Superposition of electric fields and causality
Sylvie Rainson, 1995. 
This study focuses on : 
•	Undergraduate students' ways of reasoning about superposition of electric fields. 
•	The design and evaluation of a teaching sequence on this topic, at this level. 
The principle of superposition stipulates that all the electric charges present in a system contribute to the total field according to the same law: Coulomb's law. It is essential to take this principle into account if one is to reach a unified comprehension of electrostatics and electric circuits. The research is based on the hypothesis that students have difficulties in using this principle, which are linked to a narrow conception of causality. This hypothesis shapes the inquiry about students' ways of reasoning, and some "levers" of the teaching strategy. 
After a preliminary phase of interviews, paper and pencil questionnaires were used to probe students' views. Two obstacles to a proper comprehension of superposition of electric fields were found: -students often have difficulties in admitting the existence of a field in a material where charges cannot move, as if the following statements hold: "field only if mobility", or "no effect, therefore no cause"; -many students ascribe a causal content to literal relationships, thus excluding causes which are not "visible" in the formula. For instance, the field near a conducting material is given by the formula E = 'sigma'/'epsilon-zero' n, and students often think that only the charges on the conductor are responsible (via the surface charge density s) for this field, thus forgetting the direct contribution of external charges. This is the : "cause only in the formula" obstacle, sometimes reinforced by the idea that there is "one cause only". 
An analysis of 19 French textbooks shows that these obstacles are not commonly taken into account. 
The teaching sequence proposed to foster a better understanding of this topic was intended for a normal teaching context: same syllabus, duration (15 hours) and (very rigid, in this case) boundary conditions in test group and control groups. It was built after a process of successive adjustment (three years). In the final version of this sequence, the causal aspects of students' reasoning are strongly called on, in particular by the frequent used of situations in which some changes occur. The intention is to first motivate students to use a causal reasoning, and then to help them overcome the usual limitations linked to the preceding obstacles. 
The evaluation of the sequence was done by paper-and-pencil questionnaires, one test group (each year) and four control groups (each of about 35 students) being used. The "conceptual profiles" got with the final version of the sequence show that the corresponding levers are relevant, and permit about one third of the test students (against less than 10%) to reach the conceptual target. The persistence of some obstacles is also shown. 
A discussion of the role of causality and inherent difficulties in a unified understanding of electrostatics and electric circuits ends the thesis.