Features
Maths: Use of calculators at GCE O/L and A/L
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).
Features
Trump’s tariffs, AKD’s gazette and Sri Lanka’s diplomatic slumber
“We are rather respectable in Colombo. We go to bed fairly early, and we remain there till morning. “
According to Sri Lanka’s diplomatic folklore, the late S.W. R. D. Bandaranaike uttered these words while explaining the reasons for Sri Lanka’s abstention on the UN resolution condemning the Soviet invasion of Hungary. Apparently, SWRD’s foreign ministry officials were asleep at home when the diplomatic cable seeking instructions was received from New York. In those days, there were no cell phones, Internet, or even fax or telex machines. The diplomatic cables were sent through post offices. Decoding them was a slow and time-consuming process. Thus, the government could not provide appropriate instructions to our mission in New York in time, and the Sri Lankan delegation abstained on that sensitive UN vote.
Sri Lanka’s Absence from Section 301 Consultations
But then, how does one explain Sri Lanka’s absence from the crucial bilateral consultation held in Washington by the Office of the United States Trade Representative (USTR) during March-April on “Forced Labour” under the Section 301 of the US Trade Act of 1974? Didn’t our foreign and trade ministries send appropriate instructions to Washington in time? Even if the instructions from the foreign ministry were transmitted to our embassy in Washington by pigeon carriers, there was enough time for Sri Lanka to participate in those meetings.
In March, the USTR initiated these 301 investigations on 60 trading partners, and invited all of them for confidential consultations. Out of the 60, 46 participated in these consultations. Sri Lanka was not one of them. Other countries that didn’t participate in these consultations included China, Russia, and Venezuela! In addition to that, the Section 301 Committee conducted a public hearing with interested parties on April 28 and 29. Washington-based diplomats, representatives from few trade ministries as well as representatives from many foreign trade associations and chambers participated in these hearings. Sri Lanka was once again conspicuously absent.
As a result, when the USTR published the proposed forced labour tariffs on June 2nd, Sri Lanka ended up with a 12.5% duty. Pakistani and Indonesian diplomats participated in these consultations and took appropriate follow-up measures, and managed to enter the 10% duty category. As even a threat of a modest tariff hike could disrupt supply chains and reduce competitiveness, particularly in an industry such as garments, I discussed this issue on 15 June and underscored the importance of Sri Lanka’s participation at the next hearing, which was scheduled to be held from July 7th .
Awakening from Diplomatic Slumber and AKD’s Gazette
Fortunately, Sri Lanka finally awoke from weeks of diplomatic slumber, and Ambassador Mahinda Samarasinghe participated in the public hearing on 9 July, and promised, “…. · We have agreed to the text in our negotiations with the USTR on forced labour, …. The gazette as we speak is being printed and I’m getting the gazette tomorrow morning, and the gazette will be shared with USTR as I get it“.
As promised, President Anura Kumara Dissanayake issued a gazette on 10 July banning the imports of goods produced by forced labour. These new regulations are very similar to what Pakistan and Indonesia enacted in April, after their consultations with USTR in March. Why couldn’t we do it in April? Why did we wait till the very last minute?
Challenges ahead
“War is too important to be left to generals alone,” is a famous saying attributed to former French Premier Georges Clemenceau. Similarly, monitoring our main markets is too important to be left to diplomats alone. The United States is the largest single-country market for Sri Lanka. Therefore, Sri Lankan trade chambers and associations should become more proactive in these markets and participate in these events. For example, the chairman of the Pakistani apparel exporters association participated in the April hearings. Similarly, representatives from the Indian Agricultural and Processed Food Products Export Development Authority, the Federation of Indian Chambers of Commerce and Industry, the Confederation of Indian Industry, and Reliance Industries also participated in July hearings. At an event where each speaker is given only five minutes (strictly enforced), having a number of speakers from a country is an advantage. The presence of industry representatives in these kinds of events also help them understand the market dynamics and the future challenges. This is important, particularly because there will be many more challenges with Trump’s tariffs.
With the gazette issued on 10 July, Sri Lanka has imposed a prohibition on the importation of goods produced with forced labour. Now, the challenge will be to effectively enforce the prohibition. And what are the goods produced with forced labour? The USTR list only focuses on aluminum, cotton, electronics, lithium-ion batteries, rice, and tobacco. However, according to the U.S. Department of Labour, the list is much longer. Hence, this list may change continuously during the next two years and tariffs may fluctuate once again.
So, this is definitely not the time to slumber.
(The writer, a retired public servant, can be reached at senadhiragomi@gmail.com)
by Gomi Senadhira ✍️
Features
Tales of Mystery and Suspense 10 Casino for Sale
After the overwhelming grotesquerie of J K Rowling’s latest Cormoran Strike novel (written, I should have noted, as the others were, under the pseudonym Robert Galbraith), I thought I should return to the world of fun, and also a much shorter description since this thriller moves quickly without the layers of detail that Rowling engages in.
I then move to the second comic thriller by Caryl Brahms and S J Simon. This, their second story to feature Vladimir Stroganoff and Adam Quill, was Casino for Sale, as lunatic a romp as the first, though without the emphasis on the ballet that characterized A Bullet in the Ballet.
This one begins with the impresario Stroganoff buying a casino cheap from Baron Sam de Rabinovich, only to find that it was a rundown place, not the grand casino of La Bazouche, a resort on the Frenc+h Riviera, as he had initially thought. The grand one belonged to Lord Buttonhooke, and Stroganoff could not compete, until he thought of bringing the Ballet Stroganoff to the casino – which of course leads to Buttonhooke deciding to have ballet performances in his Casino too.
Stroganoff invites Quill to visit him, which Quill decides to do since he has left Scotland Yard, having come into a legacy. No one believes this, and he has to face questions as to what he did to have been sacked, with sympathy for having been found out.
The day he arrives in La Bazouche there is a murder, of a vitriolic critic called Citrolo, in Stroganoff’s office. He had been going to write a damning review of the opening night of the ballet and Stroganoff, when he realizes Citrolo cannot be swayed, drugs him and dictates the review himself to the papers. He leaves Citrolo sleeping and finds him shot the next morning, whereupon he decides to muddy the waters and leave a suicide note and lots of other murder weapons. So much overkill, as it were, of course ensures that he is arrested.
But the excitable French detective who makes the arrest follows up his suggestion that Buttonhooke was also involved, and so the two casino owners find themselves in cells next door to each other, with the detective Gustave quite happy to provide creature comforts for a fee.
Quill decides he must investigate, and finds Gustave most cooperative, since he has a laid back attitude to work. So it is Quill that finds a notebook which makes it clear Citrolo is an accomplished blackmailer, and that there are lots of possible murderers, including Stroganoff’s croupier, who was crooked, Rabinovich, who was now working for Buttonhooke, a confidence trickster called Kurt Kukumber, whose prospectus for a dud gold mine was found in the office and Prince Alexis Artishok who was engaged in a deal to buy diamonds from the ballerina Dyra Dyrakova.
Stroganoff had been trying to get Dyrakova to dance for him, but having done so previously she had refused. But then to Stroganoff’s chagrin she agreed to dance for Buttonhooke. The clearly crooked Artishok had told Buttonhooke’s mistress Sadie Souse, who was not very bright, that Dyrakova possessed diamonds she was willing to sell cheap, and Sadie was determined to have them.
Quill meanwhile finds out that there was a secret passage to Stroganoff’s office, the obvious solution to what had begun as a locked room mystery, and that this was known by almost everyone apart from Stroganoff himself. And then Rabinovich is murdered, just after Gustave had released his two original suspects, leading him to blame Quill for having insisted on that and thus allowing them to kill again.
Soon afterwards Dyrakova arrives, and the town is full of posters announcing that she will appear in the casinos, elaborate posters for either one, since Stroganoff is determined that she will dance for him, and if she does not come willingly, he has devised a scheme to make her do so unwillingly. So, though Buttonhooke has her taken off to his yacht immediately she arrives at the station, Quill along with Arenskaya gets her into a launch and to Stroganoff’s casino, where she performs to tumultuous applause, not knowing for whom she is dancing.
When Quill asked her about the diamonds, she said she had sold them long ago, and that gave Quill the solution to the mystery. Rabinovich had known about this, and Artishok had killed him to prevent Sadie learning it from him, he had killed Citrolo who had recognized him for an accomplished card sharper, not a Russian prince at all. But before he is arrested, he gets away in a boat, and the police launch that pursues him is on the point of catching him up when it runs out of petrol.
Again, lots of excitement, and entertaining references – Gustave grows marrows – and if not quite as brilliant as its predecessor, Casino was certainly a delightful read.
Features
The challenge of being positive about SAARC
It was a few years back that a former President of Sri Lanka took it on himself to pronounce SAARC ‘dead’. Since then there have been other sections of Sri Lankan opinion that have joined the critics of SAARC and taken the solemn stance that SAARC has indeed died what may be called a natural death.
Their fatalism is understandable. SAARC has failed to meet at heads of government or state level for the past several years to take the SAARC process notably forward. Regional cooperation has more or less been only an appealing idea. No substantive concrete projects have taken off to make the idea a hard reality. ‘Inner paralysis’ seems to be SAARC’s lot. Hence the fatalism in these circles.
However, being one of the worst cash-strapped regions of the world and a teemingly populated one with people virtually left to their devices, what choices do the ‘SAARC Eight’ have other than to try their best to band together and continue with their cooperation efforts, however small they may be?
There is no escaping the mounting debt trap for many of these countries and bankrupt Sri Lanka is a glaring example, but ‘throwing in the towel’ and abandoning themselves entirely to the diktats of the strongest economies and their agencies will prove a ‘living death’ for many countries in the SAARC fold.
The gains may be meagre but giving-up on SAARC cooperation in full would prove self-defeating for the organization and South Asia. Right now, the collective intention ought to be to salvage what the region could from the tenuous cooperative efforts. Moreover, such initiatives could go some distance to generate a degree of goodwill among the Eight and help in sustaining a dialogue process.
Given this backdrop it proved ‘a stich in time’ for the Regional Centre for Strategic Studies (RCSS), Colombo, to recently host the SAARC Secretary General Ambassador Md. Golam Sarwar to a round table discussion on the unifying potential of SAARC and its future possibilities, besides other related issue areas.
Held on June 24th and moderated by RCSS Executive Director and former ambassador Ravinatha Aryasinha, the forum brought together a vibrant, wide ranging audience comprising academicians, diplomats, senior public servants, civil society activists and many others. Following the presentation by Ambassador Golam Sarwar titled, ‘Reigniting SAARC: Achievements, Challenges and the Way Ahead’, a lively Q&A followed.
The above forum could be described as an act of lighting the proverbial ‘candle’ rather than ‘cursing the darkness.’ It surely is a ‘darkness’ that could be seen as daunting considering that the region’s pivotal powers, India and Pakistan, are failing to act in a spirit of accord but are engaged in bitter finger-pointing on a number of questions of vital importance to SAARC.
On the other hand, what is the rest of the region doing to bring the above sides together? It is disappointing that to date the rest of SAARC has failed to launch a major diplomatic drive to bring peace between the feuding regional heavyweights. It needs to act without delay and establish its earnestness and this effort would need to prove SAARC’s staying power in the unfolding months and even years.
In assessing SAARC’s seeming failure local opinion in particular has failed to factor in what could be described as weak leadership. Since Sheikh Mujibur Rahman of Bangladesh, the founding father of SAARC, the region has failed to produce a visionary leader who could advance the SAARC cause with charisma and drive.
Among other reasons, weak leadership accounts considerably for the faltering and stuttering status, as it were, of SAARC. Badly needed are leaders who could go the extra mile, think less of narrow national interests and work diligently towards the collective well being of the region but SAARC’s millions of ordinary people have been made to wait in vain for leaders of such stature. Instead, they have been burdened with politicians who seem to be relishing the apparently moribund state of SAARC.
Looking back, it could be said that it was the dynamic leadership factor that led to the launching of the Non-Aligned Movement and for its sustenance for a few decades. True, it could be seen in some quarters that NAM is no more, but as in the case of SAARC, the former too has been unfortunate to be burdened over the years with politicians who lack the vision and drive to unflaggingly advance the fortunes of the South. NAM and SAARC lack the dynamism and vision of leaders of the stature of Jawaharlal Nehru, for example, to give them the required guidance and intellectual depth.
The reasons are complex for there not being among us currently political leaders with the vision and the steadfast commitment to advance the legitimate interests of the South. However, it could be stated with conviction that the majority of Southern leaders have too easily caved in to the demands of the global North and its financial agencies.
These leaders have failed to see, for instance, that the largely market economy oriented Northern governments would not view with favour a centrist economic model that attaches priority to the interests of the dis-empowered publics of the South. This realization ought to have dawned on the current government in Sri Lanka, for instance, some while ago but it has no choice but to abide by IMF dictates since economic survival at present is unthinkable without the latter’s succour.
Accordingly for SAARC this should be the time for some soul-searching. Priority needs to be attached to ending the feuding between India and Pakistan since at present the material fortunes of the region hinge largely on these regional giants giving peaceful relations among them a try. This is no easy challenge to meet but some daring, visionary diplomacy needs to take hold among the rest of SAARC.
There is some sense in SAARC bringing the peoples of the region together through programs that address their best collective interests. A meeting of minds among SAARC nations could enable SAARC and its agencies to build a region-wide people’s movement for progressive political and economic change that could in turn lead to the region’s political leaders sensitizing themselves more to the neglected needs of their publics.
However, the time is ‘now’ for the initiation of these progressive changes and the voice of SAARC well wishers would need to drown out those of their critics.
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