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.)