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Mathematics examinations or mathematics curriculum?

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Some people say that it is not necessary for a Grade 10 student to buy an ordinary scientific calculator because they have smartphones with built-in calculators. If not, it is easy to install a calculator app on mobile phones. A smartphone should not be used as a calculator during a mathematics test or a mathematics exam because it can be used for cheating. In the UK and other developed countries students have to keep their smartphones in their school bags or in their lockers outside the classroom during mathematics tests and exams. 

by Anton Peiris
anton25ps@gmail.com

R. N.A. De Silva has, in a recent article, provided some useful tips to students as regards preparation for mathematics examinations. Trained teachers and graduates with professional qualifications are familiar with this topic.  All mathematics teachers have a duty to help the students with revision.

The more important task is to salvage the Sri Lankan O/Level mathematics students from the abyss that they have fallen into, viz. the implications and the retarding effect of the use of obsolete Log Tables. The Minister of Education, Senior Ministry Officials and the NIA are oblivious to the important and interesting things that have happened in Grades 10 and 11 mathematics in the UK, other parts of Europe, Japan, Canada, China and elsewhere. They have been like frogs in a well for almost half a century. Here are two important facts:

1. O/Level mathematics students in Sri Lanka are 46 years behind their counterparts in the UK and in other developed countries. Ordinary Scientific calculators were introduced to the O/Level mathematics classrooms in the UK way back in 1977. Prior to that those students used Slide Rules to facilitate their mathematical calculations. Ordinary scientific calculators give the values of Sine, Cos, Tan and their Inverses, Log, LN, exponential powers, square roots, squares, reciprocals, factorials, etc., at the press of a button, in addition to performing arithmetic functions. There is no memory to store mathematical formulae, etc. It is an invaluable tool for solving sophisticated and interesting mathematical problems and also problems in ordinary statistics. It has paved the way for achieving high standards in O/Level Mathematics in those countries.

Just compare the maths questions in the Cambridge IGCSE or the London O/Level Maths Exam with the questions in the Sri Lankan O/Level maths exam and you will see how far our students have fallen behind.

The Cambridge O/Level examination was replaced by the GCSE and the IGCSE (International General Certificate of Secondary Education) a few decades ago.

I am not referring to Programmable Calculators and Graphic Display Calculators (GDC), meaning devices with a small screen that can display graphs, perform statistical calculations like the Z- Score for large samples, show Matrix calculations, provide solutions to algebraic equations, etc., at the press of a few buttons. GDC is a compulsory item for A/Level mathematics students in the UK and in all developed countries.

Some teachers say that by using ordinary scientific calculators in Grades 10 and 11, students will not acquire the ability to carry out mental arithmetic calculations. This is not true because

(i). Calculators are introduced in Grade 10. Maths teachers have five years of Primary School and three years of Middle school (Grades 7, 8 and 9) i.e. a total of eight years to inculcate sufficient mental arithmetic skills in their students before the calculators are introduced in Grade 10!

(ii). In the IGCSE and in the London O/Level Mathematics Exams calculators are not allowed for Paper 1. Preparation for Paper 1 requires the acquisition of mental arithmetic skills, e.g., one lesson per week in class in Grades 10 and 11 in which calculators are not allowed. Sri Lanka could follow suit.

Some people say that it is not necessary for a Grade 10 student to buy an ordinary scientific calculator because they have smartphones with built-in calculators. If not, it is easy to install a calculator app on mobile phones. A smartphone should not be used as a calculator during a mathematics test or a mathematics exam because it can be used for cheating. In the UK and other developed countries students have to keep their smartphones in their school bags or in their lockers outside the classroom during mathematics tests and exams.

An ordinary scientific calculator costs less than 10 % of the price of a smartphone.

Sri Lankan students in International Schools sit the IGCSE or the London O/Level mathematics exams where ordinary scientific calculators are allowed. These students have made big strides in learning mathematics by using the calculators. Only the rich can send their children to International Schools in Sri Lanka. Millions of poor Sri Lankan students do not have calculators.

Our Minister of Education has announced that the government was planning to transform the country’s education system by introducing ‘’STEAM’ (Science, Technology, Engineering, Arts and Mathematics). Maintaining high standards in O/Level Mathematics is the key to a successful implementation of STEAM programme. Unfortunately, the Education Minister and top education official are not aware of the fact that the only way to improve the standard of O/Level Mathematics is to do what the developed countries have done, i. e., revamping the O/Level mathematics syllabus and to introducing the ordinary scientific calculator in Grades 10 & 11. If they do it, it will be an important piece of curriculum development.

Bear in mind that the UK and other developed countries have taken another important step during the last 20 years; they have introduced the Graphic Display Calculator (GDC) to the O/Level Mathematics class and by providing a Core Exam and an Extended Exam. In the Cambridge IGCSE Mathematics Exams, Papers 1, 3, and 5 constitute the Core Exam. Papers 2 ,4 and 6 constitute the Extended Exam. Calculators are not allowed in Papers 1 and 2.

The Core Exam is a boon to students who have very little or no mathematical ability. More on this in my next article.

By using Log Tables, our Sri Lankan O/Level students have to spend a lot of time to solve an IGCSE (Extended Syllabus) exam problem or a London O/Level mathematics exam problem because the use of Log Tables takes a long time  to work out the Squares, Square Roots, exponential powers, reciprocals , LN , factorials, etc., and that is tedious work while their counterparts in developed countries do that in a few seconds by pressing a couple of buttons in an ordinary scientific calculator.

The Calculator has given them more motivation to learn mathematics.

O/Level students in the UK have graduated from the ordinary scientific calculator to the Graphic Display Calculator (GDC) thereby improving their ability to solve more sophisticated, more important and more interesting problems in mathematics, statistics and physics. Sri Lankan O/Level students are compelled to use obsolete Log Tables.

Hats off to that Minister of Education who introduced the ordinary scientific calculator to the Sri Lankan A/ Level Mathematics classroom and to the A/Level Mathematics Exam a few years ago. That was a small step in the right direction. Minister Susil Premjayantha, please revamp the O/Level mathematics syllabus and introduce the ordinary scientific calculator to Grades 10 and 11 now. That will ensure a big boost for your STEAM programme and yield benefits for the Sri Lankan economy.

(To be continued. Topic 2:  The necessity for introducing an O/Level Mathematics Core Exam and an Extended Exam. The writer has taught O/Level and A/Level Mathematics and Physics for 45 years in Asia, Africa and Europe and is an Emeritus Coordinator for International Baccalaureate, Geneva.)



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High govt. revenue and low foreign exchange reserves High foreign exchange reserves and low govt. revenue!

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First shipment of vehicles imported to Sir Lank after the lifting the ban on automobile imports

Government has permitted, after several years, the import of motor cars. Imports, including cars, were cut off because the government then wisely prioritised importing other commodities vital to the everyday life of the general public. It is fair to expect that some pent-up demand for motor vehicles has developed. But at what prices? Government seems to have expected that consumers would pay much higher prices than had prevailed earlier.

The rupee price of foreign exchange had risen by about half from Rs.200 per US$ to Rs.300. In those years, the cost of production of cars also had risen. The government dearly wanted more revenue to meet increasing government expenditure. Usually, motor cars are bought by those with higher incomes or larger amounts of wealth. Taxes on the purchase of cars probably promote equity in the distribution of incomes. The collection of tax on motor cars is convenient. What better commodity to tax?

The announced price of a Toyota Camry is about Rs.34 million. Among us, a Camry is usually bought by those with a substantially higher income than the average middle-income earner. It is not a luxury car like a Mercedes Benz 500/ BMW 700i. Yes, there are some Ferrari drivers. When converted into US dollars, the market price of a Camry 2025 in Sri Lankan amounts to about $110,000. The market price of a Camry in US is about $34,000, where it is usually bought by income earners in the middle-middle class: typically assistant professors in state universities or young executives. Who in Lanka will buy a Camry at Rs.34 million or $110,000 a piece?

How did Treasury experts expect high revenue from the import of motor cars? The price of a Toyota Camry in US markets is about $34,000. GDP per person, a rough measure of income per person in US, was about $ 88,000 in 2024. That mythical ‘average person’ in US in 2024, could spend about 2.5 month’s income and buy a Toyota Camry. Income per person, in Lanka in 2024, was about $ 4,000. The market price of a Camry in Lanka is about $ 133,000. A person in Lanka must pay 33 years of annual income to buy a Toyota Camry in 2025.

Whoever imagined that with those incomes and prices, there would be any sales of Camry in Lanka? After making necessary adjustments (mutatis mutandis), Toyota Camry’s example applies to all import dues increases. Higher import duties will yield some additional revenue to government. How much they will yield cannot be answered without much more work. High import duties will deter people from buying imported goods. There will be no large drawdown of foreign exchange; nor will there be additional government revenue: result, high government foreign exchange reserves and low government revenue.

For people to buy cars at such higher prices in 2025, their incomes must rise substantially (unlikely) or they must shift their preferences for motor cars and drop their demand for other goods and services. There is no reason to believe that any of those changes have taken place. In the 2025 budget, government has an ambitious programme of expenditure. For government to implement that programme, they need high government revenue. If the high rates of duties on imports do not yield higher government revenue as hypothesised earlier, government must borrow in the domestic market. The economy is not worthy of raising funds in international capital markets yet.

If government sells large amounts of bonds, the price of all bonds will fall, i.e. interest rates will rise, with two consequences. First, expenditure on interest payments by government will rise for which they would need more revenue. Second, high interest rates may send money to banks rather than to industry. Finding out how these complexities will work out needs careful, methodically satisfactory work. It is probable that if government borrows heavily to pay for budgetary allocations, the fundamental problem arising out of heavy public debt will not be solved.

The congratulatory comments made by the Manager of IMF applied to the recent limited exercise of handling the severity of balance of payments and public debt problems. The fundamental problem of paying back debt can be solved only when the economy grows fast enough (perhaps 7.5 % annually) for several years. Of that growth, perhaps, half (say 4 % points) need to be paid back for many years to reduce the burden of external debt.

Domestic use of additional resources can increase annually by no more than 3.5 percent, even if the economy grows at 7.5 percent per year. Leaders in society, including scholars in the JJB government, university teachers and others must highlight the problems and seek solutions therefor, rather than repeat over and over again accounts of the problem itself.

Growth must not only be fast and sustained but also exports heavy. The reasoning is as follows. This economy is highly import-dependent. One percent growth in the economy required 0.31% percent increase in imports in 2012 and 0. 21 percent increase in 2024. The scarcity of imports cut down the rate of growth of the economy in 2024. Total GDP will not catch up with what it was in (say) 2017, until the ratio of imports to GDP rises above 30 percent.

The availability of imports is a binding constraint on the rate of growth of the economy. An economy that is free to grow will require much more imports (not only cement and structural steel but also intermediate imports of many kinds). I guess that the required ratio will exceed 35 percent. Import capacity is determined by the value of exports reduced by debt repayments to the rest of the world. The most important structural change in the economy is producing exports to provide adequate import capacity. (The constant chatter by IMF and the Treasury officials about another kind of structural change confuses the issue.) An annual 7.5 percent growth in the economy requires import capacity to grow by about 2.6 percent annually.

This economy needs, besides, resources to pay back accumulated foreign debt. If servicing that accumulation requires, takes 4% points of GDP, import capacity needs to grow by (about) 6.6 percent per year, for many years. Import capacity is created when the economy exports to earn foreign exchange and when persons working overseas remit substantial parts of their earnings to persons in Lanka. Both tourism and remittances from overseas have begun to grow robustly. They must continue to flow in persistently.

There are darkening clouds raised by fires in prominent markets for exports from all countries including those poor. This is a form of race to the bottom, which a prominent economist once called ‘a policy to beggar thy neighbour (even across the wide Pacific)’. Unlike the thirty years from 1995, the next 30 years now seem fraught with much danger to processes of growth aided by open international trade. East Asian economies grew phenomenally by selling in booming rich markets, using technology developed in rich countries.

Lanka weighed down with 2,500 years of high culture ignored that reality. The United States of America now is swinging with might and main a wrecking ball to destroy that structure which they had put up, one thought foolishly, with conviction. Among those storms, many container ships would rather be put to port than brave choppy seas. High rates of growth in export earnings seem a bleak prospect. There yet may be some room in the massive economies of China and India.

Consequently, it is fanciful to expect that living conditions will improve rapidly, beginning with the implementation of the 2025 budget. It will be a major achievement if the 2025 budget is fully implemented, as I have argued earlier. Remarkable efforts to cut down on extravagance, waste and the plunder of public funds will help, somewhat; but not enough. IMF or not, there is no way of paying back accumulated debt without running an export surplus sufficient to service debt obligations.

Exports are necessary to permit the economy to pay off accumulated debt and permit some increase in the standard of living. Austerity will be the order of the day for many years to come. It is most unlikely that the next five years will usher in prosperity.

By Usvatte-aratchi

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BLOSSOMS OF HOPE 2025

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An Ikebana exhibition in aid of pediatric cancer patients

This Ikebana exhibition by the members of Ikebana International Sri Lanka Chapter #262, brings this ancient art form to life in support of a deeply meaningful cause: aiding the Pediatric Cancer ward of the Apeksha Cancer Hospital, Maharagama and offering hope to young warriors in their fight against illness.

Graceful, delicate, and filled with meaning—Ikebana, the Japanese art of floral arrangement, is more than just an expression of beauty; it is a reflection of life’s resilience and harmony. “Blossoms of Hope”, is a special Ikebana exhibition, on 29th March from 11a.m. to 7p.m. and 30th March from 10a.m. to 6p.m. at the Ivy Room, Cinnamon Grand Hotel and demonstrations will be from 4p.m. to 5p.m. on both days.

Each floral arrangement in this exhibition is a tribute to strength, renewal, and love. Carefully crafted by skilled Ikebana artists, who are members of the Chapter. These breathtaking displays symbolize the courage of children battling cancer, reminding us that even in adversity, beauty can bloom. The graceful lines, vibrant hues, and thoughtful compositions of Ikebana echo the journey of resilience, inspiring both reflection and compassion.

Visitors will not only experience the tranquility and elegance of Japanese floral art but will also have the opportunity to make a difference. Proceeds from “Blossoms of Hope” will go towards enhancing medical care, providing essential resources, and creating a more comforting environment for young patients and their families.

This exhibition is more than an artistic showcase—it is a gesture of kindness, a symbol of solidarity, and a reminder that hope, like a flower, can grow even in the most unexpected places. By attending and supporting “Blossoms of Hope”, you become a part of this journey, helping to bring light and joy into the lives of children who need it most.

Join in celebrating art, compassion, and the Power of Hope—one flower at a time.

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St. Anthony’s Church feast at Kachchativu island

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Fort Hammenhiel

The famous St. Anthony’s Church feast this year was held on 14 and 15 March. St. Anthony, as per Catholic belief, gives protection and looks after fishermen and seafarers like me. Many Buddhist seafarers are believers in St. Anthony and they usually keep a statue of the saint in their cabins in the ship or craft.

St. Anthony died on 13th June 1231 at age of 35 years, at Padua in Holy Roman Empire and was canonized on 30 May 1232 by Pope Gregory IX.

I was unable to attend last year’s feast as I was away in Pakistan as Sri Lanka’s High Commissioner. I was more than happy to learn that Indians were also attending the feast this year and there would be 4,000 devotees.

I decided to travel to Kankesanturai (KKS) Jaffna by train and stay at my usual resting place, Fort Hammenhiel Resort, a Navy-run boutique hotel, which was once a prison, where JVP leaders, including Rohana Wijeweera were held during the 1971 insurrection. I was fortunate to turn this fort on a tiny islet in Kytes lagoon into a four-star boutique hotel and preserve Wijeweera’s handwriting in 2012, when I was the Commander Northern Naval Area.

I invite you to visit Fort Hammenhiel during your next trip to Jaffna and see Wijeweera’s handwriting.

The train left Colombo Fort Railway Station on time (0530 hrs/14th) and reached KKS at 1410 hrs. I was highly impressed with the cleanliness and quality of railway compartments and toilets. When I sent a photograph of my railway compartment to my son, he texted me asking “Dad, are you in an aircraft or in a train compartment? “

Well done Sri Lanka Railways! Please keep up your good work. No wonder foreign tourists love train rides, including the famous Ella Odyssey.

Travelling on board a train is comfortable, relaxed and stress free! As a frequent traveller on A 9 road to Jaffna, which is stressful due to oncoming heavy vehicles on. This was a new experience and I enjoyed the ride, sitting comfortably and reading a book received from my friend in New York- Senaka Senaviratne—’Hillbilly Elegy’ by US Vice President JD Vance. The book is an international best seller.

My buddy, Commodore (E) Dissanayake (Dissa), a brilliant engineer who built Reverse Osmosis Water Purification Plants for North, North Central and North Western provinces to help prevent chronic kidney disease is the Commodore Superintendent Engineering in the Northern Naval Area. He was waiting at the KKS railway station to receive me.

I enjoyed a cup of tea at Dissa’s chalet at our Northern Naval Command Headquarters in KKS and proceeded to Fort Hammenhiel at Karainagar, a 35-minute drive from KKS.

The acting Commanding Officer of Karainagar Naval Base (SLNS ELARA) Commander Jayawardena (Jaye) was there at Fort Hammenhiel Restaurant to have late lunch with me.

Jaye was a cadet at Naval and Maritime Academy, (NMA) Trincomalee, when I was Commandant in 2006, NMA was under artillery fire from LTTE twice, when those officers were cadets and until we destroyed enemy gun positions, and the army occupied Sampoor south of the Trincomalee harbour. I feel very proud of Jaye, who is a Commander now (equal to Army rank Lieutenant Colonel) and Commanding a very important Naval Base in Jaffna.

The present Navy Commander Vice Admiral Kanchana Banagoda had been in SLNS ELARA a few hours before me and he had left for the Delft Island on an inspection tour.

Commander Jaye was very happy because his Divisional Officer, when he was a cadet, was Vice Admiral Kanchana (then Lieutenant Commander). I had lunch and rested for a few hours before leaving Karainagar in an Inshore Patrol Craft heading to Kachchativu Island by1730 hrs.

The sea was very calm due to inter-monsoon weather and we reached Kachchativu Island by 1845 hrs. Devotees from both Sri Lanka and India had already reached the island. The Catholic Bishop of Sivagangai Diocese, Tamil Nadu India His Eminence Lourdu Anandam and Vicar General of Jaffna Diocese Very Rev Fr. PJ Jabaratnam were already there in Kachchativu together with more than 100 priests and nuns from Sri Lanka and India. It was a solid display of brotherhood of two neighbouring nations united together at this tiny island to worship God. They were joined by 8,000 devotees, with 4,000 from each country).

The church

All logistics—food, fresh water, medical facilities—were provided by the Sri Lanka Navy. Now, this festival has become a major annual amphibious operation for Navy’s Landing Craft fleet, led by SLNS Shakthi (Landing Ship tanks). The Navy establishes a temporary base in a remote island which does not have a drop of drinking water, and provides food and water to 8,000 persons. The event is planned and executed commendably well under Commander Northern Naval Area, Rear Admiral Thusara Karunathilake. The Sri Lankan government allocates Rs 30 million from the annual national budget for this festival, which is now considered a national religious festival.

The Indian devotees enjoy food provided by SLN. They have the highest regard for our Navy. The local devotees are from the Jaffna Diocese, mainly from the Delft Island and helped SLN. Delft Pradeshiya Sabha and AGA Delft Island. A very efficient lady supervised all administrative functions on the Island. Sri Lanka Police established a temporary police station with both male and female officers.

As usual, the Sinhalese devotees came from Negombo, Chilaw, Kurunegala and other areas, bringing food enough for them and their Catholic brothers and sisters from India! Children brought biscuits, milk toffee, kalu dodol and cakes to share with Indian and Jaffna devotees.

In his sermon on 22nd December 2016, when he declared open the new Church built by SLN from financial contributions from Navy officers and sailors, Jaffna Bishop Rt Rev Dr Justin Bernard Ganapragasam said that day “the new Church would be the Church of Reconciliation”.

The church was magnificent at night. Sitting on the beach and looking at the beautiful moon-lit sea, light breeze coming from the North East direction and listening to beautiful hymns sung by devotees praising Saint Anthony, I thanked God and remembered all my friends who patrolled those seas and were no more with us. Their dedication, and bravery out at sea brought lasting peace to our beloved country. But today WHO REMEMBERS THEM?

The rituals continued until midnight. Navy Commander and the Indian Consul General in Jaffna Sai Murali attended the Main Mass.

The following morning (15) the Main Mass was attended by Vice Admiral Kanchana Banagoda and his family. It was a great gesture by the Navy Commander to attend the feast with his family. I had a long discussion with Indian Consul General Jaffna Sai Mulari about frequent incidents of Indian trawlers engaging in bottom trawling in Sri Lankan waters and what we should do as diplomats to bring a lasting solution to this issue, as I was highly impressed with this young Indian diplomat.

The Vicar General of the Jaffna Diocese, my dear friend, Very Rev Father P J Jabarathnam also made an open appeal to all Indian and Sri Lankan fishermen to protect the environment. I was fortunate to attend yet another St. Anthony’s Church feast in Kachchativu.

By Admiral Ravindra C Wijegunaratne WV,

RWP& Bar, RSP, VSV, USP, NI (M) (Pakistan), ndc, psn,
Bsc (Hons) (War Studies) (Karachi) MPhil (Madras)
Former Navy Commander and Former Chief of Defense Staff
Former Chairman, Trincomalee Petroleum Terminals Ltd
Former Managing Director Ceylon Petroleum Corporation
Former High Commissioner to Pakistan

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