Effects of consistency and adequacy of language information on understanding elementary mathematics word problems

Annals of Dyslexia, 2001 by Leong, Che Kan, Jerred, Wendy D

While prompting from the interviewer would help, some students needed to understand the relationship between subsets within a larger set of quantities. In answer to the problem: "One half of the flowers in the garden were tulips. If there were 12 tulips in the garden, how many flowers were in the garden?" a less able Grade 4 student verbalized this way:

Student: 12, I'm pretty sure. Researcher: 12 flowers in total? Student: Yeah. No, not 12, yeah.

Researcher: So that means all of the flowers were tulips? Student: No. Half of them were tulips in the garden and the other half were flowers.

(After further discussion, the student said "24 [flowers])." Structured interviews with appropriate prompts with the students showed their progressive level of sophistication even though they might arrive at a correct answer. For the inconsistent language division problems such as: "Julie can run three times farther now than when she first started running. If she can run 9 km now, how far could she run when she first started running?" some students arrived at the answer by adding 3 3 3 instead of dividing 9 by 3. Similar answers were given by a more able Grade 5 student and a less able Grade 4 student as shown below. At some point in the interview, they realized the need to revise their mental representation.

Student: I'd probably say 9 take away 3 or something like that.... It's hard.

Researcher: What does 3 times farther mean? What arithmetic operation (step) is needed?

Student: Multiplication.

Researcher: Do you want to multiply 9 by 3? Student: Ummm... No.

Researcher: Why not?

Student: 'Cause that's more than she's running right now and she has to find less.

(After some more discussion, the student said "divide" and came to the answer of "3" [km]).

There were similar patterns of responses from the interviews on the adequacy of language information items. In some cases, students might classify correctly the levels of adequacy of language information but gave the wrong verbal answers. In more extreme cases, less able students had difficulties in understanding the information and operating on it. This is shown by a less able Grade 3 student in answer to this adequacy/inadequacy language information word problem: "Jean ate 10 marshmallows for a contest. Fred ate 4 times as many marshallows as Jean. How many marshmallows did they eat altogether?"

Student: It'd be 10 - 10 ... umm ... 10 plus 4... Researcher: But did Fred eat 4 marshmallows? Student: Mmm ...

Researcher: He ate ...

Student: 4 times as many marshmallows as Jean. That's 8. The interviews showed that the "not enough" word problems were sources of difficulty for both classifying the level of adequacy of information and the computation based on incorrect premises. In answer to the NE word problem of: "There were 14 children swinging in the playground. Some children jumped off to go to the slide. Soon 6 more children came to swing. How many children are now swinging?" Those who classified the problem as containing enough information invariably gave 14 6 or 20 (children) as the answer. For the "not needed" kinds of problems, many students classified them as having just enough information but some needed help in arriving at the classifying and the correct answers. The following was the excerpt of the interview with a less able Grade 5 student in answer to the problem: "Heather sold 5 of her 10cent comic books. Before she sold them, she had 43 comic books. How much did Heather make when she sold her 5 comic books?"