So you are about to write the end-of-year examinations!
Some of you are about to write the most important examination of your life, the Grade 12 final examinations.
This is a “high-stakes” examination since the results will determine the course of your life. A good result may open up doors which a poor result will not. And among the subjects, it is Mathemtics and Mathematical Literacy are those which are valued highly for entrance to university and other tertiary studies, and also for entrance to a wide range of further studies. For example, Engineering, Sciences, and Computer Sciences are not available if you do not ave a reaonsable pass in Mathematics.
This article provides a simple approach to answering the questions presented in the mathematical papers to help you improve your marks. By now there is little time left to increase your mathematical knowledge, and so I am focussing rather on how you can present your knowledge to the marker of the examination to show that you know and that you do not lose marks by presenting your knowledge in the wrong way.
In reality there are few right or wrong ways, but for every question in the exam paper there is also a memorandum which helps the markers to provide the marks to you. If a question provides 3 marks, than you are expected to show 3 things, not 2 and not 4, just 3. I will now help you in how to answer, using a method I use with all of my students, and which I call “APEX”.
I have developed the APEX method based upon the well-known work of Polya (“How to Solve It”) which is one of the most widely used mathematical books of all time. Polya’s work was directed at more complex problem situations, and I have applied this to the most simple of mathematical problems, since all such mathematical problems can be solved in this way.
Polya did not give a name to his 4-step method, and I have restructured this and called is the “APEX” approach, which consists of the following 4 steps.
- A : Analyse
- P : Plan
- E : Execute
- X : Crosscheck
For this step you will do the following:
- Read the Question: do not assume that you know the question by just looking at it quickly. Read it in detail.
- See what you are given:
- See what you have to produce:
- See how many marks there are for this question: For every mark you are expected to do something specific. There will not be a situation in which you get two marks for doing one thing, or one mark for two things. Every question / problem is structured
- Determine what the marks are for: Knowing how many marks you can get for this question, and also what you are expected to produce as outputs from the inputs which you are given, you need to start to consider what you should be providing in your written answer to be able to get the full marks. However, to continue with this you need to move to step : PLAN.
Some questions are presented in a way that you know what type of mathematics you are to use, but in others this is not specified and you need to use your knowledge of mathematics to match the question to the right mathematical approach.
Once you have identified the mathematics you will be using, you can then plan what you will be doing.
In many cases you are also given the formulas, and thus you are not required to remember each and every formula, but you are required to know how to use the right formula and how to apply these to the problem.
For the PLAN step you will do the following:
- What Mathematics?: select the type of mathematics which you think you will need. If this is not clear then consider a shortlist and see which may be more applicable than another.
- Plan the attack: determine how you will use the mathematics and what specific actions you will do.
- Map to the marks: you need to see what you will get marks for, since this may not be clear initially. You need to ensure that you provide enough information to get full marks, and also that you reduce the amount of work which will not contribute to the marks.
- Predict the Answer: given the nature of the problem, you may be able to predict the nature of the answer expected. This is important in step 4, CROSSCHECK, in which you will check whether your answer is reasonable or not. For this you will check back to the initial question.
If the question has a mark of one (1), then you only need to provide the mark.
If there are two marks (2), then you need to provide two things, generally a first element of your workings / actions, and the answer.
If there are three marks (3), then you need to provide some workings, and one or more answers.
However, you will NEVER get marks from repeating the question! If you do repeat this it may help to provide the solution and will also help if it is not evident which question it is in case you wrote the wrong question number onto your paper.
You now have the following:
- The actions you will undertake, which may be clear or may not be depending on how much still had to be worked out.
- Which of these actions you are likely to get marks for, and which should be emphasised.
- The sequence in which you will carry out the actions to arrive at teh solution.
Now you have to actually do the work, and we move onto the EXECUTE step of the APEX method.
In this step you must carry out the actions you identified in the PLAN step. In most cases the PLAN is not written down, but will be structured in your head, but for larger problems it may be better to at least write the steps as an aide for your work.
You will now perform the actions, and at this time will write these down as part of your response and answer.
The following must be considered:
- When writing the workings and the answers, be sure to highlight those for which you expect to get marks.
- This could be done by positioning them differently on the page, such as in the centre of the page.
- All other workings should be positioned elsewhere, such as on the left of the page.
- However, some of these workings may also contribute to marks, so do not put them elsewhere.
You now must check your answer to see if it reasonable to what was expected, which you may have already identified in step 1, ANALYSE.
The CROSSCHECK step is perhaps the most difficult for learners, since it is not always obvious what a correct answer should look like, and may learners create answers which are wrong, but for which they cannot see that they are wrong.
In many cases, mathematics exists in a real-world setting, and for these cases it is important to understand the nature of the real world from your own experience.
Practice, practice, practice!
There is a quote attributed to the famous golfer Tiger Woods when someone remarked how lucky he was to always get his low scores, with good drives down the fairway, and good putts to get the golf ball into the hole. His response “yes, but the more I practice, the luckier I get!”.
You need to practice how to write examination questions, and I would like to deal with this in my next blog.
Good luck for the examinations, and be sure to write to me by email about your experiences and whether this is useful to you.