Features
English in Mathematics
By R.N.A. de Silva
“Which subject did you have most difficulties with, having switched the medium of instruction from Sinhala to English?” I posed this question to a Sri Lankan student who was following a pre-University course in an educational institution in Hong Kong, having completed studies up to the GCE Ordinary Level programme in the Sinhala medium in a leading girls’ school in Colombo. “It is definitely mathematics,” she replied. Having served as a teacher for a long period of time at this educational institution with students from over 80 countries, I realised the above-mentioned view was shared by other students, too, who had to change the medium of instruction to English. This does not seem to make sense as one would have expected mathematics to be the easiest subject to follow as it has its own symbolic language. Why then has this situation arisen?
I would like to separate these difficulties into two categories:
1. Hastiness due to mindset
2. Vocabulary issues
Sometimes hastiness can automatically occur due to the mindset that mathematics should be easy to follow even if you change the medium of instruction as you are dealing with symbols. This attitude can cause enormous problems as students may skip instructions or avoid reading the question fully and concentrate only on the symbolic part of the problem
As an example, consider the following question.
The graphs of lines 3y = 5x + 1 and 2y = 7 – 3x intersect at point P. Find the coordinates of P.
Seeing the word ‘graphs’ and the two equations, a student maybe tempted to draw the graphs of the two lines and thereby find the point of intersection, which is a time-consuming affair. If it was read properly, the student could have noticed that the solution can be obtained by solving the two equations algebraically, which is much more efficient.
To a fast reader, obtaining the correct answer to the following question can be a problem as it may end up with just finding the value of x.
If 2x+3 = 5x-3, find the value of 2x+3.
The students need to be trained to read the question fully and understand what is required to be done, before attempting it.
The time spent to grasp the aim of the question is not wasted time.
Many children consider mathematics as an alien language consisting of symbols and expressions. Most of the difficulties that students encounter is related to vocabulary. The mathematical interpretation of the meaning of a word may differ from the meaning given to it in the English language. The word ‘find’ in mathematics means to obtain an answer showing the working while in the English language, it refers to discover or search. The following sketch shows the funny side of this difference.
Two of the words that has caused much confusion are ‘or’ and ‘and’.
In general usage, A or B is considered as either A or B but not both, as shown in picture.
However, in mathematics ‘A or B’ means ‘it can belong to A or B including intersection’. This is shown in picture.
The above, in normal usage is interpreted as ‘A and B’. However, in mathematics A and B refers to only what is common to A and B as shown in picture.
Here are the mathematical meanings of some of the other words which can have a different meaning with the English language definitions.
Determine
– Obtain the only possible answer
Plot
– Mark the position of points on a diagram
Write down
– Obtain the answer (Working need not be shown)
Constant
– A number that does not change
Similar
– Having the same shape but not the same size
Deduce
– To show a result using known information
Operation
– A procedure such as addition, subtraction, multiplication, etc.
Element
– A member of a set
Volume
– The extent of space occupied by a solid
The following illustrate some of the difficulties that the difference of meanings brings:
How odd these odd numbers are? The even numbers are even stranger.
Don’t be mean and help me to find the mean of these numbers.
Is right angle the right answer? Let me write it on the board.
The polysemous nature of some of the mathematical terms make it confusing for the students in the understanding of mathematical concepts. Mathematical terms have precise definitions to describe numerical relationships. At times these definitions resemble the everyday usage meaning but there are instances where the definitions notably differ. Consider ‘in general’ as an example. In mathematics there can be no exceptions to a result if it is considered to hold in general. However, in everyday usage, if a claim is said to be true in general, it would mean that it is true most of the time, but exceptions are possible.
To add to the problem, there are some terms such as ‘degree’ that can have many different meanings within mathematics while having a different meaning in everyday use. In mathematics, degree can refer to the measurement of an angle, the complexity of an algebraic equation and a unit of temperature.
Although mathematics deals essentially with symbols, it is taught through the medium of language which is the major means of communication. Students build understanding as they process ideas through language. It is important for students to give emphasis to the familiarisation with the mathematical vocabulary and at the same time understand the difference of meanings of terms mathematically and everyday usage. Teachers have an important role to play here in highlighting such terms and using them in different contexts for comfortable acclimatization. As Marcus Quintilianus quoted, “One should not aim at being possible to understand, but at being impossible to misunderstand.”
(The author is a senior mathematics examiner of the International Baccalaureate Organization and a member of the faculty of the Overseas School of Colombo.)
Features
Ranking public services with AI — A roadmap to reviving institutions like SriLankan Airlines
Efficacy measures an organisation’s capacity to achieve its mission and intended outcomes under planned or optimal conditions. It differs from efficiency, which focuses on achieving objectives with minimal resources, and effectiveness, which evaluates results in real-world conditions. Today, modern AI tools, using publicly available data, enable objective assessment of the efficacy of Sri Lanka’s government institutions.
Among key public bodies, the Supreme Court of Sri Lanka emerges as the most efficacious, outperforming the Department of Inland Revenue, Sri Lanka Customs, the Election Commission, and Parliament. In the financial and regulatory sector, the Central Bank of Sri Lanka (CBSL) ranks highest, ahead of the Securities and Exchange Commission, the Public Utilities Commission, the Telecommunications Regulatory Commission, the Insurance Regulatory Commission, and the Sri Lanka Standards Institution.
Among state-owned enterprises, the Sri Lanka Ports Authority (SLPA) leads in efficacy, followed by Bank of Ceylon and People’s Bank. Other institutions assessed included the State Pharmaceuticals Corporation, the National Water Supply and Drainage Board, the Ceylon Electricity Board, the Ceylon Petroleum Corporation, and the Sri Lanka Transport Board. At the lower end of the spectrum were Lanka Sathosa and Sri Lankan Airlines, highlighting a critical challenge for the national economy.
Sri Lankan Airlines, consistently ranked at the bottom, has long been a financial drain. Despite successive governments’ reform attempts, sustainable solutions remain elusive.
Globally, the most profitable airlines operate as highly integrated, technology-enabled ecosystems rather than as fragmented departments. Operations, finance, fleet management, route planning, engineering, marketing, and customer service are closely coordinated, sharing real-time data to maximise efficiency, safety, and profitability.
The challenge for Sri Lankan Airlines is structural. Its operations are fragmented, overly hierarchical, and poorly aligned. Simply replacing the CEO or senior leadership will not address these deep-seated weaknesses. What the airline needs is a cohesive, integrated organisational ecosystem that leverages technology for cross-functional planning and real-time decision-making.
The government must urgently consider restructuring Sri Lankan Airlines to encourage:
=Joint planning across operational divisions
=Data-driven, evidence-based decision-making
=Continuous cross-functional consultation
=Collaborative strategic decisions on route rationalisation, fleet renewal, partnerships, and cost management, rather than exclusive top-down mandates
Sustainable reform requires systemic change. Without modernised organisational structures, stronger accountability, and aligned incentives across divisions, financial recovery will remain out of reach. An integrated, performance-oriented model offers the most realistic path to operational efficiency and long-term viability.
Reforming loss-making institutions like Sri Lankan Airlines is not merely a matter of leadership change — it is a structural overhaul essential to ensuring these entities contribute productively to the national economy rather than remain perpetual burdens.
By Chula Goonasekera – Citizen Analyst
Features
Why Pi Day?
International Day of Mathematics falls tomorrow
The approximate value of Pi (π) is 3.14 in mathematics. Therefore, the day 14 March is celebrated as the Pi Day. In 2019, UNESCO proclaimed 14 March as the International Day of Mathematics.
Ancient Babylonians and Egyptians figured out that the circumference of a circle is slightly more than three times its diameter. But they could not come up with an exact value for this ratio although they knew that it is a constant. This constant was later named as π which is a letter in the Greek alphabet.
It was the Greek mathematician Archimedes (250 BC) who was able to find an upper bound and a lower bound for this constant. He drew a circle of diameter one unit and drew hexagons inside and outside the circle such that the sides of each hexagon touch the sides of the circle. In mathematics the circle passing through all vertices of a polygon is called a ‘circumcircle’ and the largest circle that fits inside a polygon tangent to all its sides is called an ‘incircle’. The total length of the smaller hexagon then becomes the lower bound of π and the length of the hexagon outside the circle is the upper bound. He realised that by increasing the number of sides of the polygon can make the bounds get closer to the value of Pi and increased the number of sides to 12,24,48 and 60. He argued that by increasing the number of sides will ultimately result in obtaining the original circle, thereby laying the foundation for the theory of limits. He ended up with the lower bound as 22/7 and the upper bound 223/71. He could not continue his research as his hometown Syracuse was invaded by Romans and was killed by one of the soldiers. His last words were ‘do not disturb my circles’, perhaps a reference to his continuing efforts to find the value of π to a greater accuracy.
Archimedes can be considered as the father of geometry. His contributions revolutionised geometry and his methods anticipated integral calculus. He invented the pulley and the hydraulic screw for drawing water from a well. He also discovered the law of hydrostatics. He formulated the law of levers which states that a smaller weight placed farther from a pivot can balance a much heavier weight closer to it. He famously said “Give me a lever long enough and a place to stand and I will move the earth”.
Mathematicians have found many expressions for π as a sum of infinite series that converge to its value. One such famous series is the Leibniz Series found in 1674 by the German mathematician Gottfried Leibniz, which is given below.
π = 4 ( 1 – 1/3 + 1/5 – 1/7 + 1/9 – ………….)
The Indian mathematical genius Ramanujan came up with a magnificent formula in 1910. The short form of the formula is as follows.
π = 9801/(1103 √8)
For practical applications an approximation is sufficient. Even NASA uses only the approximation 3.141592653589793 for its interplanetary navigation calculations.
It is not just an interesting and curious number. It is used for calculations in navigation, encryption, space exploration, video game development and even in medicine. As π is fundamental to spherical geometry, it is at the heart of positioning systems in GPS navigations. It also contributes significantly to cybersecurity. As it is an irrational number it is an excellent foundation for generating randomness required in encryption and securing communications. In the medical field, it helps to calculate blood flow rates and pressure differentials. In diagnostic tools such as CT scans and MRI, pi is an important component in mathematical algorithms and signal processing techniques.
This elegant, never-ending number demonstrates how mathematics transforms into practical applications that shape our world. The possibilities of what it can do are infinite as the number itself. It has become a symbol of beauty and complexity in mathematics. “It matters little who first arrives at an idea, rather what is significant is how far that idea can go.” said Sophie Germain.
Mathematics fans are intrigued by this irrational number and attempt to calculate it as far as they can. In March 2022, Emma Haruka Iwao of Japan calculated it to 100 trillion decimal places in Google Cloud. It had taken 157 days. The Guinness World Record for reciting the number from memory is held by Rajveer Meena of India for 70000 decimal places over 10 hours.
Happy Pi Day!
The author is a senior examiner of the International Baccalaureate in the UK and an educational consultant at the Overseas School of Colombo.
by R N A de Silva
Features
Sheer rise of Realpolitik making the world see the brink
The recent humanly costly torpedoing of an Iranian naval vessel in Sri Lanka’s Exclusive Economic Zone by a US submarine has raised a number of issues of great importance to international political discourse and law that call for elucidation. It is best that enlightened commentary is brought to bear in such discussions because at present misleading and uninformed speculation on questions arising from the incident are being aired by particularly jingoistic politicians of Sri Lanka’s South which could prove deleterious.
As matters stand, there seems to be no credible evidence that the Indian state was aware of the impending torpedoing of the Iranian vessel but these acerbic-tongued politicians of Sri Lanka’s South would have the local public believe that the tragedy was triggered with India’s connivance. Likewise, India is accused of ‘embroiling’ Sri Lanka in the incident on account of seemingly having prior knowledge of it and not warning Sri Lanka about the impending disaster.
It is plain that a process is once again afoot to raise anti-India hysteria in Sri Lanka. An obligation is cast on the Sri Lankan government to ensure that incendiary speculation of the above kind is defeated and India-Sri Lanka relations are prevented from being in any way harmed. Proactive measures are needed by the Sri Lankan government and well meaning quarters to ensure that public discourse in such matters have a factual and rational basis. ‘Knowledge gaps’ could prove hazardous.
Meanwhile, there could be no doubt that Sri Lanka’s sovereignty was violated by the US because the sinking of the Iranian vessel took place in Sri Lanka’s Exclusive Economic Zone. While there is no international decrying of the incident, and this is to be regretted, Sri Lanka’s helplessness and small player status would enable the US to ‘get away with it’.
Could anything be done by the international community to hold the US to account over the act of lawlessness in question? None is the answer at present. This is because in the current ‘Global Disorder’ major powers could commit the gravest international irregularities with impunity. As the threadbare cliché declares, ‘Might is Right’….. or so it seems.
Unfortunately, the UN could only merely verbally denounce any violations of International Law by the world’s foremost powers. It cannot use countervailing force against violators of the law, for example, on account of the divided nature of the UN Security Council, whose permanent members have shown incapability of seeing eye-to-eye on grave matters relating to International Law and order over the decades.
The foregoing considerations could force the conclusion on uncritical sections that Political Realism or Realpolitik has won out in the end. A basic premise of the school of thought known as Political Realism is that power or force wielded by states and international actors determine the shape, direction and substance of international relations. This school stands in marked contrast to political idealists who essentially proclaim that moral norms and values determine the nature of local and international politics.
While, British political scientist Thomas Hobbes, for instance, was a proponent of Political Realism, political idealism has its roots in the teachings of Socrates, Plato and latterly Friedrich Hegel of Germany, to name just few such notables.
On the face of it, therefore, there is no getting way from the conclusion that coercive force is the deciding factor in international politics. If this were not so, US President Donald Trump in collaboration with Israeli Rightist Premier Benjamin Natanyahu could not have wielded the ‘big stick’, so to speak, on Iran, killed its Supreme Head of State, terrorized the Iranian public and gone ‘scot-free’. That is, currently, the US’ impunity seems to be limitless.
Moreover, the evidence is that the Western bloc is reuniting in the face of Iran’s threats to stymie the flow of oil from West Asia to the rest of the world. The recent G7 summit witnessed a coming together of the foremost powers of the global North to ensure that the West does not suffer grave negative consequences from any future blocking of western oil supplies.
Meanwhile, Israel is having a ‘free run’ of the Middle East, so to speak, picking out perceived adversarial powers, such as Lebanon, and militarily neutralizing them; once again with impunity. On the other hand, Iran has been bringing under assault, with no questions asked, Gulf states that are seen as allying with the US and Israel. West Asia is facing a compounded crisis and International Law seems to be helplessly silent.
Wittingly or unwittingly, matters at the heart of International Law and peace are being obfuscated by some pro-Trump administration commentators meanwhile. For example, retired US Navy Captain Brent Sadler has cited Article 51 of the UN Charter, which provides for the right to self or collective self-defence of UN member states in the face of armed attacks, as justifying the US sinking of the Iranian vessel (See page 2 of The Island of March 10, 2026). But the Article makes it clear that such measures could be resorted to by UN members only ‘ if an armed attack occurs’ against them and under no other circumstances. But no such thing happened in the incident in question and the US acted under a sheer threat perception.
Clearly, the US has violated the Article through its action and has once again demonstrated its tendency to arbitrarily use military might. The general drift of Sadler’s thinking is that in the face of pressing national priorities, obligations of a state under International Law could be side-stepped. This is a sure recipe for international anarchy because in such a policy environment states could pursue their national interests, irrespective of their merits, disregarding in the process their obligations towards the international community.
Moreover, Article 51 repeatedly reiterates the authority of the UN Security Council and the obligation of those states that act in self-defence to report to the Council and be guided by it. Sadler, therefore, could be said to have cited the Article very selectively, whereas, right along member states’ commitments to the UNSC are stressed.
However, it is beyond doubt that international anarchy has strengthened its grip over the world. While the US set destabilizing precedents after the crumbling of the Cold War that paved the way for the current anarchic situation, Russia further aggravated these degenerative trends through its invasion of Ukraine. Stepping back from anarchy has thus emerged as the prime challenge for the world community.
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