The aim of this thesis was to explore several important aspects of word problems: the nature of word problems used in school mathematics textbooks and the difficulty level of different types of word problems. The specific goals were to investigate students’ performance when solving various types of word problems and to determine whether students’ word-problem skills and their beliefs about word problem-solving can be improved by enriching word problems used in mathematics teaching. To achieve the goals, this thesis reports on five original studies, as follows.

Study I showed a comparison between the characteristics of word problems presented in Thai and Finnish school mathematics textbooks. The analyses included 1,565 word problems from a series of second- to fourth-grade Thai and Finnish mathematics textbooks. The overall results show that the nature of word problems used in Finnish textbooks vary from Thai textbooks in many ways. Finnish textbooks contain more multistep word problems, while in Thai textbooks, one-step word problems appear more frequently. Thai textbooks have a smaller percentage of repetitive sections (ones that include only the same type of problems) than Finnish textbooks. In both countries, the percentage of word problems requiring the use of realistic considerations is extremely low, less than five percent of the total.

Studies II and III presented the impacts of a Word Problem Enrichment (WPE) programme, developed to encourage teachers to use innovative self-created word problems to improve student mathematical modelling and problem-solving skills. Participants comprised 10 classroom teachers and their 170 students from fourth and sixth grades, from elementary schools in southwest Finland. In Study II, the intervention effectiveness on student problem-solving performance was investigated. The results suggested that enriching word problems used in mathematics teaching is a promising method for improving student problem-solving skills when solving non-routine and application word problems. However, it is not known if WPE has an effect on student beliefs about word problem-solving, and how the programme works for students with different initial motivation in learning mathematics. Study III examined the effectiveness of WPE on student beliefs about word problem-solving by using latent profile analysis (LPA) and structural equation modelling (SEM) to analyse relationships among the different cognitive, motivation, and belief factors. Results indicated that the impacts of WPE are various depending upon the initial motivation level of students. The effects of WPE on student beliefs appeared only in students with a low initial motivation level, while its impacts on student problem-solving performance were found only in students with a high initial motivation level.

Studies IV and V were conducted to examine hypotheses regarding (1) the dimensionality of students’ performance on word problems and (2) difficulty level of three types of word problems: routine, non-routine and application word problems by utilizing item response theory (IRT) modelling. The data used in Study IV was collectedas part of the Word Problem project (Studies II and III). Participants comprised 170 fourth- and sixth-grade students. Students’ problem-solving performance was assessed with a word problem-solving test, including five word problems: one routine, three non-routine, and one application. The results of Study IV show that students’ performance on word problems can be seen as a unidimensional construct that denies the original assumption. The results of the IRT model indicate that the theoretically demanding application word problem has a higher difficulty level than non-routine and routine word problems.

Nevertheless, the results are obscure if this application word problem (used in Study IV) is harder because of its demand for realistic considerations or other possibly relevant factors (e.g. decimal numbers included, division, more problem-solving steps required). Moreover, the sample size of Study IV could be considered relatively small for this kind of complicated IRT model. Therefore, Study V uses a larger sample size and a bigger set of word problems with more variety in application and non-routine word problems. The data used in Study V was collected as part of the Quest for Meaning project. Participants comprised 891 fourth-grade students (446 boys and 445 girls) from different elementary schools situated in cities, small towns, and rural communities in southern Finland. On the same lines as Study IV, the results of Study V indicated that students’ performance on word problems can be seen as a unidimensional construct. Concerning item difficulty level, the results of the IRT model do not show a clear distinction among word-problem types and reject the hypothesis that application word problems have a higher difficulty level than non-routine word problems. Some non-routine word problems appear to be more difficult than the application word problem, even though other characteristics of these two types of word problems were very similar (e.g., they required the same type of operation and the same number of problem-solving steps).

The results of the five studies reveal that even though the mathematics textbooks were highly regarded in Thailand and Finland, most given word problems frequently include a simple goal without demanding any realistic considerations. These results strongly suggest that more innovative application word problems are definitely needed in classroom mathematics. In our study, we developed the WPE to encourage teachers to develop their own meaningful non-routine and applications word problems, and to use these self-created word problems to improve mathematical modelling and students’ word problem-solving performance. The results show that WPE is a promising approach to improve not only student problem-solving skills but also student beliefs about word problem-solving. The impacts of WPE are different depending upon students’ initial motivation level. The impacts of WPE on student beliefs were found only in students with a low initial motivation level, while its impacts on student problem-solving performance were found only in students with a high initial motivation level. These results suggest that in classroom practice, it is important that teachers provide enough support for students to be more confident and feel less overwhelmed when facing non-routine and application word problems. Teachers should be aware of differences of word-problem types and utilise this information in planning how to scaffold students’ word problem-solving by giving word problems based on their difficulty level.