No abstract

Este estudo visa perceber como se desenvolveu o sentido espacial num momento de brincadeira livre na creche entre 11 crianças (12/24 meses) e um adulto, no episódio denominado torre dos cubos. Adotando o paradigma interpretativo, recorreu-se à   observação participante para aceder aos dados. Os resultados revelam comportamentos das crianças e do adulto (e.g., as crianças aproximam-se e afastam-se do local da construção; o adulto modela comportamentos) que nos levam a inferir que a criança desenvolve o sentido espacial de forma intuitiva e espontânea, na interação com objetos, com pares e com adulto(s) responsivo(s).

No abstract

This paper presents some results of the project (H)ISTO é MATEMÁTICA -História da Matemática no Ensino da Matemática (History of Mathematics in teaching), a research project that has as one of its main goals: to describe the initial and continuous training of Portuguese teachers in History of Mathematics (HM), as well as their conceptions and practices on the use of HM in teaching. In particular, we present the results of applying an online questionnaire to a group of 259 Mathematics teachers from the 2nd Cycle of Basic Education in Portugal (5th and 6th grades). With this survey our purpose is precisely to characterize teachers': (i) training in HM; and (ii) conceptions and practices about the utilization of HM in the classroom. Notice that this study intends to respond, among others, the lack of studies on this subject, particularly at the level of the first years. We use quantitative data analysis methods, namely descriptive statistics. The main conclusions of this study are: 1) most teachers considered the training in HM obtained in their higher education as non-existent or reduced; 2) the overwhelming majority categorized as non-existent or reduced their continuous education in HM; 3) most teachers reported using HM as a didactic resource in Mathematics class (many of them in a regular basis); 4) teachers resorted more frequently to textbooks and favoured the use of HM in the introduction to new mathematical subject; 5) regarding to the potential of using HM in teaching, teachers evaluated the didactic potential of HM very positively; the biggest constraints were related to the extension of the official curricula, the scarcity of support materials and the difficulty of evaluation.

Several studies point out that History of Mathematics (HM) can have a relevant role in mathematics teaching and learning. Still, in Portugal its use in non-higher education is very limited, which brings challenges to trainers of future teachers (FT). It seemed important to us to find out how the FT: (i) characterise their training in HM, obtained in their first cycle academic degree; (ii) evaluate the impact that the use of HM had on their learning of mathematical topics; and (iii) appreciate the didactic potential of using HM in mathematics classes. To this goal, we design a mixed study with FT graduating at two Portuguese institutions. Data were collected from questionnaires (N=28) and semi-structured interview (N=2). Data analysis combines qualitative and quantitative aspects. It reveals that, FT of both institutions had contact with HM mainly in the introduction to contents and mentions to the history of symbology, they also show having more memories of HM in course units that HM as a focus of study. In terms of the impact of HM on their learning of mathematics, the FT highlight that it facilitated the understanding of mathematical content and connections between mathematics and reality, promoting also the development of transversal skills. In terms of appreciation of the didactic potentialities of using HM in teaching, the FT highlight that it allows illustrating relationships of Mathematics with other subjects. The interviewed FT also revealed difficulty to present/explain the didactic potential of HM, which may occur because in this initial degree they still have little contact with teaching practices and also because HM is used as a tool and less as a didactic approach that they may use in the professional master's degree.