14 January is World Logic Day

On 14 January 2022, global communities will celebrate World Logic Day. The United Nations Educational, Scientific and Cultural Organization (UNESCO) declared the day in partnership with the International Council for Philosophy and Human Sciences (CIPSH). This global day of observance aims to bring the intellectual history, conceptual significance and practical implications of logic to the attention of interdisciplinary science communities and the broader public.

The South African Mathematics Foundation (SAMF) highlights the importance of mathematics as a tool to help develop logical thinking. In a study published on 29 July 2020, researchers found "that, in general, the greater the mathematics training of the participant, the more tasks were completed correctly, and that performance on some tasks was also associated with performance on others not traditionally associated."

The study further reports that "intensive training has been shown to impact the brain and cognition across a number of domains from music, to video gaming, to Braille reading."

The SAMF offers two learner development programmes to help primary and high school children sharpen their logical thinking skills, amongst others. The NESTLÉ NESPRAY South African Mathematics Challenge (SAMC) is for Grades 4 to 7, and the Old Mutual South African Mathematics Olympiad (SAMO), co-sponsored by the South African Institute for Chartered Accountants (SAICA) is for Grades 8 to 12. Both competitions consist of non-routine  mathematical problems, which stimulate learners to think further than in the classroom.

"The idea of the Challenge is to start developing logical thinking at a young age," says Mr Ashley Ah Goo, Vice-chair of the Problem Committee for the SAMC. "Teachers, parents, and learners must realise that the questions will be difficult. Why else would we call it the Mathematics Challenge?"

An example of a question that develops logical thinking skills, taken from a previous paper of the Challenge for Grades 4 to 7, would be:

Janet and Zoe have new bikes. On day 1, Janet rode 8 kilometres and Zoe 1 kilometre. If each girl rides one kilometre per day after that, by which day will Janet have ridden twice as far as Zoe?

The answer is 7.

Mr Ah Goo explains that a table could help the learner solve the problem.

Thomas Hagspihl, a member of the Problem Committee for the SAMO and Headmaster at St Martin's School in Johannesburg, explains that the questions for high school learners get increasingly tricky. "Creative problem-solving skills are essential and very marketable in today's technology-oriented marketplace. This marketplace is now global, and South Africa needs to be very competitive. Hence we need expert problem solvers. Practice in problem-solving will help to train our future leaders in technological development."

He continues by saying that "the Problem Committee had a delightful question in the first round of the SAMO some years ago:

Aarnout, the full grown hippo weighs:  (a)  2kg    (b)  20kg    (c) 200kg     (d) 2 000kg     (e)  20 000kg

"The results were devastating," says Hagspihl. "Being a multiple-choice exam, we could see who had answered what.  Each of the five distractors had been chosen.  In other words, there are high school kids who believe that a full-grown hippo weighs 2kg!"

He further explains that the absence of logical and critical thinking in high school kids is a pandemic of frightening proportions.  "Unfortunately, the teaching of Mathematics has, in most classrooms, become recipe style, chalk-and-talk, with the lame excuse of never having enough time to finish the curriculum.  Incorrectly taught, the high school Math curriculum teaches no thinking at all.  How much thinking can there be if a teacher teaches you how to factorise a trinomial, then does five examples for you and then gives you 20 more for homework?"

"That's the beauty of the South African Mathematics Olympiad," concludes Hagspihl.  "The Problem Committee works hard at designing questions that are non-routine and that pupils have not seen before.  You have to thus engage in an activity called thinking.  De Bono claims this kind of thinking is painful and contrary to what humans typically do – and it is!  There can be no greater satisfaction when you finally get an answer to a problem, especially if it is a complex problem.  Our problems require only a basic knowledge of the curriculum and can thus be attempted by anyone."

Here is an example of a question from a past paper of the high school Olympiad:

48 identical coins are arranged in 6 piles of different heights.  What is the smallest number of coins there could be in the largest pile?

Answer: 11

The steps below explain one of the possible solutions.

48 ÷ 6 = 8

1 + 2 + 3 + 4 + 5 + 6 = 21

48 - 21 = 27

27 ÷ 6 = 4.5

Therefore

1+4    2+4    3+4    4+4    5+4    6+4

Then there are three coins left. Because the highest pile must have the lowest number of coins, one must start by adding the left-over coins there.

5   6   7   8+1   9+1   10+1

Answer = 11

A study published on 7 February 2019 points out that "critical thinking skills, acquired through a process of education, can equip learners with the ability to analyse and solve problems and make decisions. Societal problems such as crime, poverty, and pollution are sometimes the result of the decisions made at a policy level in government and business, which were not subject to critical thinking aided by research and due diligence in implementation. In such instances, for problems to be solved, adequate and relevant knowledge, an open disposition, and critical thinking skills are required."

The research paper further states that "critical thinking and sustainable development is an approach to meaningful dialogue for social, economic, political and environmental problem-solving and decision-making for current and future generations."

"We, therefore, encourage teachers nationwide to register their learners for the upcoming Challenge and Olympiad," says Prof. Kerstin Jordaan, Executive Director of the SAMF and Mathematics Research Associate at the University of South Africa (UNISA). "Registration for Quintile 1 and 2 schools are free, whereas Quintile 3, 4 and 5 and private schools pay a nominal entry fee."

Registration for the SAMO and SAMC opens on 3 January 2022. Parents who want to register their children must reach out to the school's mathematics teacher. The entry forms will be available on www.samf.ac.za. Registrations for the Olympiad closes on 21 February 2022 and for the Challenge on 24 February 2022. For more information, send an email to [email protected].