Considerando que o processo de elaboração, aplicação e refinamento de tarefas que façam uso de TDIC configura-se como uma importante atividade no âmbito do ensino, o objetivo deste texto é apresentar uma reflexão sobre os resultados de uma experiência de ensino na qual foi proposta uma tarefa com uso do Geogebra na disciplina de Cálculo Diferencial e Integral. Para tanto, adota pressupostos da pesquisa baseada em design e apresenta uma análise retrospectiva de dados oriundos do trabalho com uma tarefa para exploração de ideias necessárias à compreensão do conceito de derivadas. Como resultado desta reflexão, evidencia-se uma suposta “falha” na interação entre os estudantes e o aplicativo, relacionada com aspectos do ambiente de aprendizagem, por sua vez inter-relacionados entre si, a constar: o enunciado da tarefa; a TDIC; a interpretação das ações, explicações e interação dos estudantes; a interação entre professor e estudantes no processo de formalização. Este resultado confirma a importância de uma análise integrada de experiências de ensino e permite apontar sugestões específicas para um melhoramento da interação entre os estudantes e o aplicativo em termos de elaboração da tarefa e do ambiente de ensino e de aprendizagem.
Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the integral-as-accumulation-function. This is based on the notion of accumulation in general and the notion of accumulative distance function in particular. Through a case-study methodology we investigate how this approach elicits 11 th grade students' mathematical thinking and reasoning. The results show that the integral-as-accumulationfunction has potential, since the notions of accumulation and accumulative function can provide a strong intuition for mathematical reasoning and engage students in mathematical dialogue. Implications of these results for task design and further research are discussed.
Interactive Virtual Math (IVM) is a visualization tool to support secondary school students’ learning of graphs by dynamic events. In the prototype version students construct a graph and try to improve it themselves and with the feedback of the tool. In a small-scale experiment, which involved four classes at secondary and tertiary education and their mathematics teachers we investigated how the students used the tool in the classroom. In this study we focus on the students learning experience and the results are expected to provide knowledge and directions for further development of the tool. The corpus data consists of self-reported questionnaires and lessons observations. One main finding is that students, at different school levels, find the tool useful to construct or improve graphical representations and it can help to get a better understanding of the subject. The tool features that helped students most were the self-construction of the graphs and to get feedback about their own graph at the end. Other findings are that the students can work independently with the tool and we know more about the tool features that are attractive or need to be improved.
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