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Teaching Approaches/Inquiry: Difference between revisions
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=Inquiry and Mathematics Teaching= | =Inquiry and Mathematics Teaching= | ||
{{adaptedfrom|Fibonacci Project|Reference|Ideas of how to solve particular types of mathematical problems, e.g. involving fractions or negative numbers, are built up through bringing together experiences of tackling a range of related problems. In some cases, a conceptual step may also force to deconstruct, then to reconstruct a new and more encompassing idea. Such progression of ideas is only understood if they make sense to the learner because they are products of their own thinking. This view of learning argues for students to have experiences which enable them to work out for themselves how to make sense of different aspects of the world. First-hand experiences are important, particularly for younger children, but all learners need to develop the skills used in testing ideas – questioning, predicting, observing, interpreting, communicating and reflecting. | |||
As is the case in natural science, inquiry-based mathematics education (IBME) refers to an education which does not present mathematics to pupils and students as a ready-built structure to appropriate. Rather it offers them the opportunity to experience | |||
* how mathematical knowledge is developed through personal and collective attempts at answering questions emerging in a diversity of fields, from observation of nature as well as the mathematics field itself, | |||
* how mathematical concepts and structures can emerge from the organization of the resulting constructions, and then be exploited for answering new and challenging problems. | |||
It is expected that the inquiry-based approach will improve students’ mathematical understanding which will result in their mathematical knowledge becoming more robust and functional in a diversity of contexts beyond that of the usual school tasks. It will help students develop mathematical and scientific curiosity and creativity as well as their potential for critical reflection, reasoning and analysis, and their autonomy as learners. It will also help them develop a more accurate vision of mathematics as a human enterprise, consider mathematics as a fundamental component of our cultural heritage, and appreciate the crucial role it plays in the development of our societies. | |||
If it is to be more than a slogan, IBME requires the development of appropriate educational strategies. These strategies must acknowledge the experimental dimension of mathematics and the new opportunities that digital technologies offer for supporting it. | |||
The history of mathematics shows that such an experimental dimension is not new, but in the last decades technological evolution has dramatically changed its means, economy, and also made it more visible and shared by the mathematical community. Compared with experimental practices in natural sciences, one must however be aware that the terrain of experience for mathematics learning is not limited to what is usually called the “real world”. | |||
As they become familiar, mathematical objects also become the terrain for mathematics experimentation. Numbers, for instance, have been used for centuries and are still an incredible context for mathematics experiments, and the same can be said of geometrical forms. Patterns play a great role in mathematics, whether they are suggested by the natural world or fully imagined by the mathematician’s mind. Playing with patterns is a stimulating mathematical activity in the context of inquiry, even for elementary school children. Digital technologies also offer new and powerful tools for supporting investigation and experimentation in these mathematical domains. | |||
IBME must, therefore, not just rely on situations and questions arising from real world phenomena, even if the consideration of these is of course very important, but use the diversity of contexts which can nurture investigative practices in mathematics. | |||
Mathematics has a cumulative dimension to a greater extent than the natural sciences. Mathematical tools developed for solving particular problems need to build on each other to become methods and techniques which can be productively used for solving classes of problems, eventually leading to new mathematical ideas and even theories, and new fields of applications. Moreover, connections between domains play a fundamental role in the development of mathematics. Thus it is important in implementing IBME that students do not deal only with isolated problems, however challenging they may be, since this may not enable them to develop the over-arching (or more generally applicable) mathematical concepts. | |||
Selecting appropriate questions and tasks for promoting IBME thus requires the consideration of their potential according to a diversity of criteria, and the building of a coherent organization and progression among these, having in mind the characteristics of mathematics as a scientific discipline and the ambition of such education of emphasizing the interaction between mathematics and other scientific disciplines, between mathematics and the real world. | |||
A further crucial point is that, even when they emerge from real world situations, mathematical ideas are not directly accessible to our physical senses, and are thus worked out through a rich diversity of semiotic systems: standard systems of representation such as graphs, tables, figures, symbolic systems, computer representations, etc., but also gestures and discourse in ordinary language. IBME must be sensitive to this semiotic dimension of mathematical learning and to the progressive development of associated competences, without forgetting the evolution in semiotic potential and needs resulting from technological advances. | |||
Modern technological tools have an impact on inquiry-based education through the immediate access given to a huge diversity of information, whatever the topic. This situation means that the “milieux” with which students can interact in investigative practices are potentially much richer than those usually used for developing investigative practices in mathematics. However, the necessity of selection and the critical use of such information create new demands that iBMe must take into account. | |||
=Inquiry and Science Teaching= | =Inquiry and Science Teaching= | ||
