[DOWNLOAD] "Investigating Functions: Exploring Calculus Concepts." by Australian Senior Mathematics Journal " Book PDF Kindle ePub Free

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eBook details

• Title: Investigating Functions: Exploring Calculus Concepts.
• Author : Australian Senior Mathematics Journal
• Release Date : January 01, 2005
• Genre: Education,Books,Professional & Technical,
• Pages : * pages
• Size : 290 KB

Description

In a previous article in this series, I suggested that it is part of our responsibility as teachers to attempt to induce perturbations in our students' mathematical thinking. Especially when teaching seniors and capable students at any level, it is important that we unsettle them, shake their perceptions and attempt, wherever possible, to ensure that they regularly question those things that they take for granted. In this article, we consider some more of my favourite problems: borrowed from a variety of sources, classroom-tested over many years, and always guaranteed to induce discussion, questions and even flashes of inspiration. The great mathematics educator, Pierre van Hiele, speaks of mathematics teaching and learning in terms of what he calls structure and insight (1986). Mathematics abounds with structures: patterns and regularities, which form the basis, both for the 'nuts and bolts' work, and also for the wonderful connections which give mathematics its joy and excitement. Van Hiele is a bit coy about defining this term, structure, but he is quite clear about insight: it is recognition of structure! Consider, for example, teaching students about the difference of two squares. We expect them to acquire a familiarity with this form (this structure), which will enable them to recognise it quickly and intuitively: to know what to do when they encounter it, and to then act appropriately and with purpose.

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