STUDENTS’ MEASUREMENT EXPERIENCES AND RESPONSES TO LENGTH COMPARISON, SERIATION AND PROPORTIONING TASKS Prajakt P. Pande, Jayashree Ramadas Homi Bhabha Centre for Science Education, TIFR, Mumbai, India prajaktp@hbcse.tifr.res.in , jr@hbcse.tifr.res.in Measurement is central to the practice of science and should be to science learning as well. Seen from the perspective of science, measurement essentially involves movement from qualitative to quantitative accounts of phenomena. We propose that qualitative experiences of attributes of objects could develop into quantitative measures through some intermediate steps like comparison, seriation and use of a referent. We observed 6 students’ measurement experiences and responses to a sequence of questions and tasks on length measurement, starting from experiencing the attribute qualitatively to quantifying it through these steps. INTRODUCTION Difficulties in the teaching and learning of measurement are well documented in the mathematics education literature (Hiebert, 1984; Bragg & Outhred, 2000; Barrett, Jones, Thornton & Dickson, 2003). This research problematizes measurement as an adult skill to be taught to students while taking account of their difficulties in performing the required tasks. Historically however, measurement arose out of certain needs, admittedly of the adult world, which eventually helped shape the development of science. The underlying motivation, whether arising from commerce, communication or science, was to move from a qualitative understanding of the world to a quantitative one. We suggest that in children too this transition should be seen from a developmental perspective, driven by real-world experiences and actions on the world. The Piagetian concepts of classification, comparison and seriation are used in this paper to frame pre- measurement tasks for students in the primary school. The students' responses are interpreted in terms of epistemic actions. MEASUREMENT IN SCIENCE Quantification and measurements are central to discoveries and inventions in science and technology. Measurements are important in testing scientific theories or proposing new ones (Kuhn, 1961). Quantitative techniques bring uniformity and universality to the data and their interpretations, reduce distances in communication and thus, contribute objectivity to the practice of science (Porter, 1995). Scientific theories and explanations have not always been quantitative. Quantification of time, space and weight emerged out of practical demands that forced an attention to numerical measurements and calculations (Crombie, 1961). For Aristotle, ‘qualitative’ and ‘quantitative’ were distinct categories of phenomena and his explanations were largely based on classification. Although Aristotle predicted some quantitative relationships, the predictions did not aim for measurement and calculation. Grosseteste and Bacon in the 13 th century began characterizing the Aristotelian ‘nature’ mathematically. Medieval Platonists, unlike Aristotle, looked for explanations not in immediate experiences but in theoretical concepts capable of quantification. In the 16 th century, Galileo’s contributions to measurement through his experiments set a milestone in the history of measurement in science (Crombie, 1961). Kepler, Galileo and later Newton contributed to the dynamics that has influenced, to a great extent, the nature of physical science. Gerard (1961) describes how historically scientific practices in biology moved towards quantification. Sense experiences give us direct qualitative understanding of the objects around. We tend eventually to classify those sensed objects into categories (analogous with observation and