ABSTRACT
In word problem solving, the child needs to understand the text (De Corte & Verschaffel, 1985, Cummins et al., 1988) and to reconstruct the situations mentally, or analogically, in order to elaborate the corresponding mathematical symbolism using arithmetical operations (Fagnant, 2005). This last step is called mathematical modelling (Verschaffel & de Corte, 2005). Then, the child will have to carry out the calculations to obtain the final result and to evaluate this result with regard to the initial situation and the question asked. If the problem requires several steps, students need to identify the main problem and the sub-problems and plan the different steps that are needed and execute them in the right order.
Research has shown that the major challenge in word problem solving is the mathematical modelling step. Indeed, different word problems which are solved using the same arithmetic operation (for example, 8 – 5) may lead to dramatically different performances according to the sentences used to present the problem. Typologies that differentiate between the semantic structures of the problems have been proposed.
Research has shown that word problem solving is challenging for children with math learning difficulties, even when the calculation errors are not taken into account. This is especially the case for those who also suffer from associated reading difficulties (e.g., Fuchs & Fuchs, 2002). Hopefully, word-problem tutoring can be used efficiently with children with math learning difficulties (Fuchs, Powell, Seethaler et al., 2009). The use of schemas is especially helpful for students to build a correct representation of the problem (Jitendra, Griffin, Haria et al., 2007).
Based on these considerations, we propose concrete guidance on how to assess word problem abilities in children and how to analyse the origin of the difficulties. Then, in the last section, we give very practical tools on how to help students to solve verbal problems by using a developmentally based progression, schemas to support mathematical modelling, and the use of a heuristic. Concrete examples are then provided.
