   # trigonometry

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Teaching trigonometry using Empirical Modelling
0303417

Abstract
The trigonometric functions sin(x), cos(x) and tan(x) are relationships that exist between the angles and length of sides in a right-angled triangle. In Empirical Modelling terms, the angles in a triangle and the length of the sides are observables, and the functions that connect them are the definitions.
These well-defined geometric relationships can be useful when teaching GCSE-level students about the functions, as they provide a way to visualise what can be thought of as fairly abstract functions.
This paper looks at how different learning styles apply to Empirical Modelling, and presents a practical example of their use in a model to teach trigonometry.

1 Introduction
The trigonometric functions sin(x), cos(x) and tan(x) are relationships that exist between the angles and length of sides in a right-angled triangle. In Empirical Modelling terms, the angles in a triangle and the length of the sides are observables, and the functions that connect them are the definitions. These welldefined geometric relationships can be useful when teaching GCSE-level students about the functions, as they provide a way to visualise what can be thought of as fairly abstract functions. Rather than teaching students by showing them diagrams in an instructive way (already a good way of doing it), a constructive approach may allow students to gain a better understanding (Beynon).
Empirical Modelling upholds a set of principles that are in some ways similar to the different learning styles identified by Felder and Silverman (1988).
This paper explores the similarities and differences between Empirical Modelling and a selection of the learning and teaching styles, with a view to creating a practical model. Schools are keen to promote the development of ICT skills alongside learning (OCR,
2007), so a model that teaches trigonometry through interaction with a computer will be useful.
The

References: Beynon, W. M., “Empirical Modelling for Educational Technology”, “Edexcel GCSE in Mathematics A (1387)”, London Qualifications, 2004, Felder, R Teaching Styles in Engineering Education”, Engineering Education, 78 (7), pp. 674-681 (1988) Harfield, A., “Presentation Environment”, “OCR GCSE in Mathematics A (Linear Assessment)”, Oxford Cambridge and RSA Examinations, 2007,

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