“What is the subject that you find most difficult?”
“What is your least favourite subject?”
These are two questions that adults usually ask youngsters when they discuss academic matters. But, these are two questions which have very different interpretations. It is to be expected for students to consider mathematics difficult due to the abstract nature of the subject and the challenges that it offers. But, generally young people are risk takers and enjoy challenges. Therefore, it is a concern if a student states that it is a subject that he or she dislikes.
Recently, newspapers reported that the Ministry of Education has initiated steps to increase the percentage of students that pass in mathematics at the GCE O/L examination from the current 62% to a targeted 80%. It was reported that a new assessment book has been published to popularize maths among students and that teachers will be trained to adopt modern methods used in developed countries in the teaching of mathematics.
These steps are to be appreciated. In fact, the pass rate will automatically increase if the students follow the subject with interest and enthusiasm. For this to happen, I feel that three groups of people must work in harmony: students, teachers and parents.
If the topic of mathematics is brought up in a conversation when parents get together or at a parent teacher conference, we hear comments such as “I was never good at mathematics”, “I don’t blame my son as I hated mathematics when I was in school” or “this is one subject where we are completely clueless to help our child”. Such negative comments will not help a child struggling to cultivate a positive attitude towards learning mathematics. The same parents will acknowledge the importance of the subject in the modern world. Therefore without amplifying the difficulties it is important that parents and children work together to find ways of overcoming the problems.
It will be helpful if parents join their children in solving mathematical riddles, puzzles and even filling Sudoku grids. The interest in the subject can be enhanced through these activities and students will gradually increase an awareness of the need to have good mathematical skills. Also, it would help immensely if parents show that they are willing to learn. Getting your children to teach you something that you don’t understand, but have an interest in, provides a valuable learning atmosphere. Teaching another person is one of the best ways of enhancing a skill.
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We are all lifelong learners. This idea is very important for teachers. Mathematical concepts that are taught in schools may not have changed over the last few centuries, but the methods of delivery, analytical tools and processes of conceptualization have changed drastically over the last few years. It is important for teachers to remember that the students under their care enter a job market that values mathematical thinkers.
Solving a problem using an algorithm is important but the ability to view a problem from different angles and choose the right option reflecting on the constraints is much more important. It is not useful to judge a student as either good or bad in mathematics. Allen Broyles and Tom Pittard who researched on the neuro-developmental demands that mathematics places on a student beautifully analyse a situation where four students may get the same problem wrong for four completely different reasons.
The first student understands the process but makes a simple fact error; the second also understands the process but is unable to complete it due to memory deficits; the third inaccurately transcribes on paper the correct number that he is holding in his head; the fourth does not understand the concept underlying the problem. To address these errors, each one needs a different approach to teaching.
A common difficulty experienced by students is the inability to connect the abstract and conceptual aspects of mathematics with reality. Holding a model of a cube, for example, is more meaningful to a child than simply being told that a cube has six faces. All students move through a development sequence from concrete to abstract and manipulatives are an excellent form to help them through this process. With this in view, I initiated a mathematical laboratory in 1974, at St.Anthony’s College, Katugastota, where I started my teaching career. A mathematics laboratory is a location consisting of mathematical apparatus and visual aids to enable students to involve themselves in the learning process by attempting to bridge the gap between the real and the abstract world. It also provided opportunities for students to develop inquiry based learning in a ‘mathematical atmosphere’ thereby enhancing their interest in the subject and gaining confidence to face the challenges it offers. I am happy to note that Candle Aid Lanka, a charitable organization, has appreciated the value of the formation of such laboratories in raising the mathematical standard of our students. They have already donated this facility to six needy schools.
Many students are faced with the problem of finding a way to ‘study’ for mathematics. In most subjects, they could read notes, go through texts or perform experiments in preparation for lessons and examinations. But, what could you do in mathematics? Mathematical skill acquisition comes with practice. When students solve mathematical problems, it is helpful to consider it as an exploration. Sometimes you are successful and sometimes not. But, each failed attempt can provide useful hints towards the path of success, if the mistakes could be analysed. Thomas Alva Edison said “I have not failed. I have just found 10,000 ways that won’t work”.
Another difficulty that the students face in mathematics classes is the inability to follow the lesson due to not being comfortable with what had been done previously. Mathematics is a subject where the conceptual understanding is built up in a ladder formation. You cannot move to the next level without stepping on the previous step. As such, it is useful for students to spend a few minutes at home going through and reflecting on what was covered in class, on a regular basis.
Also, in this modern age of advanced technology, it is not too difficult to check on the topic being taught on the internet, to find out about the historical development and to check on where the applications lie, thereby enhancing the motivation to know more about the topic.
The writer was a mathematics lecturer at the United World
College of Hong Kong and is now attached to the Overseas
School of Colombo. |
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