Some aspects of this work is studied by A Level students such as plotting the graphs of the trigonometric functions and using them to solve problems in simple harmonic motion. [...] the ratio method was more successful in terms of the amount of enjoyment and motivation students felt.
© ATM 2009 • No reproduction (including Internet) except for legitimate academic purposes • email@example.com for permissions. TRIGONOMETRY WITH YEAR 8: Part 1 Jessica Steer, Maria Antioneta de Vila and James Eaton explore the teaching of trigonometry using a method developed by Jeremy Burke of Kings College. A series of lessons was planned using an approach Ratio method. Using this method, trigonometric which looks at moving from a mathematical functions are defined as the ratios of the lengths of description of the topic, to a sequence plan, to a sides of right angled triangles. In order to find set of activities, which students can use to help missing lengths or angles in right angled students, them come to understand the topic. This is they merely need to identify the two sides and referred to as ‘MNO’ (Burke and Olley 2008). M is angle that interest them and apply the correct ratio the map of the terrain to be covered, in this case to the problem. A common memory aid given to the mathematical structure of the topic, connec- students to remember when to use each ratio is tions and potential problems that students might SOHCAHTOA where SOH means sin(x) encounter. A consideration of the ‘map’ might be opposite/hypotenuse, CAH means cos(x) inaugurated with the question, ‘what do we mean adjacent/hypotenuse and TOA means tan(x) by...?’ In this case, what do we mean by ‘trigonom- opposite/adjacent. Critics of this method have etry’. N is the narrative, the sequencing of the suggested that teachers jump in too early with the lessons and activities – the story being told. O is memory aid before properly deriving the formulæ ‘orientation’ the activities which will serve as and this leads to a ‘mystique about the subject’ strategies to facilitate students engagement with the (Prichard, 1993). Furthermore, students have a topic. poor grasp of what the trigonometric functions are, which means they are insufficiently prepared for The map the study of analytic trigonometry at A Level. In the 17th and 18th centuries, Euler extended Trigonometry was initially studied a couple of the subject to functional trigonometry. Some millennia ago by the Babylonians, Greeks and aspects of this work is studied by A Level students Egyptians. They observed that in mathematically such as plotting the graphs of the trigonometric similar shapes, the ratios between pairs of sides functions and using them to solve problems in were the same and could thus be used to find simple harmonic motion. In other countries, there unknown lengths and angles of triangles. It was is a greater emphasis on this side of the topic from used mainly in the practical fields of astronomy and a much earlier stage. In countries where this is the surveying. Today, students are first introduced to case, teachers have found that a better method than trigonometry in Years 9 and 10 where they are the ratio method is the unit circle method, and some taught to understand and apply Pythagoras’ Theorem in Britain f
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