The Language of Word Problems ◆ 81each other about their problem solving, how to share their thinking, make
predictions, think out loud, revise their thinking, give examples, defend
their thinking, challenge others, give explanations and express their “fuzzi-
ness” (their confusions). When focusing in on function, teachers need to
use many language frames as scaffolds.
- Math Texts Are “Dense and Concept Loaded”
Researchers have found that the language of word problems is “dense
and concept-loaded.” There is a whole lot of information in a small
amount of text, and therefore the text must be read carefully, thoroughly
and attentively so that students comprehend what the problem is about
(Heinze, 2005). This is compounded for
English language learners (Basurto,
1999). Because math word problems are
“dense and loaded,” teachers need to
teach special reading comprehension
strategies to successfully understand
and solve them (Winograd & Higgins,
1994/1995). These involve reading
slowly and often more than once to
make sure students fully understand
the problem (Kang & Pham, 1995) (see
Figure 5.1).
Let’s look at this problem, adapted from Illustrative Mathematics (2015):
The fourth-grade students were studying reptiles. They went to
the reptile exhibit at the zoo. The zoo keeper explained that the
bearded lizard was 4 feet long. It had grown 1 foot in a year.
The spotted lizard was 2 feet long. It had grown 1 foot in a year
also. The teacher asked the students which lizard grew more?
Some students thought that the lizards grew the same size
because they each grew 1 foot. Carol said she thought that the
spotted lizard grew more because it doubled its size whereas the
bearded lizard only grew ¼ more of its size. Dan said he didn’t
understand what she was talking about. Can you explain her
thinking?This problem is dense and loaded. There are a number of concepts
from the very basic to more complex. First, students need to know what
length is. Then they need to understand the unit of measure of a foot.
Next, they need to understand the difference between additive and mul-
tiplicative thinking. Moreover, they need to be able to follow the thinking
Figure 5.1“Students who have diffi-
culties with reading, com-
putation, or both are likely
to encounter difficulties
with word-problem solv-
ing.” (Jitendra & Xin, 1997,
p. 413)