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This paper describes a method aimed at pointing out the quality of the mental models undergraduate engineering students deploy when asked to create explanations for phenomena or processes and/or use a given model in the same context. Student responses to a specially designed written questionnaire are quantitatively analyzed using researcher-generated categories of reasoning, based on the physics education research literature on student understanding of the relevant physics content. The use of statistical implicative analysis tools allows us to successfully identify clusters of students with respect to the\ud similarity to the reasoning categories, defined as ‘‘practical or everyday,’’ ‘‘descriptive,’’ or ‘‘explicative.’’\ud Through the use of similarity and implication indexes our method also enables us to study the consistency\ud in students’ deployment of mental models. A qualitative analysis of interviews conducted with students\ud after they had completed the questionnaire is used to clarify some aspects which emerged from the\ud quantitative analysis and validate the results obtained. Some implications of this joint use of quantitative\ud and qualitative analysis for the design of a learning environment focused on the understanding of some aspects of the world at the level of causation and mechanisms of functioning are discussed

The paper presents some reflections and activities developed by researchers and teachers involved in teacher education programs on cultural transposition. The construct of cultural transposition is presented as a condition for decentralizing the didactic practice of a specific cultural context through contact with other didactic practices of different cultural contexts. We discuss the background theoretical issues of this approach and also give an analysis of two examples of cultural transposition experiences carried out in Italy. In particular, by means of qualitative analysis of some excerpts, discussions, and interviews, we show that the contact with different perspectives coming from China and Russia fostered educational practices and reflections on whole number arithmetic education.

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The problem of taking a set of data and separating it into subgroups where the elements of each subgroup are more similar to each other than they are to elements not in the subgroup has been extensively studied through the statistical method of cluster analysis. In this paper we want to discuss the application of this method to the field of education: particularly, we want to present the use of cluster analysis to separate students into groups that can be recognized and characterized by common traits in their answers to a questionnaire, without any prior knowledge of what form those groups would take (unsupervised classification). We start from a detailed study of the data processing needed by cluster analysis. Then two methods commonly used in cluster analysis are before described only from a theoretical point a view and after in the Section 4 through an example of application to data coming from an open-ended questionnaire administered to a sample of university students. In particular we describe and criticize the variables and parameters used to show the results of the cluster analysis methods.

1 People's reasoning is often described as the "running" of the procedures present in their mental models [1-4]. Gilbert and Boulter [5] define expressed models as the external representations expressed by an individual through actions, speech, or writing. We understand "path, or line of reasoning" as the external representation of the mental models used by an individual when they try to describe, predict, or explain the physical world.

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Research in Science Education has shown that often students need to learn how to identify differences and similarities between descriptive and explicative models. The development and use of explicative skills in the field of thermal science has always been a difficult objective to reach. A way to develop analogical reasoning is to use in Science Education unifying conceptual frameworks. In this paper we describe a 20-hour workshop focused on Feynman's Unifying Approach and the two-level system. We measure its efficacy in helping undergraduate chemical engineering students explain phenomena by applying an explanatory model. Contexts involve systems for which a process is activated by thermally overcoming a well-defined potential barrier. A questionnaire containing six open-ended questions was administered to the students before instruction. A second one, similar but focused on different physical content was administered after instruction. Responses were analysed using k-means Cluster Analysis and students' inferred lines of reasoning about the analysed phenomena were studied. We conclude that students reasoning lines seem to have clearly evolved to explicative ones and it is reasonable to think that the Feynman Unifying Approach has favoured this change.