Academic journal article The Mathematics Enthusiast

Linking Pre-Service Teachers' Questioning and Students' Strategies in Solving Contextual Problems: A Case Study in Indonesia and the Netherlands

Academic journal article The Mathematics Enthusiast

Linking Pre-Service Teachers' Questioning and Students' Strategies in Solving Contextual Problems: A Case Study in Indonesia and the Netherlands

Article excerpt

Introduction

There is now a widespread body of knowledge that identifies the potential and challenges of using contextual problems to advance children's learning of mathematics. Some studies have demonstrated that context plays a significant role as a starting point of learning for students because it allows students to start with informal strategies and offers opportunities for students to solve the problems at different levels of formality (Freudenthal, 1983, 1991; Gravemeijer & Doorman, 1999; van den Heuvel-Panhuizen, 1996, 2000; van den Heuvel-Panhuizen & Wijers, 2005). This was also reported in earlier studies from Indonesia where the use of contextual problems supported students to develop mathematical understandings (Dolk, Widjaja, Zonneveld, & Fauzan, 2010; Sembiring, Hadi, & Dolk, 2008; Widjaja, Dolk, & Fauzan, 2010). However, existing studies have also revealed the challenges of incorporating contextual problems into students' learning for two main reasons. Firstly, students bring different experiences and prior knowledge to the classroom. This may influence the students' interpretations of the contextual problem and lead them to solve the problem in an inappropriate way (Boaler, 1993; Carraher & Schliemann, 2002; Widjaja, 2008, 2013; Wijaya, van den Heuvel-Panhuizen & Doorman, 2015). Secondly, the way students solve contextual problems depends on how the students have been taught (van den Heuvel-Panhuizen, 2005).

Since 2000 a movement called 'Pendidikan Matematika Realistik Indonesia ' (PMRI) was adapted and implemented in Indonesia. This was inspired by Realistic Mathematics Education (RME) which was developed in the Netherlands (Freudenthal, 1983, 1991; Sembiring, Hadi, & Dolk, 2008; Sembiring, Hoogland, & Dolk, 2010). PMRI advocates the teaching of mathematics which moves away from teaching based on symbolic manipulation. Studies incorporating the use of contextual problems in Indonesian classrooms confirm this assertion (Widjaja, Dolk, & Fauzan, 2010; Dolk, Widjaja, Zonneveld, & Fauzan, 2010). Nevertheless, the bottom up approach in the PMRI movement implies that these changes are not mandated. As a result the PMRI movement has not been implemented nationally and is not reflected in Indonesian national curriculum. To date there are still limited opportunities for students to engage in making sense of mathematics through contexts in Indonesian textbooks (Fauzan, Plomp & Gravemeijer, 2013; Wijaya, 2015; Zulkardi, 2002). Similarly, solving contextual problems in multiple ways is another approach which is not common in Indonesia. Many concepts in mathematics are introduced without context, nor do they enable students to explore multiple meanings of the concept. For instance, fractions are only introduced as parts of a whole. Fractions as quotients and ratios are excluded. This is not in line with the RME principles where fractions are introduced through various real-life contexts such as fair sharing, measurements and money so as to enable students to understand the relationship between all the concepts involving fractions. According to RME principles, students are expected to learn fractions in informal ways using their "own investigations " before moving on to more abstract and formal mathematics (van den Heuvel-Panhuizen & Wijers, 2005).

This case study is based on teaching experiments conducted by volunteer Indonesian and Dutch pre-service teachers using contextual problems on fractions with Grade 4 children in Indonesia and the Netherlands. The study aims to examine how pre-service teachers' questioning influence students' reasoning in solving contextual problems with fractions. Whilst a number of cross-national studies on the topic of fractions have been documented (Alajmi, 2012; Cai & Wang, 2006; Moseley, Okamoto, & Ishida, 2007; Mosvold, 2008; Son & Senk, 2010; Yim, 2010), to date there is no study where pre-service teachers examine their own questioning as a way to engage students when solving contextual problems about fractions. …

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