## Calculating achievement

My 10 year old niece recently asked me to help her revise for a mathematics test. While we were going over calculations, I began working out a problem using long division. This process seemed alien to my niece who instinctively pulled out her calculator to find the answer. Her rationale was that the calculator would give her the correct answer, and that’s all that mattered. She did not understand the process of long division and could not apply the theory to the mathematics problem. I eventually convinced her to solve the problem using ‘the long way,’ but was I being too critical of her reliance on the calculator?

As one reads the academic literature [1], it is undeniable that there are both advantages and disadvantages of calculator use, but before delving into the pros and cons of calculator usage, perhaps we should take a step back and examine why mathematics is taught in the first place. Among numerous reasons, mathematics is taught for the stimulation and improvement of logical thinking for problem solving, the development of abstract thought and understanding patterns, and the application of concepts using mathematics tools. We are still trying to find the best way for learners to acquire these skills as the worrying TIMSS 2011 results showed that across the three cognitive domains tested, South African grade 9 learners achieved an average scale score of 336 for problems that required an application of mathematics, 352 for problems that required mathematical knowledge and 363 for problems requiring reasoning skills. These average scores are far below the international centerpoint of 500. This indicates that South African learners are not able to apply their maths and science reasoning and knowledge. While these results are not directly attributable to calculator use, it does require some pause for reflection.

Three dangers related to the over-reliance of calculators are noteworthy. Firstly, learners are prone to be unable to show maths and science comprehension and competency, and are unable to illustrate the procedures of arriving at an answer. Learners may consequently be unable to perform even the most basic calculations in their heads. The unlimited use of a calculator can hinder the process of thinking and coming up with creative ways of solving a mathematical problem. Instead, learners are encouraged to randomly try a variety of mathematical computations, but the overreliance on calculators may mean that they try these computations without any real understanding of which method is appropriate or why. Secondly, children can lose their previously acquired skills in maths due to unrestricted calculator use in the classroom. Mathematics mastery requires practice, as true expertise needs to have time to grow and deepen. The third danger relates to calculators providing an illusion of progress, where learners may experience a false sense of confidence about their mathematical ability. Here, getting the answer correct leads learners to believe that they have mastered the subject.

Technology is a helpful entity in society and we cannot be averse to it, even in the classroom. However, it is vital to use technology appropriately, so how do we minimise the concerns of calculator usage? A more appropriate way for educators to introduce the calculator is *gradually *– by having learners begin by only checking the computations they have already worked out manually with the calculator. This shows the need to be careful when the calculator is introduced to learners, and the frequency with which it is required for usage in the classroom. The value of showing the thought process in explicating and comprehending a problem must also be emphasized to learners from the early stages of schooling. It is important that learners are able to decide what calculators are required for and what can be done mentally, and how to assimilate the two. Sanctioning limited use of calculators helps the learners’ mastery of basic skills in mathematics. In this way, the calculator can be an aid to the learning process by assisting to simplify mathematical tasks, and allowing learners to determine the most appropriate method for solving problems. Using calculators correctly can also enable learners to reason more abstractly. So the quest is to find a balance, where the concerns regarding calculator usage can be minimised and their effective usage can be maximised.

Ms Ncamisile Zulu with Dr Andrea Juan

[1] The Ledger, 1977; McCauliff, 2003; Sheets, 2007, http://www.educationworld.com/a_curr/curr072.shtml