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Maths: Use of calculators at GCE O/L and A/L

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by Anton Peiris, Emeritus Coordinator, International Baccalaureate, Switzerland

(Reduce O/Level STRESS continued)

Sri Lankan GCE O/Level students are 40 years behind their counterparts in the UK vis-a-vis the use of calculators, which were introduced into secondary schools in the UK around 1980. These ordinary scientific calculators had arithmetic functions, squares, square roots, reciprocals, trigonometrical, exponential and logarithmic functions and their Inverses, etc. They were not graphic display calculators (i. e. calculators that can display graphs, statistical functions, answers to definite integrals,etc. on a small screen at the press of a few buttons). 

Cambridge O/L Exams were replaced by the GCSE/IGCSE (General/International General Certificate of Secondary Education) exams about 35 years ago. Use of Graphic display Calculators are allowed in some maths papers in the GCSE / IGCSE Exams. Cambridge IGCSE Maths Exam has 6 Papers. Papers 1, 3 and 5 constitute the Core Exam and Papers 2, 4 and 6 constitute the Extended Exam. Graphic display Calculators are allowed in Papers 3, 4, 5 and 6. In the London O/Level Maths Exam, calculators are not allowed in Paper 1. In Paper 2, ordinary scientific calculators are allowed. 

Use of calculators does not mean that a student no longer needs proficiency in mental arithmetic calculations. Calculators should be introduced in Grade 9. That provides sufficient time for the maths teachers in Grades 6, 7 and 8 to build up on the mental arithmetic skills that the students have acquired in the Primary school. Note that, in the Cambridge GCSE / IGCSE Maths Exam and in the London OL Maths Exam there is a Paper in which calculators are not allowed. It should be the same for the Sri Lankan O/L Maths Exam. Our O/L maths teachers (in Grades 9, 10 and 11) will then be entrusted with the task of preparing our students for that Exam Paper. It will further reinforce the mental arithmetic skills of our students. The argument that calculators should be avoided because they are a hindrance to the acquisition of mental arithmetic skills is a fallacy. The advantages of using calculators in the O/L and A/L classrooms and in the Exams are given below.

Calculators are an important tool in the teaching of Mathematics in secondary schools because students can use them to solve more sophisticated maths problems. Also, it takes less time to solve a maths problem by using a calculator than by using log tables and trigonometrical tables. In many countries, students are trained to use ordinary scientific calculators for O/Level and Graphic display Calculators for A/Level. 

Consider the following excerpts from the document titled ‘National Curriculum Framework, ‘published by our National Institute of Education:

Mathematics education contributes to the creation of citizens who are logical, analytical and critical in thinking and able to make decisions that enable them to find the best possible solutions to the problems they encounter in real life.

Science, Technology, Engineering and Mathematics Education (STEM) provide energy for any society to march forward in the diverse and complex world where we are. 

Prof. G.L. Peiris has hit the nail on the head when he stated the following at the NIE last September: ‘’Focus should be ade on two areas, viz. the method of teaching and the school curriculum. The present method of teaching does not focus on the development of a child’s analytical and critical thinking skills. The school curriculum should be revised ‘’.

 

Question:

What is the difference between mathematics Syllabus and mathematics Curriculum?

 

Answer:

Syllabus is a list of topics to be taught. Curriculum includes the whole mathematical experience of the pupil, i.e. both what is taught and how it is taught. The Curriculum therefore includes the Syllabus; it is concerned with the way in which the Syllabus is presented in the classroom as well as with other matters which are important. For example, problem solving, logical deduction, abstraction, generalisation, conjecture, testing and use of calculators should play a part in the work of all pupils. Introduction of calculators into the O/L and A/L Mathematics classrooms and for the Mathematics Exams will constitute a major revision of the Curriculum. 

Ordinary scientific calculators are now allowed in the A/Level classrooms and in the A/Level Mathematics Exam in Sri Lanka. It is a step in the right direction. It should be Graphic display Calculators for A/Level. The reasons are given below.

Graphic display Calculators will help our A/Level students to solve more sophisticated maths problems, to do precision graphical work on the display Screen, to solve Definite Integral Calculus questions on Areas, Volumes, etc., and also to solve problems in Probability and Statistics (e. g. Calculation of Standard Deviation, use of the Normal distribution, Binomial distribution and the Poisson distribution ) quickly. These Calculus and Statistical topics involve solutions to some real-life problems. Graphic display Calculator does not tell the student how to solve a maths problem. It only helps the student to solve the problem by performing cumbersome mathematical calculations quickly. Note that teaching Permutations, Combinations, Probability and Statistics in O/Level and in A/Level classrooms is one sure method of sharpening the analytical, critical and logical thinking skills of our students. That is, calculators can make a contribution towards the achievement of some of the objectives of the National Institute of Education. 

O/L and A/L students in the U.K., in all European countries, in Japan, Russia, China, and in many other countries have made good progress in solving mathematical and statistical problems by using calculators in the classroom. Our Sri Lankan students are trailing far behind because our Ministry of Education has turned a blind eye on this important technological tool for decades. It’s high time for the Ministry of Education and the NIE to wake up and face this reality. A small minority of O/Level students in Sri Lanka (i. e. those who attend International Schools and prepare for the London O/L Exams) are using calculators and the vast majority of Sri Lankan O/L students are left in the lurch. They remain bogged down in the old log tables.

Sri Lankan O/L students do online learning with their smartphones but they have been denied a very basic technological tool, viz. the ordinary scientific calculator.

It is far cheaper to equip a student with a calculator than with a laptop or a tablet or a smartphone. The need of the hour is for our secondary schools to invest in ordinary scientific calculators and in Graphic display Calculators. The Ministry of Education and the NIE should take the steps to satisfy this long felt need. Introduction of calculators will necessitate some changes in the format of the O/L and A/L Mathematics Exams. e.g. Calculators should be allowed only in Paper 2. I hope that the Ministry of Education and the NIE will take the necessary steps to start Training Courses in Graphic display Calculators for our A/L maths teachers. 

 

(The writer has taught O/L, A/L and IB mathematics and physics for 45 years in Sri Lanka, Kenya and Switzerland).



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New US sanctions on ICC, a fillip to worldwide political repression

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The International Criminal Court in session. UN Photo/Eskinder Debebe

US Secretary of State Marco Rubio’s warning to the International Criminal Court (ICC) was stark: ‘Either the ICC will end its threats, or we will end the ICC.’ It followed US central administration accusations that the court was unfairly targeting Americans on the basis of trumped-up war crimes charges.

However, a new plethora of sanctions has been clamped on the ICC by the US, which in turn has spurred accusations by sections of the world that the latter has unleashed an ‘assault’ on the international legal order.

What some of the sanctions would mean for the ICC was outlined by Rubio: ‘We will ban transactions with this rogue court, cutting off their resources and crippling their ability to operate against us.’

The ICC has shown consistency of purpose over the years. Despite some operational constraints it has indicted a large number of political strongmen from around the world, accused of war crimes and other governance excesses that come under its purview. Two such recent figures are: Russian President Vladimir Putin and Israeli Prime Minister Benjamin Netanyahu.

Rather than enjoy a mere nominal presence in the world community, the ICC has proved its effectiveness by detaining and bringing to justice scores of VIP politicians and others of their ilk who have been found guilty of human rights abuses and kindred excesses that come within the terms of reference of the ICC.

Accordingly, the international justice system would be stymied considerably as a result of the ICC being dis-empowered, particularly financially. Needless to say, potential and real perpetrators of the species of crime coming under the jurisdiction of the ICC would stand to gain most from such anarchic tendencies. That is, political repression globally would be enabled to enjoy a new lease of life.

A detailing of the types of crime coming under the purview of the ICC provides an idea of what it would cost the international community if the ICC’s operations are gravely hampered. They are mainly: genocide, war crimes, crimes against humanity and the crime of aggression.

That is, the part of the world to be worst affected would be the global South, since the latter is awash with the mentioned crimes. Needless to say, a chronically-disaffected South will sooner rather than later undermine the well being of the world dangerously. The world is already being put through these paces.

At the time of writing, ‘illegal migrants’ from the South, for example, are aggravating many a Western economy’s woes, besides creating for them acute law and order issues. The fact that these migrants’ presence goes on to become a virtual test of the migrant receiving states’ ability to forge domestic social inclusion in the face of jingoistic protests by mainly white supremacist groups is evidence of the latter. As is known, the US, to take just one example, has been up against this crisis for quite a while.

Accordingly, it will be in the best interests of the West if ‘illegal’ migrant arrivals on their shores are stemmed. If the socio-political and economic problems assailing the South are effectively managed through North-South collaborative, ‘trouble-shooting’ efforts the causes leading to ‘illegal’ migration and connected issues could be resolved at source as it were. For, it is the aggravation of the South’s material questions that lays the basis for the emergence of repressive and anti-democratic regimes in the hemisphere.

Until such time that the aforementioned issues in North-South relations are visited afresh and addressed urgently, a vibrantly functioning ICC would be needed. For, the latter would prove a deterrent to Southern political and military strongmen, highly prone to power abuse and like excesses, from coming into being in the wake of the South’s chronic material woes and the wars and conflicts that result from them.

It stands to reason then that the US would be acting in its own interests by enabling the ICC to perpetuate its mandate without hindrance. For a crop of issues that impinges negatively on internal law and order would be defused.

Meanwhile, there needs to be a meeting of minds among the rest of the West to put back in place a North-South dialogue process aimed at reducing some of the economic pressures that are weighing on the South.

Since economics usually drives politics it will be in the interests of the world community to scrutinizingly re-visit North-South issues of the past and put in place economic relief packages for Southern publics that would enable them to tide over their material hardships rather than permit the latter to aggravate into social disaffection and eventually armed militancy. It is the latter juncture that paves the way for the emergence of authoritarian rulers in the South who then go on to be a blight on their publics.

Accordingly, the Southern-based global development thinking of the past that envisaged a more equitable world economic order needs to be seen as an urgent need. That is, NAM’s international development paradigms need to be resuscitated to the extent possible.

It is unlikely that rightist governments of the West, such as the current Republican administration in the US, would find these projects feasible, but democratic states of Europe, led by perhaps the UK, are likely to think otherwise. For it would not be beneficial for the democratic world to be having on their hands repressive governments in the South who would be gravitating towards the major military and economic actors of the South, such as Iran and North Korea, who tend to be in constant power struggles with the West.

However, until such time that the mentioned, pro-people initiatives are given serious thought the ICC would need to be enabled by the international community to be in place comfortably and carry on with its mandate of bringing repressive rulers to book. Besides the ICC should pave the way for the peoples of the developing world to enjoy some substantial respite from the political repression and even terror which tend to be their lot.

Meanwhile, the wars of West Asia are relentlessly aggravating the economic hardships of people everywhere, driving the point home to enlightened sections that there is no alternative to peacemaking. A challenge is to convert the US under President Trump to this line of thinking.

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Clear, soft and shine-free skin

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This week, I give you five simple, time-tested homemade remedies that help reduce the appearance of blemishes, control excess shine and leave your skin feeling softer and smoother.

The Honey and Lemon Brightening Dab:

For stubborn blemish marks, this is a classic. Mix one teaspoon of pure bee honey with three to four drops of fresh lemon juice. Apply gently, only on the affected spots, and leave for 10 minutes before rinsing with lukewarm water. While honey soothes and softens, lemon helps to brighten naturally. Use twice a week in the evening.

Besan and Rose Water Oil-Control Pack:

An ideal remedy to combat shine, especially on the T-zone. Take two teaspoons of besan (gram flour) and mix with sufficient rose water to form a smooth paste. Add a pinch of turmeric for its antiseptic goodness. Apply evenly, keep for 15 minutes and wash off. It absorbs excess oil without over-drying, leaving a beautiful matte finish.

Aloe Vera and Cucumber Ice Soother:

Blend fresh aloe vera gel with the juice of a grated cucumber and freeze the mixture in an ice tray. Each morning, wrap one cube in a soft muslin cloth and gently rub over a cleansed face for 30 seconds. It calms, tightens pores and imparts a baby-soft smoothness.

Oatmeal and Curd Gentle Polish:

Roughness and old blemish marks need gentle exfoliation. Combine one tablespoon of finely powdered oatmeal with one tablespoon of fresh curd (yoghurt). Massage very gently, in circular motions, for one minute, leave for five minutes and rinse. It removes dead cells and unveils softer, clearer skin.

 Multani Mitti and Green Tea Magic Mask:

Brew some green tea and allow it to cool completely. Mix one and a half teaspoons of Multani Mitti (Fuller’s Earth) with the tea water to make a fine paste. Apply for 10 to 12 minutes – do not let it dry and crack completely – and wash off. It draws out impurities, fades blemishes and bestows a fresh, shine-free glow.

A Gentle Reminder:

As with any natural remedy, always do a patch test on your inner arm first. For those with oily or combination skin, avoid heavy coconut oil application and harsh scrubbing, as they tend to aggravate shine and blemishes.

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Features

Compete, shine and be discovered at WCOPA 2027

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Dream of performing on a world stage? Well, here is your unique, golden opportunity!

The World Championships of Performing Arts (WCOPA) — the one and only official “Talent Olympics” — is the world’s premier global platform for aspiring singers, dancers, actors, models, instrumentalists, etc., to compete, shine and be discovered!

And, yes, this world stage is open to YOU, Sri Lankans living in Sri Lanka and overseas!

Held annually in glittering Las Vegas, WCOPA brings together over 70 countries, all competing for Gold, Silver and Bronze Medals, just like the traditional Olympics.

Lakisha Bernard: Will represent Team Sri Lanka at WCOPA 2027

Outstanding performers vie for the coveted titles of Junior and Senior Grand Champion Performer of the World, with winners and standout participants awarded over $500,000 in scholarships, cash awards and prizes to catapult their education and careers!

Sri Lanka is already making waves! At WCOPA 2026, Natharie Wickramasinghe, representing Team Sri Lanka, made the nation proud by winning a Bronze Medal in the Ethnic/Folklore Dance category!

Lakisha: Accomplished freelance Model and Fashion Design graduate

Recruitment for this prestigious competition is handled through a system of scouts and licensed National Directors — and this is where our very own Chris Rajendra, now based in Las Vegas, and National Director for Team Sri Lanka, comes into the scene.

If you are a singer, dancer, actor, model, instrumentalist — if you have talent burning inside you — contact Chris Rajendra today for registration and, who knows, you may find yourself in Las Vegas, and proudly draped in the Sri Lankan flag, at WCOPA 2027!

The contact address is: Chris Rajendra, wcopa.nationaldirector.sl@gmail.com

or chris.rajendra@gmail.com

Meanwhile, a star is born for 2027, in the form of Lakisha Bernard who is all set to represent Team Sri Lanka at WCOPA 2027.

Originally hailing from the sun-drenched coastal city of Colombo and now carving out her creative career in Canada, 22-year-old Lakisha is stepping into the international spotlight.

This accomplished freelance Model and Fashion Design graduate has officially been appointed as the Team Sri Lanka Promoter for Canada as she prepares to represent Team Sri Lanka at WCOPA in Las Vegas.

Lakisha brings a unique blend of high-fashion sensibility, captivating camera presence and expert garment design to the Team.

Having built her career, from local college shoots to high-glamour concepts, Lakisha’s inspiring journey embodies the true spirit of cultural bridge-building and creative resilience, bringing immense pride and recognition to Sri Lanka on the global stage.

WCOPA 2027 will be held at the legendary Westgate Hotel & Casino, Las Vegas, from 12th to 20th July – the very same iconic arena where the late, great Elvis Presley himself performed!

Your moment is now. Your stage is Las Vegas, so hurry and contact Chris Rajendra.

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