One of reasons why fractions are a topic which many students find difficult to learn is that there exist many rules calculating with fractions. In addition, students have been trained for the skills and should have mastered such procedures even they do not ‘understand’. Some previous researcher confirmed that the problem which students encounter in learning fraction operations is not firmly connected to concrete experiences. For this reason, a set of measuring context was designed to provide concrete experiences in supporting students’ reasoning in addition of fractions, because the concept of fractional number was derived from measuring. In the present study we used design research as a reference research to investigate students’ mathematical progress in addition of fractions. In particular, using retrospective analysis to analyze data of fourth graders’ performance on addition of fractions, we implemented some instructional activities by using measuring activities and contexts to provide opportunities students use students’ own strategies and models. The emergent modeling (i.e. a bar model) played an important role in the shift of students reasoning from concrete experiences (informal) in the situational level towards more formal mathematical concept of addition of fractions. We discuss these findings taking into consideration the context in which the study was conducted and we provide implications for the teaching of fractions and suggestions for further research.
Keyword: measuring context, addition of fractions, design research, emergent modeling