1 Quantity/potential-related elementary concepts in primary school teacher education Federico Corni, Enrico Giliberti, Cristina Mariani Faculty of Education, University of Modena and Reggio Emilia, Italy Abstract Primary school teachers need a training in physics robust enough to enable them to understand phenomena and new and complex situations they encounter as well as to answer the children questions and to design teaching activities. In initial teacher education, it must also be taken into account the limited scientific and mathematical background of students enrolling in university courses. Starting from an analysis of the misconception to construct a formal knowledge that teachers need to make then non-formal to teach children, is ineffective. One more appropriate way seems to be based on research in the fields of cognitive sciences that focuses on the simple structure of imagination that are used to interpret everyday phenomena. The contents of the Physics course of the Degree in Primary Education of the University of Modena and Reggio Emilia have been structured in order to highlight the common conceptual structures, and the specific differences, between the various contexts of the discipline. The elementary concepts such as quantity, storage, capacity, potential, current and resistance have been clarified, differentiated and built qualitatively though rigorously through a series of examples taken from everyday experience and known contexts. Analogy was introduced in the study of fluids, electricity, motion and heat, as a result of the use of the same elementary concept to interpret phenomena and processes. In this contribution we present the structure and the contents of the course according to this approach, and the results of the analysis of the worksheets about motion filled by students. Introduction One of the main effort in the training of primary school teachers is to develop some basic skills, both in the scientific understanding of the world and in the methodological abilities. Scientific concepts are usually not well developed in students at a degree level who are going to became primary school teachers, due to poor results in previous secondary school curricula. Our proposal aims to develop an effective understanding of the physical phenomena coming from everyday life experience, but with a special focus on few elementary concepts and not relying on a large knowledge of scientific laws and principles, which, in most cases remain misunderstood and lead to misconceptions. To describe and explain the natural phenomena, a teacher has to rely on some elementary concepts, which have to be few, clearly identifiable and recognizable in different contexts. The same elementary concepts are suitable to be understood and employed by children, considering the different age levels, helpful for the didactical transposition and useful to plan and perform class activities. In this way the same understanding skills can be fostered in children, helping them to recognize elementary concepts in different contexts and situation, helping the use of some key-words expressing
2 the same concept, and forming a language with which children can compare their opinions and make predictions. We found suitable to this approach the images at the basis of scientific thought identified within the theory of Force Dynamic Gestalts having the aspects of quantity or substance, quality or intensity, and force/power or energy . The tools for this identification can be found mainly in cognitive linguistics, particularly in Talmy's  theory of embodies schemas of causation (called the theory of Force Dynamics by Talmy). Our effort is to connect both with the everyday experience and with the curriculum of primary school. In particular we focus on the elementary concepts of quantity, difference of potential, capacitance, current, and resistance. To introduce and discuss about elementary concepts, analogy is often used. However, it is worth distinguish between the use of analogy as a way to understand an unknown phenomenon by projecting a known context, and the recognition of analogies among contexts due to the application of the same elementary concepts. In the first case analogy is a knowledge tool (analogical thought), in the other case it is a support for the thought based on elementary concepts. In this paper we analyze the training activities carried on with students attending the second year of the degree course for Primary School Teachers in The activities took place during a 5-weeks/30 hours course and were performed as a series of 3 paths on the contexts of water, electricity and motion, respectively. The last path about motion, assumed to be the most difficult one, is analyzed here to highlight the role of elementary concepts and of analogy in describing and understanding motion-related phenomena. Research questions Our research is devoted to the role of FDG as basis for scientific description and interpretation, pointing out advantages and disadvantages related with their use. We are investigating if and how the FDG of quantity, quality and force-power can be a base for a scientific understanding of phenomena at the level of primary school, both for teachers and for pupils. In this paper in particular we try to answer the following research questions referred to students of the degree course for Primary School Teachers: Are FDG-related elementary concepts adequate for students becoming primary school teachers? Are some elementary concepts more useful than others? The experimentation The main goal of the training activities is to introduce and to develop the use of elementary concepts such as quantity, difference of potential, capacitance, current, and resistance applied to different contexts, suitable both for students understanding and for their future teacher work. The paths consisted, according to the Prediction-Experiment-Comparison (PEC) cycle, in performing series of ex-cathedra experiments, preceded by individual motivated prediction, followed by comparison of the prediction with the results, and, eventually, correction. The three paths have been preceded by an introduction of the elementary concepts with reference to everyday life phenomena and from contexts not directly connected to the scientific world.
3 1) Introduction of the elementary concepts The aim of the activity was to recall and differentiate the elementary concepts with reference to everyday experience, helping to recognize these concepts as already part of student s knowledge. The concept of quantity have been analyzed in relation to many different examples of countable and mass substances (e.g. people or water) and students have been asked to propose their own examples. Then a distinction with the concept of intensity (corresponding to the generalized concept of potential) was made: the idea that some qualities can be linked with a quantity, such as height of books in a library, water pressure etc.. Related with the previous two is the concept of capacitance, expressing how a quantity changes its quality when disposed into a container, or, complementarily, how a container affects the quality of a contained quantity (e.g. water in different types of container). The concept of difference of potential followed: quality level difference is the driving force for quantity motion (e.g. water under pressure difference). Then the concept of current expresses the amount of quantity per unit time that passes through a certain point (e.g. people that passes through a door). Finally, the concept of resistance has been introduced as the control parameter for the current. 2) Didactical path about fluids The second activity aimed to explore the context of fluids, here water, using the elementary concepts introduced in the first activity to predict, describe and understand 15 simple experiments arranged into a path (see  where the same sequence of experiments is reported, together with the following electricity path). Before the experimental activity, students have been asked to situate the elementary concepts of quantity, difference of potential, current, capacitance and resistance, giving a description with words and with a drawing. The concepts were introduced in the following order: 1) difference of levels of two free water surfaces (pressure difference) as driving force for water flow 2) communicating vessels in equilibrium state and in water dynamic conditions 3) current as the amount of water that flows through a section of a pipe per unit time; the rotation velocity of a fan as a measure of current and level of a free water surface as a measure of local pressure 4) resistance (due to pipes, connections and fans) and its effect on current 3) Didactical path about electricity The third activity aimed to recall the same elementary concepts seen during the previous activities and using them to explain experiments in a context, such electricity, which we suppose that few students were familiar with. Concepts were introduced following the same sequence of the previous activity, but more emphasis was placed on quantity and its potential, because electricity was not directly observable and the potential had to be measured by means of a voltmeter. Besides, new words had to be introduced to identify some objects, unusual for the majority of the students, such as the battery, the voltmeter, the conductors, the open and closed circuit. The concepts were introduced in the following order: 1) difference of potential as driving force for current flow; 2) electrical potential distribution in open and in closed circuits; 3) current as the amount of electricity that flows through a section of a wire per unit time; the intensity of the light of a lamp as a measure of current;
4 4) resistance (due to wires, connections and lamps) and its effect on current. 4) Didactical path about motion The fourth activity aimed to explore a context, probably encountered by most of the student in secondary school, but which is not dealt with in terms of FDG elementary concepts. Momentum corresponds to the elementary concept of quantity. The experiments were made by means of a low friction rail on which carts could move and hit each other. The collisions between the carts occurred either through a spring (that leaves the two carts separated) or using an adhesive strip (that makes the two carts connect and proceed together). Students were also requested to draw an analogous situation in the water context. The steps of the path were slightly different from the ones for water and electricity. Table I reports the list of the experiments with a sketch for every experiment in which the meter represents the velocity. Table I. Step # Situation Sketch of the initial and final situation 1 The cart 1 (on the left) arrives with a certain speed and hits, by means of a spring, the cart 2 (on the right) which stands still 2 As #1 but with a adhesive strip 3 As #2 but with cart 2 having double mass 4 As #2 but with cart 1 having double mass 5 As #1 but with cart 1 having double mass 6 A compressed spring on the cart is released, with no contact neither with another cart nor the wall 7 A compressed spring is relased between two bodies of same mass which stand still 8 As #7 but with the two bodies moving initially at a certain speed
5 9 As #7 but with cart 1 having mass double than cart 2 10 As #8 but with cart 1 having a mass double than cart 2 11 As #7 but with cart 2 having mass double than cart 1 12 As #8 but with cart 2 having a mass double than cart 1 13 As #6 but with the relased spring pushing against the wall 14 As #13 but with the trail over two cylinders allowing it to slide 15 As #1 but with two magnets instead of the spring The idea of conservation has been taken into account, with special care to the identification of the system in which the total amount of momentum is a constant (insulated system). The total amount of momentum can be zero, but also in this case we can make the bodies move by introducing an amount of energy by means of a compressed spring (positive and negative momentum). The velocity represents the generalized potential for motion: momentum is spontaneously transferred from the body with higher velocity to the body with lower velocity. The concept of capacitance as the container of momentum is represented by the inertial mass: bodies with greater mass acquire and loose a certain amount of momentum modifying their speed less than bodies with lower mass. The current is the rate of transfer of momentum from one body to another, that corresponds to the concept of force. Collisions mediated by different springs or magnets facing poles of the same kind transfer the same amount of momentum in different time intervals. Resistance is a less relevant concept for what concerns motion. Data analysis In this paper we analyze in particular the worksheets of the last of the four activities, the path about motion, in which students had to identify the elementary concepts in the specific context, and then, for every step, to write the following elements: - a description of the experiment - the prediction about the phenomenon
6 - the reason for the prediction, using the elementary concepts - the explanation of the phenomenon in terms of cause-effect - after the experiment, in case, the correction of the prediction explaining where and why it was wrong. Figure 1 shows the structure of the worksheet for every experiment of the path. Figure 1. Our assumption is that the elementary concepts show their power and effectiveness if they are able to help students to describe phenomena, to make predictions, to modify their point of view, to help correcting their answer. The motion context is suitable because it is very close to everyday experience, source of possible (well-known) misconceptions, and apparently far from the idea of being interpreted in terms of FDG elementary concepts. For the analysis we focus on: the more used concepts; the more useful ones for understanding; which ones lead to misconceptions or which are helpful to avoid them; if some concepts, such as capacitance, help students in making quantitative predictions. The available data refer to 35 students that began to fill in the worksheets in the classroom during the execution of the experimental steps and that had the opportunity to finish the work at home. Results and discussion Results are discussed referring to some topics, taking into account the number of students and, where needed, the number of steps of the path relevant for that topic. 1) Quantity Momentum, as the product of mass and velocity, is identified as the quantity from all the students. This is a good result considering the traditional way of treating motion at secondary schools in terms of kinematical quantities (position, velocity and acceleration) separated from mass. Very high results the average number of steps (78%), 10.9 (standard deviation 3.2) over 14 (all steps except the 6 th one), in which students explicitly refer to transfer and conservation of momentum, meaning that momentum is consistently identified as a quantity not only at the
7 level of definition. Within the incorrect answers, the most frequent error (though in some cases it could be a problem of language) is the transfer of velocity. In 4 steps (7, 9, 11, 13) the carts are placed motionless in the centre of the rail in contact through a compressed spring and made move in opposite direction after the release of the spring. 14 students over 35 (40%) introduce correctly the idea of negative momentum, that s to say the idea of motion direction. Among these, the average of steps over 4 in which students express this concept is 2.1 (53%). To avoid the idea of creation of motion, students, due to their weak mathematics background that makes it difficult to introduce the minus sign, chose to compare the momentum of one mass with that of the other, and even, sometimes, express quantitative relations. 2) Potential The velocity is identified as the (generalized) potential by 26 students over 32 (81%). Some of the students that do not identify the velocity as the potential, report a formal but abstract definition ( level of motion ), 1 student uses difference of motion and 2 students use difference of speed of the two carts after the collision. 3) Capacitance The capacitance concept referred to inertial mass is explicitly used in the interpretation of the 10 experiments (steps 2, 3, 4, 5, 9, 10, 11, 12, 13, 14) in which carts of different masses are considered in an average of 7.1 (standard deviation 2.2) cases (71%) per student. In the direction of increasing this value, we expect that sometimes students would not repeat the explanations given to quite similar experiments in sequence. 4) Current 11 students over 34 (32%) make considerations on the current of momentum, evidencing the role of the time interval required for the transfer process, and 12 students over 34 (35%) explicit the conceptual correspondence between the momentum transfer through a spring between the two carts (step 1) and the momentum transfer through the magnetic field of two magnets facing poles of the same kind mounted on the two carts (step 15). It is a good result, considering that the concept of current was never mentioned in other parts of the path and the difficulty in distinguishing the two different ways in which momentum is displaced: owned by a moving cart and transferred between two carts through a collision. 5) Quantitative considerations An index of effectiveness and utility of the elementary concepts is evidenced by the inclination of student to make quantitative considerations. Quantitative considerations in predictions or explanations could be made in 8 non trivial situations (case of carts with different masses in steps 2, 3, 4, 5, 9, 10, 11, 12). 33 over 35 students (94%) made quantitative considerations, even if not explicitly requested. They made on average 2.7 over 8 (34%) quantitative considerations, with an individual percentage of correctness of 85%. This result must be related to the poor scientific bases of the students and to their dislike to use any mathematical relation even in easy situations. The two students who made more incorrect quantitative considerations (S26: 3 over 8, 38%; S30: 3 over 5, 60%) are the ones who made superficial and not organic use of the elementary concepts within the path steps. 4 students made wrong predictions because of mathematical mistakes or, more likely, incorrect use of the mathematical language (for example the speed is reduced to 1/3 instead of the speed is reduced by 1/3 ).
8 Conclusions Are FDG-related elementary concepts adequate for students becoming primary school teachers? Are some elementary concepts more useful than others? The FDG-related elementary concepts, due to the high fraction of positive cases, result adequate for students of the degree course for Primary School Teachers. The most useful concepts to explain phenomena related with motion are: quantity, potential and capacitance. These concepts are acquired and used from most of the student and seems to be able to predict and explain phenomena in which motion is transferred, also in case of different masses involved, and also making use of quantitative relations expressed by means of words. Finally, it is worth taking into account the FDG-related elementary concepts of quantity, difference of potential, capacitance, current, and resistance in educational courses for their basic character and general validity, as well for the simplicity of their transfer into educational paths for pupils. References  Fuchs H.U. (2009), Figurative Structures of Thought in Science An Evolutionary Cognitive Perspective on Science Learning, Talk presented to the General Assembly of the Conférence des directeurs de gymnase de Suisse Remande et du Tessin, Mendrisio, September 18, 2009  Talmy, L. (1988), Force Dynamics in language and cognition, Cognitive Science, 12, p  Mariani C., Corni F., Altiero T., Bortolotti C., Giliberti E., Landi L., Marchetti M., Martini A., Experiments and models for physics learning in primary school, in Physics Community and Cooperation: Selected Contributions from the GIREP-EPEC & PHEC 2009 International Conference, Ed. D Raine, C Hurkett, L Rogers (Lulu/The Centre for Interdisciplinary Science, Leicester, 2010), p