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Santana Coutinho Alves Delgado, Catarina Raquel
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- Desenvolver o raciocínio matemático dos alunos: práticas e desafiosPublication . Delgado, Catarina; Brocardo, Joana; Mendes, Fátima
- Developing flexible-adaptive reasoning and computingPublication . Brocardo, Joana; Kraemer, Jean-Marie; Mendes, Fátima; Delgado, CatarinaThe project ‘Numerical thinking and flexible calculation: critical issues’ aims to study students’ conceptual knowledge associated with the understanding of the different levels of learning numbers and operations. We follow the idea proposed by several authors that flexibility refers to the ability to manipulate numbers as mathematical objects which can be decomposed and recomposed in multiple ways using different symbolisms for the same objet (Gravemeijer, 2004; Gray &Tall, 1994;). The project plan is based on a qualitative and interpretative methodology (Denzin & Lincoln, 2005) with a design research approach (Gravemeijer & Cobb, 2006). This article focus the preparation of a teaching experience centered in the flexible learning of multiplication. It describes the analysis of a clinical interview where Pedro (9 years) solves the task 'Prawn skewers'. It illustrates how we identify and describe Pedro’s conceptual knowledge associated with the different levels of understanding of numbers and multiplication/division and analyzes if and how this knowledge facilitates adaptive thinking and flexible calculation.
- Teachers' pratices and number sense development in elementary schoolPublication . Delgado, Catarina; Brocardo, Joana; Oliveira, Hélia
- Números e operações: 1º ano: números naturais, operações com números naturais, regularidadesPublication . Brocardo, Joana; Delgado, Catarina; Mendes, Fátima
- Práticas de seleção e construção de tarefas que visam o desenvolvimento do sentido do número: o caso do professor ManuelPublication . Delgado, Catarina; Brocardo, Joana; Oliveira, HéliaA primeira autora deste texto desenvolveu um projeto colaborativo de desenvolvimento curricular com dois professores do 1º Ciclo e realizou um estudo focado na caracterização das práticas destes professores. Neste texto analisam-se as práticas de um dos professores, Manuel, na seleção e construção de tarefas que visam o desenvolvimento do sentido de número dos alunos. A metodologia do estudo, de natureza qualitativa e interpretativa, segue a modalidade de estudo de caso e a recolha dos dados foi realizada através de entrevistas, observação de sessões de trabalho conjunto, observação de aulas e análise documental. Os resultados indicam que na seleção e construção de tarefas que visam o desenvolvimento do sentido do número, Manuel valoriza a relação entre o seu contexto e os cálculos a efetuar, a possibilidade das tarefas poderem suscitar o uso de métodos e números eficazes e de proporcionarem o uso de diversas estratégias.
- Exploring students adaptive use of domain specific knowledgePublication . Brocardo, Joana; Delgado, Catarina; Mendes, Fátima; Kraemer, Jean MarieAdaptive use of meaningful knowledge is widely adopted as key learning objective in the changing society. This paper presents the results of a teaching experiment in the domain of partitive division. It is designed to explore how grade-3 students do adapt personal knowledge to the variation in task conditions. Under the first condition groups of four and six students explore the process of distributing 52 carts between four/six persons. They can use 52 unifix cubes to model the process directly. The second condition requires that they mentally anticipate the results of sharing the same quantity of carts between respectively two and three children. The study shows that the variation in conditions combined with classroom climate challenge a great part of the students to use adaptively “pieces of knowledge” acquired in different areas of reasoning in equal group situations.
- Flexible calculation: key ideas from students' solutionsPublication . Brocardo, Joana; Mendes, Fátima; Delgado, Catarina
- Challenging preservice teachers to produce varied mathematical problem solving strategiesPublication . Boavida, Ana Maria; Delgado, Catarina; Mendes, Fátima; Brocardo, JoanaThis paper presents preliminary results of a research project that aims to investigate preservice teachers’ capacity to produce and analyse solution strategies to solve mathematical problems. From a methodological point of view, the study is of a qualitative nature and is being developed with future kindergarten and primary teachers who are enrolled in mathematical courses of a bachelor degree in elementary education at a public teacher education institute in central Portugal. The results suggest that although there has been an incipient progress concerning the production, by the future teachers, of more than one strategy to solve the same problems, reaching this goal is not an easy endeavour. It requires a deep and flexible knowledge about the mathematical content in order to be able to analyse problems from several points of view.
- Selecting and adapting mathematical tasks that foster number sense development: the practice of one primary teacherPublication . Delgado, Catarina; Brocardo, Joana; Oliveira, Hélia
- Números e operações: 3.º ano: números naturais, operações com números naturais, números racionais não negativosPublication . Mendes, Fátima; Brocardo, Joana; Delgado, Catarina; Gonçalves, Fátima