Tuesday, February 14, 2012

Add parents, teachers and students to solve the maths problem

, The Island.

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By R.N.A. de Silva

ndesilva@osc.lk

Why do so many youngsters have problems with mathematics? Is it because they find it too much to handle or is it because they dislike it compared to the other subjects that they learn in school? 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 they enjoy taking up challenges. Therefore, it is a concern if a student states that it is a subject that he or she dislikes. How do we create an appreciation for mathematics learning so that the students are motivated to follow the subject with interest? 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, it is to be expected to 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.

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 choosing the right option reflecting on the constraints is much more important. It is not useful to judge a student being 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 analyses a situation where four students may get the same problem wrong for four completely different reasons. First student understands the process but makes a simple fact error; Second also understands the process but unable to complete due to memory deficits; Third inaccurately transcribes on paper the correct number that he is holding in his head; 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.

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 following list is an attempt of mine to provide three important tips to the three categories of people for whom this article is intended to.

PARENTS

1. Be prepared to listen to your children when they talk to you about their academic work.

Encourage them to discuss their classroom achievements and difficulties with you. Rather than telling them what to do, discuss with them about possible solutions to their difficulties.

2. Create opportunities of demonstrating the use of mathematics at home.

You could do this by solving puzzles that may appear in newspapers or magazines that you purchase or involving your children in the calculation of paint required for a paint job or tiles required for a tiling job etc.

3. Show them that you are willing to learn from them.

In this age of such rapid technological advancement there is much that we can learn from youngsters and it is important to give them that opportunity in the sharing of knowledge. Value their opinions and discuss the feasibility of options.

TEACHERS

1. Be prepared to think as a student.

Visualising may not be as easy for your students as you think and try to use manipulatives and visual aids as far as possible. Remember that you are dealing with abstract concepts and it is necessary to move from known to the unknown in a simple way.

2. Be abreast of new developments.

It is important to be aware of current trends and the use of technology as a teaching tool. Have an attitude of learning and be not afraid to try out new teaching techniques.

3. Create an atmosphere of friendliness in your classroom.

Mathematics is a subject where much discussion is needed and therefore students should have no fear of raising their questions or initiating a discussion. Also, have courage to admit mistakes or to confess that you need time to refer to either a problem or a concept, which will be appreciated by the students.

STUDENTS

1. Be aware that success can be achieved through determination.

It is not unnatural to make mistakes in mathematics but it is important to analyse mistakes to check why they occurred. Perfection in mathematics can be achieved only through practice. Remember that the failures are the pillars of success.

2. Find means of minimizing careless errors.

Reading questions carefully and writing down what is given and what needs to be found is important in mathematics as a good number of mistakes are made due to the misunderstanding of the question. Neatness and showing steps in a logical order can also help in cutting down careless errors.

3. Be prepared to discuss your difficulties.

You will be able to spot your mistakes and improve your thinking process through discussion either with your teacher or colleagues. Try not to give up when unable to proceed. If not in a classroom, phone a friend for clues or use the internet to get ideas. If everything fails, make a note of it to discuss with your teacher on the following day.

The writer is now in the Overseas School of Colombo having returned to Sri Lanka after a long service at the United World College of Hong Kong.

Ecological footprint and sustainable human development

, The Island.

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By Jagath C. Savanadasa

The title above sounds abstract and even distant. But as we go on we will feel that we are on fairly familiar ground.

In early January I attended a Seminar on Cleaner Production which was an awareness programme on connected policies and regulatory measures for the benefit of officials of Chambers of Commerce. It was in the course of this learning exercise that I realized how important cleaner production and connected activity were for the sustenance of the economy and human development. Of course as far back as the 1970’s there emerged early warnings relating to the depletion of the Ozone layer caused by industrial pollution. The leading industrial nations were said to the primary cause of such depletions and there was a sustained cry by environmentalists to take measures to prevent further damage. But such protests had little effect.

From a global perspective one learns these days of depleting material resources. It seems that consumption of such resources has led to what is known as dematerialization or a decline of product output per unit.

An interesting concept linked material and natural resources with land. This concept centred on the Ecological Footprint.

Before the advent of the 1980’s for example, the total resources generated by the earth were sufficient for sustenance of the life of the world’s population. But since that time the resources have gone down to the extent that it is today difficult to meet the demands of the population. In other words, transferring this concept to the usage of land it has emerged that the total land area required for a person’s existence has gradually diminished. To put it is yet another way, the living patterns of man has led to creating a situation where the ecological footprint is currently low. And if unchecked such a situation will lead to serious problems with living and in finding the means for human survival.

It is important to note that in Sri Lanka too her resources are less than her ecological footprint. In these circumstances the fundamental aim of an Institution known as the International Footprint Network is to generate awareness worldwide of the declining bio diversity.

The National Cleaner Production Centre attached to this network (which has the support of the U.N. and which conducted the Seminar referred to) has been active in creating the ground work for cleaner production in industry.

At the introductory stage of the Seminar it was pointed out that though the world has seen huge advances in industry conferring many benefits on mankind, such benefits have been counteracted in some instances to a crippling degree by, concurrent environmental degradation.

A simple yet vital illustration related to atmospheric increases experienced in recent times. Principally such increases have been in terms of global atmospheric concentration of Carbon Dioxide (Co2) .

Mr. Sena Peiris an Engineer by profession and the Director of the National Cleaner Production Centre first addressed the Seminar on the need for a plan and strategy to create a consciousness about the importance of Cleaner Production nationally. Obviously in the effective implementation of such a task the Chamber of Commerce network, he felt, could play a useful role. Peiris added that the Centre that he headed had for sometime been engaged in raising the level of understanding of the essentials of Cleaner production with individual industrial units mostly city and suburban based.

But it was necessary to generate an awareness and also compliance, the latter through legislative measures and regulation especially in the outstations which had less access to related information. Following this introductory note the seminar proceeded with a discourse on what is now high up in the international development agenda – sustainable human development.

Yet another vital matter that emerged at this stage related to consumption. When consumption patterns continued to increase the demands on natural resources a need arose for sustainable utilization of such resources, principally centering on either preventing or minimizing environmental pollution. According to the policy strategy defined cleaner production is an integrated environmental plan for products and services so as to increase efficiency, reduce risks to humans and the surroundings in which they exist.

Pollution reduction measures

Dr. Mrs. L P Batuwitage, Adviser, Ministry of Environment, observed that it was important to implement pollution reduction measures so as to control what she called "the shrinking environmental span". This could to an extent be done through improving social responsibility. Mrs. Batuwitage emphasized the need to infuse into the minds of people the concept of cleaner production through the medium of education. Of course education and driving home the relevance of such production alone would not suffice. Of greater significance were the responses of various segments of society especially the manufacturers and industrialists to this rallying call to adhere to the production concepts outlined.

Equally, the collaboration of all segments of the community was vital to ensure sustainability of production in the manner desired so as to prevent the shrinkage of environmental assets Batuwitage said that quite apart from the gentle art of persuasion and the responses, measures needed to be taken to ensure compliance through regulation.

The Kyoto Protocol

At this point of the discussion my thoughts diverted briefly to the degradation of environment and pollution and its devastating consequences on the international scale. These had been responsible for global warming and the green house effect. Many countries had in recent times been victims of callous neglect by some of the world’s most powerful industrial nations. They had persistently ignored the cry of environmentalists of the dangers posed by the release of pollutants, the decrease of forest coverage the exploitation of land, the sea and the water in the search for short-term material gains. Surely, big industrial nations were aware of the harm that they were causing but did they heed the call to reduce industrial emissions or to adopt measures in the over exploitation of resources that would harm man’s natural habitat?. No. It would be recalled that at the first international parley leading to the agreement to introduce a universally agreed mechanism to control harmful emissions, the famous Kyoto to Protocol, the U.S during the Bush administration was not a signatory (to the protocol). Even at the latest parley at Durban major industrial nations failed to reach a consensus on vital issues and measures necessary to prevent especially atmospheric degradation. Among new industrial powers are China, India and Brazil, but are they doing enough to control the harmful impact of their surging and driving industrial expansion, which often is accompanied by pollution?.

Views of an expert

Mr. Gamini Senanayake an expert in this field, who heads a firm with sustainable and cleaner production provided an effective insight through the under mentioned illustration.

According to Senanayake the following key inputs needed to come into play to ensure sustainability of production and consumption.

Senanayake after an explanatory session in which he clarified many issues also spoke of the introduction of new international standards pertaining to production.

ISO – 50000 (EMNS) Green labeling

ISO 50000 (EMNS) it appears is the latest ISO standard in the sphere of Cleaner Production which is also alternately referred to as green labeling. This standard was introduced in January 2011. A leading manufacturer of garments, Brandix Ltd which has acquired a rightful reputation for "going green" has already entered the somewhat exclusive club of ISO, 50000.

Another rather new initiative is MBI which is a definition conforming to Cleaner Production. Senanayake finally dealt with the importance of a sustained and all round effort needed to ensure that various forms of production in addition to the way we conduct ourselves at home or on the domestic front, to ensure that society is responsive and alive to the preservation of good living within a healthy environment.

The legal framework

Some useful information was also provided by the last speaker Mrs. Himali Karunaweera, Assistant Director, Environmental Pollution Control division of the Central Environmental Authority. She brought to light that as far back as 1980 (when the J R Jayawardena regime was in power) a National Environment Act had come into force despite the fact that issues connected with environmental degradation had been not as serious as during the subsequent decades.

As a consequence activities or measures at that period of time taken to counteract debilitation of surroundings were not pronounced.

During the last decade there came into being active policies, though they were mostly of a regulatory nature. Mrs. Karunaweera opined that regulation alone was not sufficient to ensure cleaner production.

Legal standards had been established in respect of

a. Noise pollution – industry, traffic, the use of electrical equipment like loudspeakers.

b. Waste pollution

c. Air- pollution

d. Solid waste management

e. House management

She concluded that it remains to be seen how effective the laws are and whether they are applied in a way that would lead to desired results.

Conclusion

Some key features of the entirety of this valuable exercise were the discussions at the conclusive session of the seminar. Since most of the representatives came from outstation Chambers of Commerce the use of Sinhala was very helpful to elicit their participation.

A matter of particular importance was brought forth by the Head of SMED – the Small and Medium Enterprise Developers, a n arm of the Federation of Chambers of Commerce and Industry of Sri Lanka (FCCISL), in fact an intregal component of it which has played a highly valuable role on a national scale in the development of SME’s.

Mr. Wijekoon the head of SMED pointed out the dangers arising out of a cyanide mixed raw material in the end manufacture of copper and silver based products. Additionally in the disposal of the waste or the left over on the soil. These harmful elements needed to be controlled and the damage to workers and the environment prevented.

Wijekoon an experienced Consultant in the mechanics of rural manufacture was evidently fully aware of the ignorance on the part of small manufacturing units in especially the Kandyan Provinces (from where he hailed) and in the North Central range which are traditionally associated with craftsman who have made a name for themselves in this field. He said that importers of raw materials in Colombo too had to be made aware of the dangers inherent in the Chemicals they brought to Sri Lanka and which were distributed all over the country, particularly in the provinces mentioned.

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Wijekoon concluded that there were other options in the form of substitutes available for importation and advocated the need to eliminate this serious problem.

A lady representative from the Galle Chamber of Commerce pointed out that the refuse of fish disposed of by the fisherman in the district resulted in environmental damage. Also the manner in which the waste water after the washing of the fish is disposed of. She suggested that the local government authorities should be also made aware and regulatory measures enforced to eliminate this serious problem which apparently affected most of the Southern fishing belt.

This writer too brought to the notice of those present the problem connected to disposal of waste-water in desiccated coconut mills. The D/C industry was a traditional one which was employment oriented and has also been a source of regular foreign exchange earnings. He stressed the need to infuse better technology in the manufacturing processes and waste control in such mills. Sri Lanka had over 50 such mills.

Emerging from this thought provoking discussion the Cleaner Production Centre agreed that they would proceed to take action along with other relevant agencies in order to infuse new thinking and also compliance on Cleaner Production especially in the distant districts which at present sorely lacked commercial and industrial information that facilitates growth and even future survival. In this laudable process the Centre will definitely count on the goodwill and support of the nation’s Chamber of Commerce system.

The writer is Secretary General, Business Chamber of Commerce. Earlier he was Senior Consultant – Economic Affairs of the Federation of Chambers of Commerce and Industry of Sri Lanka (FCCISL) and Secretary – General/CEO of the National Chamber of Commerce of Sri Lanka (NCCSL)