Context-based mathematics tasks in Indonesia: Toward better practice and achievement

Abstract

The Indonesian national curriculum mandates that mathematics education must be relevant to the needs of life and should offer students opportunities to develop the ability to apply their knowledge in society. Furthermore, there are educational movements in Indonesia that promote the application of mathematics and place a premium on using context-based tasks; see the projects Pendidikan MatematikaRealistik Indonesia (Indonesian Realistic Mathematics Education) and Pembelajaran Kontekstual (Contextual Teaching and Learning). Nevertheless, the results of the Programme for International Student Assessment (PISA) studies showed that Indonesian students have poor performance on context-based tasks. Therefore, this PhD research was aimed to get a better insight into the teaching and learning of context-based mathematics tasks in Indonesia. For this research four studies were carried out. The first studyinvestigated what difficulties Indonesian students experience when solving context-based tasks. For this purpose, an error analysis was conducted for which a framework was developed on the basis of Newman’s error categories and the stages of problem modeling. The error analysis revealed that Indonesian students mostly had difficulties with comprehending context-based tasks and transforming a task into a mathematical problem. To identify possible reasons for these difficulties, in the second and third studyit was investigated whatopportunity-to-learn to solve context-based tasks is offered in Indonesian mathematics textbooks and teachers’ teaching practice. It was found that the students’ difficulties corresponded to the opportunity-to-learn the students got. It was revealed that the Indonesian textbooks contain only a very low number of context-based tasks. Moreover, most of these tasks contain precisely the information that is needed to solve atask. Thus, students do not get experience in selecting relevant information. With respect to students’ difficulty in transforming real-world problems into a mathematical problem, it was found that most context-based tasks in Indonesian textbooks used camouflage contexts and provided explicit suggestions about the mathematical procedure for solvingthe tasks. Finally, in the fourth study it was investigated how the performance of Indonesian students on context-based tasks can be improved. In a field experiment,students were provided with opportunity-to-learn which comprisedtwo components: a set of context-based tasks and a consultative teaching approachincluding giving metacognitive prompts. The results showed that providing students with such opportunity-to-learn improved students’ ability to comprehend context-based tasks, in particular the ability to select relevant information. On the basis of the findingsthree recommendations are given for teaching context-based tasks. The first recommendation is to include more context-based tasks in the learning materials; especially context-based tasks that use relevant and essential contexts, have superfluous or missing information, and do not explicitly signify what mathematical procedure is suitable. The second recommendation addresses the teaching practice; that is,usinga consultative approach and making use in the teaching practice of the knowledge about students’ difficulties. The third recommendation is to pay attention in teacher education and professional development to teachers’ beliefs and their knowledge about context-based tasks, because these two aspects are essential for selecting good tasks (or designing them) and creating learning opportunities for students.