Approching the concept of atmospheric pressure : an interview based on Torricelli ' s barometer

The ambition of our study is to highlight spontaneous reasoning involved in hydrostatic problems and to identify key steps in students' learning processes that could be useful for teaching hydrostatics. More specifically, this article aims at observing and modifying the spontaneous reasonings involved in the interpretation of Torricelli's experiment (the mercury barometer). Our study consists of three forty-minute interviews during which several experiments are either performed or presented to a student. The sequence of experiments has been designed by taking into account the History of Sciences, especially regarding the role of the atmospheric pressure. The analysis of the interviews confirms a marked tendency towards localized reasoning established in previous research, while clarifying its nature : according to the students, the test-tube mercury either floats on that of the container or is drawn upwards by the effect of capillarity. Our study also modulates previous research about the concept of vacuum, both in itself, and applied to Torricelli's experiment and suction pumps: whereas they consider that this vacuum cannot physically exist, they spontaneously use the concept to interpret and predict the phenomenon of suction. Also, the students retain a notion of “vacuum” corresponding to a total absence of matter. The interview designed and carried out for the experiment aims not only to observe students' difficulties, but also to modify them. For two of the three students, the sequence does indeed contribute to an understanding of the significance of the role played by the air surrounding the tube. This study is also an interesting example of the role that History of Science can play for Teaching Sciences in anticipating reasoning strategies or difficulties on one hand and providing ideas to modify reasoning on the other. Introduction The ambition of our study is to highlight spontaneous reasonings involved in hydrostatic problems and to identify students' key learning steps, in order to contribute to the understanding of problems involved in teaching hydrostatics. In order to do this we chose a problem which is both classic and rich: Torricelli's experiment. Torricelli's barometer experiment consists of a one-meter glass tube filled with mercury, stood upside-down in an unsealed container also filled with mercury. This experiment is a common illustration of the hydrostatic equation ΔP = ρgΔh. However, as is the case in most of the other problem of hydrostatics, several of its more complex physical characteristics are masked by the mathematical simplicity of this equation. The aim of this study is firstly to observe students' strategies in their interpretation of Torricelli's experiment. Given previous research results which strongly suggest that students fail to understand the experiment from a systemic point of view, we aim to identify more closely their localized reasoning. Secondly, we aim to develop a strategy which will allow teachers to modify their students' reasoning, leading them towards a systemic point of view. Three individual interviews were carried out. They consisted of several experiments which were either presented to the students or performed in front of them. The sequence of experiments was designed by considering not only previous research about students' spontaneous reasoning concerning Torricelli's experiment, but also the historical development of the question, and of scientists' responses. Historical guideline Ancient Greek scientists considered the phenomenon of suction to be a consequence of the Aristotelian doctrine, 'Nature abhors a vacuum'. However Galileo reported, in Two new sciences (1638), that a suction pump could not lift water more than about 10 meters. In 1644, Evangelista Torricelli transformed the technical problem of the water-pumps into a scientific question by proposing a new experiment using mercury. Torricelli suggested two new hypotheses : firstly, that the space above the mercury is a vacuum; secondly, that air has mass. These hypotheses led to the interpretation that it is the weight of the air outside, pushing on the mercury in the container, which maintains the height of the column. Each of Torricelli's two assumptions raised controversies among the scientific community and several experiments were designed to assess them. These consisted in modifying the environment of Torricelli's device: in Pascal's experiment (1648), it is placed at different heights in the atmosphere [1]; in Boyle's experiment (1660), it is performed in a suction device [2]; in Mariotte's experiment (1676), it is placed at different depths in water [3]. It is the explicit analogy between water and air established in Mariotte's experiment which definitively confirms Torricelli's interpretation. Research background Several studies analyse students' reasoning concerning aspects of the experiment. The unifying concept of "fluid" doesn’t always seem to be operational for students: although most rightly assert that pressure increases with depth in liquids [4], some incorrectly think that atmospheric pressure increases with altitude [5]. However, some difficulties arise which apply both to liquids and gases: the pressure in a fluid is usually confused with the forces exerted by the fluid [4]; pressure is often associated with the volume of fluid surrounding an immersed solid, and not only with depth (or altitude) [6], and its effects are widely seen as directional (usually down) [7, 4, 8]. “Vacuum” is another problematic concept for students. While a high percentage of young people struggle to admit the existence of an absolute vacuum [9], any degree of “vacuum” is commonly considered to have mechanical properties, most importantly, that of aspiration [10, 11]. Elements of the History of Science can be useful for anticipating students' difficulties and providing ideas for teaching sciences. In 2009, Hosson & Caillarec [12] used Pascal's experiment to study students' understanding of Torricelli's experiment. They asked the students why the height of the column of mercury changed at different altitudes. Over three-quarters of the 128 students surveyed did not explicitly take the air outside the device into account in their explanation. Indeed, instead of using a systemic point of view, they tended to use localized reasonings, based on the following elements of the experiment: the content of the space above the mercury, which, according to the students, would dilate or contract; the column of mercury which would dilate or contract, like in a thermometer; and the mercury in the container which would support the mercury in the tube. In the end, as was the case for scientists in the 17th century, the study found that Pascal's experiment alone was not sufficient to convince students of the mechanical influence of the air. Hence, two questions emerged: firstly, how to confirm and complete these results, and secondly, how to lead students to take into account the mechanical effect of air. Like the previous study, ours will be based on a framework drawn from the History of Science: this time, using Boyle's experiment to illustrate and clarify Torricelli's experiment to students.