Comprehension of arithmetic word problems by fifth-grade pupils: representations and selection of information

Understanding word problems leads to the construction of different levels of representation. Some levels specify the elements which are indispensable for solving the problem (problem model, PM) and others specify the agents, actions and events in everyday concepts (situation model, SM).

By studying how the information is selected, we try to specify the nature of the representations constructed during the reading of a word problem: understanding a problem leads to the construction of two complementary levels of representation (PM and SM) or to the construction of only one representation (PM)?

Ninety-one fifth-grade pupils (mean age 10 years 9 months) took part in this study and were divided into two groups according to their mathematical ability.

As well as the information considered as indispensable for solving the problems (solving information), different types of information (situational information) were introduced into standard word problems. In a first task, participants were asked to select the information in order to 'make the word problem as short as possible' (locate the elements used for developing PM). In a second task, they were asked to select the information in order to 'make the word problem easier to understand' (determine whether the participants developed a SM).

The participants successfully differentiated between the solving information and the situational information. An interaction was also observed between the type of information and the task. The mathematical ability of the participants was seen to have an influence on the selection of situational information.

Understanding leads to the construction of two complementary representation levels: the problem model and the situation model.