Opinion
Mathematics curriculum, and examinations – II
by Anton Peiris
anton25ps@gmail.com
In my last article, I stressed the importance of introducing the Ordinary Scientific Calculator to Grades 10 & 11. There is also the concurrent need to revamp the O / Level Mathematics Syllabus.
Revamping the O / Level Mathematics Syllabus cannot be a difficult task. The Ministry of Education and the NIA need to look at the Cambridge IGCSE Mathematics Syllabus (1990 – 2000) and a few Examination Papers, i.e. a good look at O / Level Mathematics in the U.K. before they introduced the Graphic Display Calculator (GDC) to the O / Level mathematics classroom at the beginning of this century. Also, the London O / Level Mathematics Syllabus and Examination Papers. They will notice that a small amount of Ordinary Statistics and Probability has been built into the O / Level Mathematics syllabus.
The harder part will be to equip each and every Grade 10 student in Sri Lanka with an Ordinary Scientific Calculator.
There is a pressing need to introduce an O / Level Mathematics Core Exam and an Extended Exam in Sri Lanka.
There are many students who are weak in mathematics. Parents in Sri Lanka spend a lot of money on private tuition for their children. We need to look at how the other countries (the UK, in particular) have solved this problem. They have introduced an IGCSE Core Exam for these students and an Extended Exam for the others. The Core Exam is also for those students who do not need mathematics for their future studies.
The Core Exam should provide a sufficient mathematical basis for students planning to follow university courses in medicine, law, commerce, geography, psychology, liberal arts, etc. and also for the students planning to follow technical education courses. The Core exam should be an easier option. It should not be a diluted version of the Extended Exam.
Here’s a suitable syllabus for an O / Level Mathematics Core Exam for Sri Lanka. It is not exhaustive:
Arithmetic: Fractions and percentages. Simple problems on Percentages. Use of Compound Interest formula (Ordinary Scientific Calculator required). Areas and Volumes: Triangle, Rectangle, Parallelogram, Trapezium, Rhombus, Kite, Cuboid, Cylinder, Cone, Pyramid, Sphere. Ratio and proportion. Converting a number into standard form. Binary arithmetic.
Algebra: Solution of simple linear equations. Solution of simple simultaneous equations using addition or subtraction method. Problems solved by linear equations and simultaneous equations. Solution of quadratic equations by using the formula (Proof of formula not required. Ordinary Scientific Calculator is required to find the square root, etc.). Direct and Inverse variation.
Geometry: Geometrical properties of the isosceles triangle, equilateral triangle, right angled triangle and other shapes mentioned above. Circle theorems (no proofs required). Arc length and sector area. Angle properties of Parallel lines with transversal. Simple questions on Pythagoras’ theorem, e.g. given two sides of a right-angled triangle to calculate the third side. Similarity; Areas of similar shapes, Volumes of similar objects.
Trigonometry: Trigonometry of the right-angled Triangle, i.e. use of Sine, Cos or Tan to calculate a side or an angle of a right-angled triangle. Use a clinometer to determine the angle of elevation of the top of a tall tree and to calculate its height. Scalene triangle: use of Sine rule and Cosine rule (no proofs required. The calculation becomes easy and routine with the use of the ordinary scientific calculator).
In order to give these students a fair chance of passing the O / Level mathematics Core Exam, about 66 % of the Exam questions on the above topics should be straight forward, i.e. there should be no hidden mathematical catch in them. After working several drill questions on each topic, they will gain sufficient confidence to tackle an exam question of the same type.
Statistics and Probability:
About 35 % of the Core syllabus should consist of Ordinary Statistics and Probability:
Simple problems on Permutations, Combinations. Addition and multiplication of Probabilities. Histogram, pie chart, mean, mode, median, cumulative frequency graph and quartiles, mean deviation, standard deviation, variance, calculation of Z-Score for a small sample of exam marks. Use of the Normal Curve (bell-shaped curve) and Normal Curve Area Tables to calculate the probability in some real-life problems. Proof of the formula is not required.
Calculation of Z-Score involves arranging the given data into columns, using the ordinary scientific calculator to calculate the totals, the mean, squares, square roots, etc. and substitution in the formula. This is within the capability of students who have little or no ability in traditional mathematics. The same is true about the use of the Normal Curve (bell-shaped curve) to calculate probabilities. 60 years ago, these statistical topics were part of the A / Level mathematics syllabus. Now, they have been brought down to the O/Level Core syllabus. After working a couple of drill questions on these statistical topics, they will be able to work any such question thereby increasing their chances of Passing the O / Level Mathematics Core exam. We have noticed that the use of the ordinary scientific calculator has given these students more motivation. The majority of them have become self-reliant in learning their mathematics.
This course in ordinary statistics and probability will be useful in their university studies. What they have lost in missing the Extended Mathematics course they have gained in learning Statistics and Probability.
We have noticed that, after introducing this O / Level Mathematics Core syllabus, the demand for private tuition classes in the U.K. has been significantly reduced. Sri Lankan parents will be able to save tens of thousands of Rupees in private tuition fees.
Z- Score has been in the news since 1990. In order to make the readers of The Island newspaper familiar with the two topics: 1. how to calculate the Z- Score for a small sample of exam marks and 2. how to calculate probabilities using the bell-shaped curve, I will present a couple of worked examples in my next instalment. Also, suggestions on how to provide an ordinary scientific calculator to each and every 10 th Grade student in Sri Lanka.
After producing an O / Level Mathematics Extended syllabus and an O / Level Mathematics Core syllabus, it will be necessary for the Ministry of Education to organise a couple of in-service training courses for teachers who are not familiar with the new topics in the syllabus.
(The writer has taught O / Level and A / Level mathematics and physics for 45 years in Asia, Africa and Europe. He is an emeritus coordinator for International Baccalaureate, Geneva.)
Opinion
A harsh reflection of Sri Lanka’s early-warning gap
Cyclone Ditwah:
Cyclone Ditwah, which swept across Sri Lanka at the end of November, caused massive damage to the country, the extent of which need not be mentioned here, as all are aware of it by now. Heated arguments went on among many parties with regard to how this destruction could have been mitigated and who should take responsibility. Although there may have been shortcomings in several aspects of how we responded to Ditwah, this article highlights a critical area that urgently requires attention if we are to protect ourselves from similar hazards in the future.
As is common in many situations, it has once again showcased a concerning weakness in the country’s disaster-management cycle, the gap between issuing early warnings and the expected public response. The Meteorological Department, the Irrigation Department, the National Building Research Organization, and other authorities issued continuous warnings to evacuate well in advance of imminent threats of flooding, landslides, and water hazards. However, the level of preparedness and community reaction fell short, leading to far greater personal property damage, including loss of a few hundred lives.
Sri Lanka is not unfamiliar with natural disasters. One of the most devastating disasters in our history could be considered the 2004 Tsunami event, which resulted in over 35,000 deaths and over $1 billion in property damage in the coastal belt. After the event, the concepts of disaster management were introduced to the country, which we have been adhering to since then. Again in 2016, the country faced massive river flooding, especially in western and southern regions, and until recently experienced repeated floods and landslides due to rains caused by atmospheric disturbances, though less in scale. Each of these events paved the way for relevant authorities to discuss and take appropriate measures on institutional readiness, infrastructure resilience, and public awareness. Yet, Cyclone Ditwah has demonstrated that despite improvements in forecasting and communication, well supported by technological advancements, the translation of warnings into action remains critically weak.
The success of early-warning systems depends on how quickly and effectively the public and relevant institutions respond. In the case of Ditwah, the Department of Meteorology issued warnings several days beforehand, supported by regional cyclone forecasting of neighbouring countries. Other organisations previously mentioned circulated advisories with regard to expected flood risk and possible landslide threats on television, radio, and social media, with continuous updates. All the flood warnings were more than accurate, as low-lying areas were affected by floods with anticipated heights and times. Landslide risks, too, were well-informed for many areas on a larger spatial scale, presumably due to the practical difficulties of identifying such areas on a minor scale, given that micro-topography in hill country is susceptible to localised failures. Hence, the technical side of the early-warning system worked as it should have. However, it is pathetic that the response from the public did not align with the risk communicated in most areas.
In many affected areas, people may have underestimated the severity of the hazard based on their past experiences. In a country where weather hazards are common, some may have treated the warnings as routine messages they hear day by day. As all the warnings do not end up in severe outcomes, some may have disregarded them as futile. In the meantime, there can be yet another segment of the population that did not have adequate knowledge and guidance on what specific actions to take after receiving a warning. This could especially happen if the responsible authorities lack necessary preparedness plans. Whatever the case may be, lapses in response to early warnings magnified the cyclone’s impact.
Enforcing preventive actions by authorities has certain limitations. In some areas, even the police struggled to move people from vulnerable areas owing to community resistance. This could be partly due to a lack of temporary accommodation prepared in advance. In some cases, communities were reluctant to relocate due to concerns over safety, privacy, and the status quo. However, it should be noted that people living in low-lying areas of the Kelani River and Attanagalu Oya had ample time to evacuate with their valuable belongings.
Hazard warnings are technical outputs of various models. For them to be effective, the public must understand them, trust them, and take appropriate action as instructed. This requires continuous community engagement, education, and preparedness training. Sri Lanka must therefore take more actions on community-level disaster preparedness programs. A culture of preparedness is the need of the day, and schools, religious institutions, and community-based organisations can play an important role in making it a reality. Risk communication must be further simplified so that people can easily understand what they should do at different alert levels.
Cyclone Ditwah has left, giving us a strong message. Even an accurate weather forecast and associated hazard warnings cannot save lives or property unless the public responds appropriately. As it is beyond doubt that climate change intensifies the frequency and severity of extreme weather events, people in Sri Lanka have to consider preparedness as a routine part of life and respond to warnings promptly to mitigate damage from future disasters.
(The writer is a chartered Civil Engineer)
by Eng. Thushara Dissanayake
Opinion
Feeling sad and blue?
Here is what you can do!
Comedy and the ability to have a good laugh are what keep us sane. The good news to announce is that there are many British and American comedy shows posted up and available on the internet.
They will bring a few hours of welcome relief from our present doldrums.
Firstly, and in a class of its own, are the many Benny Hill shows. Benny is a British comedian who comes from a circus family, and was brought up in an atmosphere of circus clowning. Each show is carefully polished and rehearsed to get the comedy across and understood successfully. These clips have the most beautiful stage props and settings with suitable, amusing costumes. This is really good comedy for the mature, older viewer.
Benny Hill has produced shows that are “Master-Class” in quality adult entertainment. All his shows are good.
Then comes the “Not the Nine o’clock news” with Rowan Atkinson and his comedy team producing good entertainment suitable for all.
And then comes the “Two Ronnies” – Ronnie Barker and Ronnie Corbett, with their dry sense of humour and wit. Search and you will find other uplifting shows such as Dave Allen, with his monologues and humour.
All these shows have been broadcast in Britain over the last 50 years and are well worth viewing on the Internet.
Similarly, in The USA of America. There are some really great entertainment shows. And never forget Fats Waller in the film “Stormy Weather,” where he was the pianist in the unforgettable, epic, comedy song “Ain’t Misbehavin”. And then there is “Bewitched” with young and glamorous Samantha Stevens and her mother, Endora who can perform magic. It is amazing entertainment! This show, although from the 1970s was a milestone in US light entertainment, along with many more.
And do not overlook Charlie Chaplin and Laurel and Hardy, and all the Disney films. Donald Duck gives us a great wealth of simple comedy.
The US offers you a mountain of comedy and good humour on Youtube. All these shows await you, just by accessing the Internet! The internet channel, ‘You tube’ itself, comes from America! The Americans reach out to you with good, happy things right into your own living room!
Those few people with the ability to understand English have the key to a great- great storehouse of uplifting humour and entertainment. They are rich indeed!
Priyantha Hettige
Opinion
There is much to learn
After the recent disaster, a great deal of information has been circulating on WhatsApp and YouTube regarding our reservoirs, highways, etc.
In many of these discussions, people have analysed what went wrong and how the damage could have been prevented. My question is this: why do all these knowledgeable voices emerge only after disaster strikes? One simple reason may be that our self-proclaimed, all-knowing governing messiahs refuse to listen to anyone outside their circles. It is never too late to learn, but has any government decision-maker read or listened to these suggestions?
When the whole world is offering help to overcome this tragedy, has the government even considered seeking modern forecasting equipment and the essential resources currently not available to our armed forces, police, and disaster-management centres?
B Perera
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