Make sure it all adds up

The Age

Monday September 7, 2009

Rob Vermay. Rob Vermay teaches at St Paul's Anglican Grammar School.

Show your processes, reference given material and interpret questions correctly, writes Rob Vermay. THE Further Mathematics course explores a range of key skills listed in the dot points of the VCAA Study Design. These include appropriate and accurate calculations and the use of a technology application, such as the graphics calculator, in a variety of mathematical contexts.Relevant to such skills, the Study Design dot points use words such as calculate, solve, test, formula, formulate, graph and algorithm.The Study Design dot points also list other important skills that are relevant and essential in today's world and that are tested in both examinations.Such additional skills are identified by words such as analyse, interpret, identify, define, explain, represent, apply, select, display, describe, compare, summarise, model, demonstrate, present, conclude and relate.Examination 2 tests your ability to communicate your results and understanding using both mathematical and everyday language. In this regard, past examinations have identified three areas of student weakness: in ��explain�� questions, ��interpret�� questions and ��show that�� questions.��Explain�� questions are used to test understanding of a concept within a particular context. In such questions, you could expect, for example, to be given some data or a graph and then be asked to explain whether or not a given conclusion is warranted. Question 3b (Data Analysis �� Examination 2, 2008) is an example. The arm spans (in centimetres) of years 6, 8 and 10 girls were summarised in the three parallel box plots.The three parallel box plots suggest that arm span and year level are associated. Explain why.For such a question, an answer based only on personal experience or opinion is not satisfactory. Many 2008 students said the relationship must exist as their own arms had grown longer as they grew older and reached higher year levels.To explain an association between year level and arm lengths, a direct reference must be made to the box plots. To do this, identifying that one summary statistic changed as year level increased would have been sufficient. For example; the range of arm spans decreased with year level.Other acceptable answers can refer to the IQR decreasing or to the median arm span increasing with year level. A broad statement that the ��box plots grow smaller as year level increases�� is far too general to be acceptable.The marks available to a question can give you a guide to how much you should be writing. For a one-mark ��explain�� question, one or two sentences should be all that is necessary to cover the relevant and appropriate explanation. There is no point in writing an essay for one mark.You may also need to interpret the result of a calculation in the context of the question.For example, question 4c (Data Analysis �� 2008 examination 2) required you to ��interpret the slope of the least squares regression line in terms of the variables height and arm span��.This meant you first had to find the equation armspan = ��15.63 +1.09�height and then state that, ��on average, armspan increased by 1.09 centimetres for every 1 centimetre increase in height��.If your equation had been incorrect, you could still have gained the mark for this question by correctly interpreting your incorrect equation.In 2008, other questions that required you to ��explain�� your understanding included Data analysis (Q2, 3c), Geometry (Q 3e), Graphs (Q 3a), Networks (Q2bii, 3b) and Matrices (Q1bii).��Show that�� questions also present difficulties for some students. In a ��show that�� question, you are expected to show all the steps in a calculation required to produce the given result.Question 3b (Geometry �� examination 2, 2008) is an example.The diagram shows a tree at one corner of a triangle CNT.Show that, correct to one decimal place, the distance, NT, is 12.6 metres.This is an application of the cosine rule and the expected calculation can be shown as follows:Therefore, NT = 12.6 metres, correct to one decimal place.Besides expecting that a full calculation is to be shown, a ��show that�� question often has a secondary and important purpose. The given result is usually required in the solution of a following, related question and should be used there.On occasions, a student's calculation in a ��show that�� contains an error and produces an answer that is different to that given. If applicable, method marks may be available for a portion of the student's calculation. Regardless, the given result should be used in the subsequent question rather than the one produced by the student.For the Geometry example (left), the given length for NT = 12.6 metres should be used to help determine the area required in the subsequent question 3c.In 2008, other ��show that�� questions included Geometry (Q 2a, 2b), Business mathematics (Q 2b) and Matrices (Q1cii).Many examination questions ask for a numerical answer and these are often determined by using your calculator. But the ability to do a calculation does not always fully explore the significance of the calculation or its result. You should be prepared to write about your understanding of aspects of the Further Mathematics course.Rob Vermay teaches at St Paul's Anglican Grammar School.

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