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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.

[This paper is part of the Focused Collection on Quantitative Methods in PER: A Critical Examination.] A relevant aim of research in education is to find and study the reasoning lines that students deploy when dealing with problematic situations. This can be done through an analysis of the answers students give to a questionnaire. In this paper, we discuss some methodological aspects involved in the quantitative analysis of a questionnaire by means of two different clustering methods, a hierarchical one and a nonhierarchical one. We start from the coding procedures needed to obtain analyzable data from the questionnaire and from a definition of a correlation coefficient suitable for measuring student similarity in the case of binary coding of student answers. Then, criteria to choose the optimal number of clusters are discussed, and for the same purpose a new coefficient is introduced that measures the total amount of information we can obtain from a clustering solution. We show that each cluster can be characterized by its centroid that summarizes the answers most frequently given by the cluster students to the questionnaire. Finally, an example of the application of these procedures to a student sample is given, and a comparison between the two clustering methods is discussed.

Questionnaires are perhaps the most widely used instruments to assess conceptual learning in physics as well as in mathematics. In the field of physics and mathematics education research it is surely interesting to be able to use a questionnaire as a “diagnostic instrument,” i.e., to know details about relationships among student answers to the different questions. In recent years several research works focused on this goal by using different quantitative methodologies, like Factor, Model and Cluster Analyses. However, very few research works deepened the theoretical aspects of the Cluster Analysis. In this contribution, we discuss two Cluster Analysis methods with respect to this issue. By means of an example of application on real data, groups of students homogeneous with respect to the ways students answer a questionnaire are identified. Each of these groups is identified without any prior knowledge of what form those groups would take (unsupervised classification) and can be characterised by means of the answering strategies the students deploy when facing the questionnaire. Each characterisation allowed us to infer the students’ lines of reasoning. Finally, we show to what extent the two clustering methods are coherent with each other.