La cohérence conceptuelle d’étudiants collégiaux en mécanique
newtonienne et en métrologie

This thesis evaluates the coherence of the conceptual network demonstrated by college students in life and applied sciences. This evaluation was based on the analysis of Burt tables issuing from multiple choice questionnaires, on the creation and careful examination of a novel tool, the matrix of specific discrimination coefficients, which will be described in the main text, and on the qualitative analysis of actual laboratory work of students doing an experimentation. At the completion of this project, four research axis have been explored. 1) What is the conceptual coherence demonstrated in Newtonian mechanics? 2) Is the mastery of uncertainty quantification related to the development of logical thinking or to mathematical competency? 3) What is the conceptual coherence demonstrated in the quantification of experimental uncertainty? 4) What are the concrete procedures utilized by students to quantify experimental uncertainty in a semi-directed laboratory context? The main conclusions that emerged from each axis of research can be summerized as follow. 1) The most prevalent erroneous conceptions are not solidly set in a rigid conceptual network. For example, a student successful in a question about Newton’s third law (the most difficult subject of the Force Concept Inventory) is just slightly more likely to succeed in another related question than the other participants. Many pairs of questions displays a negative specific discrimination coefficient demonstrating a weak conceptual coherence in pre-test and a somewhat ameliorated conceptual coherence in post-test. 2) If a small proportion of students has demonstrated marked deficiencies in questions related with control of variable and in those related to the relationship between the graphical display of experimental data and a mathematical model, the majority of students can be considered as adequately mastering those subjects. However, almost every student demonstrated a lack of mastery of concepts underlying the quantification of experimental uncertainty and the propagation of uncertainty (heretofore referred to as metrology). No statistically significant correlation has been observed between the three main topics suggesting that they are largely independent cognitive abilities. Burt table has demonstrated a greater degree of conceptual coherence between control of variables questions than suggested by Pearson correlation coefficients. Equivalent question in the topic of metrology did not permit to demonstrate a clear conceptual coherence. 3) Analysis of a questionnaire entirely devoted to metrology has shown erroneous conceptions caused by prior learning (didactical obstacles), erroneous conceptions based on intuitive models and a lack of global comprehension of metrological concepts although some appear to be almost acquired. 4) When doing real experiments in semi-directed laboratory, students demonstrated the same difficulty identified in the questionnaire of 3) which could interpreted as corroborating previously obtaine results. However, many unanticipated behaviors related to measurement were observed that could not have been anticipated solely by analyzing answers in the multiple-choice questionnaire. Interviews immediately following each semi-directed laboratory permitted the participants to detail certain aspects of their metrological methodology. Most notably, the use of repeated measurement strategies, their « spontaneous » strategies to quantify uncertainty, and their explanation of numerical estimates of reading uncertainties. Overall, uncertainty propagation algorithms were adequately employed. Many erroneous metrological conceptions seem to resist strongly to be modified by learning. Among others, assignation of the resolution of a digital scale as the uncertainty value and the lack of stacking strategies to diminish uncertainty. The conception that a numerical value cannot be more precise than the tolerance of an instrument seems firmly set.

Keyphrases: Burt tables, Conceptual coherence, Experimental uncertainty, Laboratories, Metrology