Kate had 57 marbles. She got some more for her birthday. Now she has 75.
How many did she get for her birthday? A common error is for students to
add 57 and 75. Students get confused by the phrase some more. They will
often just add 57 and 75 because they are confused by the language. If
the problem is reworded:
Kate had 57 marbles. She got some more for her birthday. [She had 57 and
now she has 75. She got some more to make her total 75.] How many
did she get for her birthday?This scaffolds the phrase some more. It can be further scaffolded with a
language scaffold written in the equation. It helps students to have access
to the concept. The scaffolding would eventually be phased out. We need
students to understand the structure as 57 + __= 75.
some^ more
This is also about syntax and phraseology. We have to scaffold student
access into understanding the word problem. We must think about ways
to present the problem that make sense and scaffold conceptual under-
standing and then next scaffold the algebraic phrases we use in these
problems.
- Function Matters
We ask students to do a lot of different things in math, including reading
the word problem, writing the answer, illustrating the answer, showing their
thinking, using their math words, proving the answer with different strate-
gies, giving an explanation and sharing their thinking. These all require
different types of talking and organizing of thoughts. We have to be explicit
about what we are asking students to do and then teach them how to do
these different things. We have to practice with students how to talk with