Academic journal article International Electronic Journal of Elementary Education

Errors Made by Elementary Fourth Grade Students When Modelling Word Problems and the Elimination of Those Errors through Scaffolding

Academic journal article International Electronic Journal of Elementary Education

Errors Made by Elementary Fourth Grade Students When Modelling Word Problems and the Elimination of Those Errors through Scaffolding

Article excerpt

Introduction

The PISA survey has become an influential factor in reforming educational practices (Liang, 2010) and making decisions about educational policy (Yore, Anderson, & Hung Chiu, 2010). PISA results showed that the competencies measured in PISA surveys are better predictors for 15 year-old students' later success (Schleicher, 2007). One of the skills measured in PISA is mathematical literacy, which can be defined as "turning real-life problems into mathematics" and "interpreting existing knowledge and adapting it to reallife" (Blum & Niss, 1991; Lesh & Doerr, 2003). PISA categorizes problem solvers into seven levels. Those under the first level are the students who cannot solve problems, whereas the first level defines the students who can solve routine problems when the question is expressed clearly and all the required information is provided for solution. The second category defines the students who can reason simple relations that are evident at the first glance. The third level and above express the students who can adapt mathematics to reallife situations. PISA (2015) revealed that 45.9% of the high school students trained in OECD countries are below the third level. These results show that approximately half of the high school students in OECD countries have trouble in solving real life problems. This problem was also observed during elementary school years in some studies (e.g., Verschaffel, Greer & De Corte, 2000; Verschaffel, De Corte & Vierstraete, 1999; Xin, Lin, Zhang & Yan, 2007).

Turkish Ministry of National Education (2005) emphasized problem solving, training of problem solving strategy and skills of modeling sense-making problems in mathematics curriculum from the first years of elementary school. However, despite a strong emphasis in the curriculum, PISA (2015) revealed that 77.6% of Turkish high school students cannot solve sense-making problems. In their studies, Anderson (2010), Grimm (2008), Jordan, Kaplan and Hanich (2002) stated that it becomes harder to furnish students with problem solving skills at later ages if these skills haven't been acquired at early ages. On the other hand, Wischgoll, Christine and Reusser (2015) advocated the idea that "Errors are indicators of learners' misunderstanding. While learners are making errors, the gaps in their understanding become apparent, and learners gain understanding by bridging these gaps. Wischgoll and others (2015) regards errors as opportunities rather than disadvantages and suggests that knowing the obstacles before skill development will contribute to the studies towards skill development. In this context, it has been decided to conduct a study to determine the errors in problem solving process and to conduct the study on elementary students since problem solving is a skill that should be acquired at early ages. Afterwards, the problem type to be used in this study has been determined.

In literature, problems are divided into two: routine (exercise-type) and non-routine problems (sense-making problems) while non-routine problems are again divided into two: those with closed-ended answer and those with open-ended answer (Akay, Soybaş & Argün, 2006; Foong, 2002). According to Altun (2007), the question "Ali buys2 pencils, one at 3 TL, how much TL does he pay?" is a routine while the question "One pays 3 TL to divide an iron bar into two, how much TL is paid to divide the iron bar into four?" is a closed-ended non-routine problem. While it is simply enough to form 3x2 equation for solution in the former problem, thinking that 3 cuts are required to divide the iron bar into four, 3x3 equation should be formed in the latter, which demands real life knowledge to solve nonroutine problems. Whereas the iron bar question is close-ended since it has one answer, the question "A school with 325 students wants to take its students on a picnic by buses with 50 seats each. How many buses are needed to take all the students on a picnic? …

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