Facing challenges at mathematics examinations



BY R. N. A de Silva

When secondary school students sit examinations, for a majority of them the most challenging subject is mathematics. It is not only because of the abstract nature of the subject. Many students are not aware as to how to properly revise for an examination in this subject. For almost all other theoretical subjects, revision involves going through the taught material by reading the notes. Therefore, many feel that mathematics, too, can be revised in this manner.

But, as mathematics involves problem solving, glancing through the notes will not help much. To have a full grasp a few chosen examples need to be redone to check whether solving process can be completed successfully. As such, mathematics revision may take more time than other subjects. But many students feel that they are not able to afford that much time for revision as many lack time management skills.

In most other subjects after a test, students generally have a good idea about their performances whether it was successful or not. However, in mathematics as it involves problem solving, there is always a doubt whether the obtained answers are right or wrong. Sometimes this anxiety can creep in even before an examination thereby lowering the confidence in self-ability. This is where the parents and the teachers can play a major role in training the students to accept mistakes as a positive step in the learning process.

We adults often make mistakes in our life journey and through these experiences we try not to make the same mistake twice. Similarly, it has to be instilled in the students’ mind that mistakes and errors are essential ingredients in the learning process. When I was teaching mathematics in the upper secondary classes, I sometimes purposely made mistakes in the solving process displayed on the board. I wanted to check whether the students are able to spot the error and thereby taking down notes with understanding and also to give them the satisfaction of correcting a teacher’s error, hoping that they will remember not to make such errors in their working.

Sometimes, we notice students using white ink or an eraser to wipe off the mistakes they have made in their notes. I have always discouraged this. It is beneficial to see the mistakes that have been made to enable to minimize such errors in the future. The most powerful learning experiences often result from making mistakes. It is important that teachers create an environment in the classroom where mistakes are considered as opportunities of consolidating the understanding of a concept or a process. In the same way, parents need to show that mistakes are a part of life and consider them as an experience to minimize such errors. “Anyone who has never made a mistake has never tried anything new.” said Albert Einstein.
Let us now examine a few ways that can help students to achieve success in mathematics examinations.

Revise wisely

The only way to revise mathematics is to do mathematics. The more questions you attempt, the higher your confidence will be in dealing with similar questions. Therefore, planning your revision time well ahead of the date of the examination is important. If possible, plan to do a part of your revision with a friend.
Sharing ideas and knowledge goes a long way with the consolidation of understanding. Teaching another person is considered as a most effective way of enhancing your own understanding. It is also a good practice to have an outline of the syllabus with you when revising, to check whether all areas have been covered.

Read the questions carefully

It is very important to understand the question and figure out what exactly needs to be done before attempting it. The additional instructions such as ‘give the answer to the nearest integer’ or ‘write coordinates of the point of intersection on your graph’ can be underlined, so that you will be alerted to these conditions at the end of your working. G.K Chesterton said “It isn’t that we cannot see the solution; it is that we cannot see the problem”. I have always told my students that the time to read the question in detail is not wasted time.

Present your work well

The way you present your work is how you are communicating your knowledge and understanding to the examiner. You maybe an excellent mathematician but the examiner is unaware of this and the examiner can judge you only thorough your communication on paper. In mathematics, it is important to work through in a logical sequence until you get to your result. Knowing that method marks are available even if your final answer is incorrect, show all your working. This will also help you to spot any errors that you may have made, if you feel that the answer does not seem right.
Be sensible.

As all examinations have a time limit it is important to keep a tab of the time. If the number of marks is stated for each question, it may give you an indication about the time that you can spend on each question. Do not spend too much time on any one question just for the satisfaction of obtaining a final answer. For success, it is more important to attempt all questions even if they are not fully completed.

Also, be sensible about the solutions that you present. As an example, if the question is to find the number of people in a designated area, it cannot give you an answer going into decimals. Again, if you are asked to find an angle within a triangle, it cannot be more than 180 degrees.If the formulae are provided, make sure that you look at them when you have to apply them. Due to the exam pressure, you can make careless mistakes with formulae thereby loosing marks unnecessarily.

Let us hope that our youngsters realize that Maths is everywhere and is vital for functioning in society at any level specially with the advancement of technology. As S. Gudder quoted “The essence of mathematics is not to make simple things complicated, but to make complicated things simple”.

(The author is a senior examiner for mathematics at the International Baccalaureate Organization.)