More Info
									     © ATM 2009 • No reproduction (including Internet) except for legitimate academic purposes • for permissions.

                    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
To top