Fifth-grade students’ production of mathematical word problems

Abstract

Mathematical word problems challenge students significantly, as empirical studies have shown (e.g., Bush & Karp, 2013; Lewis & Mayer, 1987). Difficulties mostly arise from two aspects, mathematical characteristics, and linguistic structure. Mathematical characteristics of the word problem, such as number size, number and complexity of required operations, and applicable strategies, increase problem difficulties. While on the linguistic side, semantic as well as syntactical characteristics of word problems add to the difficulty (for an overview, see Daroczy et al., 2015). Besides these factors, it is building a mathematical model based on a situation described in a text that is a main difficulty to identify in empirical research (Jupri & Drijvers, 2016; Leiss et al., 2010; Maaß, 2010). We use the term “situation” to refer to a context, which serves the purpose of exemplifying a concept or set of related concepts. As a situation is related to a specific mathematical conceptual field, it formulates a mathematical problem that requires a predictive response. Thus, situations go beyond stimuli, which cause a specific behavior, but are rather typical settings in which mathematical concepts become visible. Situations can be given by illustrations and also by contextual descriptions with mathematics concepts embedded. While research on word problems has focused on contextual descriptions of situations, this chapter aims at investigating how children produce word problems from engaging with illustrated situations. Children encounter word problems that contextualize a more, or less, complex mathematical task in a real-world situation in different ways (Verschaffel et al., 2000). A typical, simple word problem is: “Alex has 3 packages of chocolate. In every package there are 5 pieces. How many pieces of chocolate does Alex have in total?” In this example, the encoded arithmetic task (3*5 = ?) is rather transparent in the word problem, as all numbers are given and the multiplicative structure is highlighted by cue words or phrases (here: “in every”) (LeBlanc & Weber-Russell, 1996). Jupri and Drijvers (2016) report that finding all these cue words and phrases is a main obstacle for students while mathematizing a situation. In such tasks, the real-world context often appears to be designed for the task, thereby casting the word problem’s authenticity into doubt