Mathematics examinations or mathematics curriculum?

Some people say that it is not necessary for a Grade 10 student to buy an ordinary scientific calculator because they have smartphones with built-in calculators. If not, it is easy to install a calculator app on mobile phones. A smartphone should not be used as a calculator during a mathematics test or a mathematics exam because it can be used for cheating. In the UK and other developed countries students have to keep their smartphones in their school bags or in their lockers outside the classroom during mathematics tests and exams. 

by Anton Peiris
anton25ps@gmail.com

R. N.A. De Silva has, in a recent article, provided some useful tips to students as regards preparation for mathematics examinations. Trained teachers and graduates with professional qualifications are familiar with this topic.  All mathematics teachers have a duty to help the students with revision.

The more important task is to salvage the Sri Lankan O/Level mathematics students from the abyss that they have fallen into, viz. the implications and the retarding effect of the use of obsolete Log Tables. The Minister of Education, Senior Ministry Officials and the NIA are oblivious to the important and interesting things that have happened in Grades 10 and 11 mathematics in the UK, other parts of Europe, Japan, Canada, China and elsewhere. They have been like frogs in a well for almost half a century. Here are two important facts:

1. O/Level mathematics students in Sri Lanka are 46 years behind their counterparts in the UK and in other developed countries. Ordinary Scientific calculators were introduced to the O/Level mathematics classrooms in the UK way back in 1977. Prior to that those students used Slide Rules to facilitate their mathematical calculations. Ordinary scientific calculators give the values of Sine, Cos, Tan and their Inverses, Log, LN, exponential powers, square roots, squares, reciprocals, factorials, etc., at the press of a button, in addition to performing arithmetic functions. There is no memory to store mathematical formulae, etc. It is an invaluable tool for solving sophisticated and interesting mathematical problems and also problems in ordinary statistics. It has paved the way for achieving high standards in O/Level Mathematics in those countries.

Just compare the maths questions in the Cambridge IGCSE or the London O/Level Maths Exam with the questions in the Sri Lankan O/Level maths exam and you will see how far our students have fallen behind.

The Cambridge O/Level examination was replaced by the GCSE and the IGCSE (International General Certificate of Secondary Education) a few decades ago.

I am not referring to Programmable Calculators and Graphic Display Calculators (GDC), meaning devices with a small screen that can display graphs, perform statistical calculations like the Z- Score for large samples, show Matrix calculations, provide solutions to algebraic equations, etc., at the press of a few buttons. GDC is a compulsory item for A/Level mathematics students in the UK and in all developed countries.

Some teachers say that by using ordinary scientific calculators in Grades 10 and 11, students will not acquire the ability to carry out mental arithmetic calculations. This is not true because

(i). Calculators are introduced in Grade 10. Maths teachers have five years of Primary School and three years of Middle school (Grades 7, 8 and 9) i.e. a total of eight years to inculcate sufficient mental arithmetic skills in their students before the calculators are introduced in Grade 10!

(ii). In the IGCSE and in the London O/Level Mathematics Exams calculators are not allowed for Paper 1. Preparation for Paper 1 requires the acquisition of mental arithmetic skills, e.g., one lesson per week in class in Grades 10 and 11 in which calculators are not allowed. Sri Lanka could follow suit.

Some people say that it is not necessary for a Grade 10 student to buy an ordinary scientific calculator because they have smartphones with built-in calculators. If not, it is easy to install a calculator app on mobile phones. A smartphone should not be used as a calculator during a mathematics test or a mathematics exam because it can be used for cheating. In the UK and other developed countries students have to keep their smartphones in their school bags or in their lockers outside the classroom during mathematics tests and exams.

An ordinary scientific calculator costs less than 10 % of the price of a smartphone.

Sri Lankan students in International Schools sit the IGCSE or the London O/Level mathematics exams where ordinary scientific calculators are allowed. These students have made big strides in learning mathematics by using the calculators. Only the rich can send their children to International Schools in Sri Lanka. Millions of poor Sri Lankan students do not have calculators.

Our Minister of Education has announced that the government was planning to transform the country’s education system by introducing ‘’STEAM’ (Science, Technology, Engineering, Arts and Mathematics). Maintaining high standards in O/Level Mathematics is the key to a successful implementation of STEAM programme. Unfortunately, the Education Minister and top education official are not aware of the fact that the only way to improve the standard of O/Level Mathematics is to do what the developed countries have done, i. e., revamping the O/Level mathematics syllabus and to introducing the ordinary scientific calculator in Grades 10 & 11. If they do it, it will be an important piece of curriculum development.

Bear in mind that the UK and other developed countries have taken another important step during the last 20 years; they have introduced the Graphic Display Calculator (GDC) to the O/Level Mathematics class and by providing a Core Exam and an Extended Exam. In the Cambridge IGCSE Mathematics Exams, Papers 1, 3, and 5 constitute the Core Exam. Papers 2 ,4 and 6 constitute the Extended Exam. Calculators are not allowed in Papers 1 and 2.

The Core Exam is a boon to students who have very little or no mathematical ability. More on this in my next article.

By using Log Tables, our Sri Lankan O/Level students have to spend a lot of time to solve an IGCSE (Extended Syllabus) exam problem or a London O/Level mathematics exam problem because the use of Log Tables takes a long time  to work out the Squares, Square Roots, exponential powers, reciprocals , LN , factorials, etc., and that is tedious work while their counterparts in developed countries do that in a few seconds by pressing a couple of buttons in an ordinary scientific calculator.

The Calculator has given them more motivation to learn mathematics.

O/Level students in the UK have graduated from the ordinary scientific calculator to the Graphic Display Calculator (GDC) thereby improving their ability to solve more sophisticated, more important and more interesting problems in mathematics, statistics and physics. Sri Lankan O/Level students are compelled to use obsolete Log Tables.

Hats off to that Minister of Education who introduced the ordinary scientific calculator to the Sri Lankan A/ Level Mathematics classroom and to the A/Level Mathematics Exam a few years ago. That was a small step in the right direction. Minister Susil Premjayantha, please revamp the O/Level mathematics syllabus and introduce the ordinary scientific calculator to Grades 10 and 11 now. That will ensure a big boost for your STEAM programme and yield benefits for the Sri Lankan economy.

(To be continued. Topic 2:  The necessity for introducing an O/Level Mathematics Core Exam and an Extended Exam. The writer has taught O/Level and A/Level Mathematics and Physics for 45 years in Asia, Africa and Europe and is an Emeritus Coordinator for International Baccalaureate, Geneva.)