The effect of semantic cues on the difficulty of word problems and the interplay with other complicating variables

ABSTRACT

Research has uncovered a semantic cue effect for short inconsistent word problems; the presence of functionally related objects makes them easier for pupils than the presence of categorically related ones. This study builds on this result by investigating other types of problems. Variants of problems differing in a semantic cue were solved by equally-abled groups of pupils. Item Response Theory was used to determine their latent ability. An independent two-sample t-test was used to determine differences in the difficulty of word problems. The above semantic cue effect was confirmed and the findings distinguished two ways a semantic cue manifests itself (as a reminder or as a helper) in other types of word problems. The study determined the variables supporting the manifestation of the semantic cue (the order of data and the presence of a complicating variable). More research is needed to elaborate the model.

KEYWORDS:

• Word problems
• semantic cue effect
• language consistency

Acknowledgments

We thank Martin Chvál for the statistical evaluation of the data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 For example, “Seventy-two commuters join car pools. There are 4 times as many commuters as automobiles. How many automobiles are there?” (p. 474).

2 In WPs with consistent language, the signal word/s is/are congruent with the operation.

3 “Alan bought an equal number of plants and flowerpots. Each plant cost three dollars and each flowerpot cost five dollars, so that he spent 48 dollars in all. How many plants did Alan buy?” “Jane has an equal number of dogs and cats. If she had twice as many dogs and four times as many cats, she would have 42 pets in all. How many dogs does Jane have?” (p. 241).

4 Additive WPs in American textbooks (Bassok, Chase, & Martin, 1998) and Russian textbooks (Tyumeneva et al., 2018) mostly contain categorically related objects while division WPs mostly concern functionally related objects.

5 English translations are provided, the original word problems and pupils’ solutions were in Czech.

6 They are identical to or inspired by Martin and Bassok's study (2005).

7 Both tests comprised problems and tasks from topics covered by the national school curriculum. Each grade had its own test. Its purpose was only to divide pupils into four equally-abled groups, thus, we will not provide detail here.

8 The remaining WPs in the tests concerned other variables (Vondrová et al., 2019a).

9 Except for the initial testing in mathematics and Czech language, the pupils took part in 2 to 4 rounds of testing focused on word problems.

10 German Rail bought 1,564 new freight carriages. They will be put into operation at the beginning of next year. They bought 17 times more freight carriages than personal carriages. [They bought 17 times more carriages than locomotives.] How many personal carriages [locomotives] did German Rail buy?

11 The same applies for University/Factory II for which no semantic cue effect was found either.

12 Vicente, Orrantia and Verschaffel (2008) call the former situationally easy and the latter situationally difficult.

13 Some low latent ability pupils solved the variant without a semantic cue.

Additional information

Funding

This work was financially supported by the Czech Science Foundation under Grant 16-06134S Context problems as a key to the application and understanding of mathematical concepts.