BUSCADOR RECOLECTA

Research in mathematics education can be understood as a system of activities addressing the basic and applied problems related to teaching and learning of mathematics. Such a system includes the activities of foundation, planning, implementation, evaluation of mathematics instruction, and teacher professional development, which are supported by different theories. This diversity of theories raises interest in their comparison, coordination, and possible integration. The paper aims to present a case of application of the Cultural Historical Activity Theory (CHAT), in its 3rd and 4th generation versions, to analyze the emergence of the Onto-semiotic Approach to mathematical knowledge and instruction as a theoretical framework that addresses the study of the five partial activities mentioned above. This use of the CHAT can be useful in studies on theory articulation by focusing not only on the subjects, the object, and the instruments but also on the community context, the ecological-normative environment in which these activities take place, and the dilemmas or contradictions between theories., Research carried out in the framework of Project PID2022-139748NB-I00 funded by. MICIU/AEI/https://doi.org/10.13039/501100011033/ and by ERDF, EU. Funding for open access publishing: Universidad de Granada/CBUA.

Sampling is a fundamental stochastic concept that bridges statistics and probability. Due to its importance, some elementary sampling ideas have been included in the latest Spanish primary education decrees; however, teachers may not be familiar with the topic, and research on the sampling knowledge of teachers is scarce. To fill this gap, the aim of this study was to assess common and advanced mathematical knowledge of sampling of 105 prospective primary school teachers by analyzing their responses to a questionnaire with open-ended questions. Common content knowledge was assessed by asking for definitions and examples of sample and population and by discriminating between correct and incorrect sampling methods. Advanced knowledge was tested by asking for an estimation of the population mean from the sample mean and of the population and proportion in a new sample from the sample proportion. Results indicated better common content knowledge than previous studies and gaps in advanced knowledge. Most participants had a multi-structural understanding of sampling concepts, where several aspects were described but not related to each other. We conclude that there is a need for better preparation of prospective primary school teachers’ sampling knowledge considering the current curricular deepening on this topic, and new research should be oriented toward designing and evaluating related teaching actions.

In this article, we describe the implementation and results of a formative experience with prospective mathematics teachers, focused on developing the competence for didactic-mathematical analysis of curriculum materials, specifically student workbooks related to probability. The research design follows a methodological approach typical of design-based research, utilizing content analysis to examine participants' responses. The study was conducted with 16 Peruvian students preparing to become mathematics teachers at the National University of the Altiplano. The responses from the prospective teachers revealed deficiencies in their common content knowledge. They also encountered difficulties in distinguishing mathematical practices and recognizing the mathematical objects involved in the study process, especially propositions and their respective arguments. Furthermore, they struggled to differentiate between intuitive, classical, and frequentist meanings of probability. To improve these outcomes, it is necessary to reinforce didactic-mathematical knowledge regarding probability.