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Introduction. Raising a research problem requires clarifying the difference between real problem, problem, problematization and research problem. At the same time, it requires thinking of the researcher as the source of the problem and of reasoning, considering the three types of reasoning: deductive, inductive and abductive. It proposes four criteria to build a research problem: 1. Description of the phenomenon 2. Description of the imbalance 3. Description of the time space 4. Description of the research subjects. Finally, the difference between the paradigms in the construction of research problems is considered. [ABSTRACT FROM AUTHOR]

We describe the procedure used by 11-12 years old students to discover counting patterns in basic combinatory problems. We emphasize the transition from manipulative strategies for direct counting to generalization. In this transition, there were students who spontaneously used tree diagrams of mathematical ideas and some students used numerical thinking strategies. We highlight the interest of solving combinatory problems in order to let the students make sense of the multiplication rule. We relate the results to the teaching of multiplication in primary school. [ABSTRACT FROM AUTHOR]

Based on a series of research results on Moroccan migration to Canada, this paper seeks to prove how focusing on the migration routes of a specific national group of migrants and using a multi-situated methodological approach will not lead to the "ethnisizing", culturalizing or nationalizing of the experienced realities, but rather to the placing of actions within their political cultural, social and economic structuring contexts. By resorting to an inductive approach, this perspective allows us to identify frontiers (in a symbolic sense) other than cultural or national belonging, reminding us of the internal heterogeneity of the studied national group, allowing us to apprehend other decisive factors in the migration route, and favoring our understanding of the plurality of the space practices and integration strategies developed by social actors when facing the concrete opportunities and limitations found during the whole migration process. [ABSTRACT FROM AUTHOR]

We present the results of two tests performed by primary school students. The first one was on finite numeric inductive reasoning and was performed by 400 students. According to its results, we selected 28 students to whom we clinically interviewed aiming to determine the evolution of the logic relations that they can establish in the field of finite natural numbers. This study originates on historic problems of the logical foundation of arithmetic. We aim to empirically determine the extent to which logic plays a key role in the origin of arithmetic or, on the contrary, if the origins of logic are predetermined by arithmetic and other fields. [ABSTRACT FROM AUTHOR]

In this paper we explore the patterns and the generalization developed by 359 students in years 9 and 10 in the resolution of the tiles problem. We pay special attention to the kinds of patterns identified, to the written ways in which students express generalization and, using inductive strategies, we present some characteristics of the generalization relating to the elements and the representations used. [ABSTRACT FROM AUTHOR]

We present an analysis of the inductive reasoning of twelve Spanish secondary students in a mathematical problem-solving context. Students were interviewed while they worked on two different problems. Based on Polya's steps and Reid's stages for a process of inductive reasoning, we propose a more precise categorization for analyzing this kind of reasoning in our particular context. In this paper we present some results of a wider investigation (Cañadas, 2002). [ABSTRACT FROM AUTHOR]