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).