South African Mathematics Foundation: Bloghttps://www.samf.ac.za/BlogThu, 23 Sep 2021 02:28:08 Zurn:store:1:blog:post:21https://www.samf.ac.za/en/mathematical-problems-on-the-chessboardMathematical problems on the chessboard<p><span style="font-size: 11pt;"><span data-preserver-spaces="true">By Prof. Kerstin Jordaan, Executive Director of the South African Mathematics Foundation (SAMF)</span></span></p>
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<p><span style="font-size: 11pt;"><span data-preserver-spaces="true">The Netflix television series, </span><a class="editor-rtfLink" href="https://www.netflix.com/za/title/80234304" target="_blank" rel="noopener"><span data-preserver-spaces="true">The Queen's Gambit</span></a><span data-preserver-spaces="true">, made chess popular again. The narrative plays off in 1950 and tells the story of a young orphan girl and her unusual talent for chess. </span></span></p>
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<p><span data-preserver-spaces="true"><img src="https://s3.amazonaws.com/ss-usa/companies/MzawMDE2srA0BAA/uploads/Queens_Gambit_June_2021.png" alt="" width="700" /></span></p>
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<p><span style="font-size: 11pt;"><strong>Chess as an aid for education</strong></span></p>
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<p><span style="font-size: 11pt;"><span data-preserver-spaces="true">Playing chess from a young age helps children </span><a class="editor-rtfLink" href="https://www.healthline.com/health/benefits-of-playing-chess" target="_blank" rel="noopener"><span data-preserver-spaces="true">develop</span></a><span data-preserver-spaces="true"> problem-solving, social and relationship-building, and thinking skills. In addition, studies reveal that chess players develop perspective, have improved memory, and increased intelligence. The game deepens focus, elevates creativity, and increases self-awareness. Scientists found that the complex mental flexibility chess demands could help protect older people from dementia. Likewise, it improves attention-deficit hyperactivity disorder (ADHD) symptoms in children.</span></span></p>
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<p><span style="font-size: 11pt;"><span data-preserver-spaces="true">Watu Kobese, an international chess master and instructor at </span><a class="editor-rtfLink" href="https://youtu.be/ZDFwlbRTadk" target="_blank" rel="noopener"><span data-preserver-spaces="true">Blue Frontier Path Academy</span></a><span data-preserver-spaces="true">, says that "historically, chess has been looked at as a sport. But chess is much more than that – it is an aid for education. I help learners understand how they can use the concepts from chess in their academics and everyday life."</span></span></p>
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<p><span style="font-size: 11pt;" data-preserver-spaces="true">"These concepts are revealed through the nature of the game, the layout of the board, and the value of the pieces. Every piece is worth a certain number of points. As players exchange pieces, they are calculating points using mathematics to gauge the effectiveness of their moves. However, it is not just a question of mathematical value since value during the game is not absolute. In the same way, value in life is not absolute. Sometimes players exchange points for an equivalent amount of benefits, which teaches them about the changing nature of value. This understanding of value can then be related to different aspects of life."</span></p>
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<p><span style="font-size: 11pt;"><strong>The relationship between chess and mathematics</strong></span></p>
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<p><span style="font-size: 11pt;" data-preserver-spaces="true">Chess is based on some mathematical elements as the values and the geometrical moves of the pieces. In essence, it is a game that requires players to apply skills that exceeds the mere calculation of variations. Playing chess is an application of capability.</span></p>
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<p><span style="font-size: 11pt;"><span data-preserver-spaces="true">Researchers conducted numerous studies on the relationship between chess and mathematics. One such </span><a class="editor-rtfLink" href="https://journals.sagepub.com/doi/pdf/10.1177/2158244015596050" target="_blank" rel="noopener"><span data-preserver-spaces="true">study</span></a><span data-preserver-spaces="true"> reveals that chess increases mathematical problem-solving skills because:</span></span></p>
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<li><span style="font-size: 11pt;" data-preserver-spaces="true">mathematics and chess are isomorphic fields; by playing chess, mathematical theories are made less obscure and thus more manageable;</span></li>
<li><span style="font-size: 11pt;" data-preserver-spaces="true"> a chess player must practice high skills like planning, abstract thought, calculation of variants, monitoring of strategies, and thoughts that are crucial for mathematical abilities; </span></li>
<li><span style="font-size: 11pt;" data-preserver-spaces="true">a chess player recognises the triumphs and losses as a result of his selections on the board, the accuracy of which is proportionate to the method and the efforts of the player himself; this is thought to improve the empowerment of the player and, consequently, the belief in his own capabilities; </span></li>
<li><span style="font-size: 11pt;" data-preserver-spaces="true">the chess player becomes mindful of the need for sustaining attention, directed to both the simple components of the game and to the analytic relationship between elements; attention that is already probably present in the participant, but that the natural environment and habits tend to diminish; and</span></li>
<li><span style="font-size: 11pt;" data-preserver-spaces="true">chess is a fun and fulfilling activity that stimulates children to play more. In other words, chess gets a "virtuous circle" started. This circle can also be instrumental in developing good mathematical abilities.</span></li>
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<p><span style="font-size: 11pt;"><span data-preserver-spaces="true">Pepe Cuenca, a Spanish chess Grand Master and civil engineer with a PhD in applied mathematics, </span><a class="editor-rtfLink" href="https://news.stlpublicradio.org/arts/2019-03-28/on-chess-chess-and-mathematics" target="_blank" rel="noopener"><span data-preserver-spaces="true">summarises</span></a><span data-preserver-spaces="true"> the relationship as follows:</span></span></p>
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<li><span style="font-size: 11pt;" data-preserver-spaces="true">Chess encourages thinking skills of higher-order;</span></li>
<li><span style="font-size: 11pt;" data-preserver-spaces="true">Interpretation of positions has a lot in common with mathematical problems;</span></li>
<li><span style="font-size: 11pt;" data-preserver-spaces="true">It introduces a coordinates system and geometric concepts (files, rows, diagonals);</span></li>
<li><span style="font-size: 11pt;" data-preserver-spaces="true">Chess demands continual calculation and promotes visual memory and spatial reasoning skills; and</span></li>
<li><span style="font-size: 11pt;" data-preserver-spaces="true">It increases the ability to predict and expect outcomes.</span></li>
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<p><span style="font-size: 11pt;"><span data-preserver-spaces="true">At the 2014 Chess and Mathematics Conference held in London, </span><a class="editor-rtfLink" href="https://www.foxandhoward.co.uk/all-authors/david-wells/" target="_blank" rel="noopener"><span data-preserver-spaces="true">David Wells,</span></a><span data-preserver-spaces="true"> a former mathematics teacher, discussed the </span><a class="editor-rtfLink" href="https://londonchessconference.com/wp-content/uploads/2014/12/The-Connections-between-Chess-and-Mathematics.pdf" target="_blank" rel="noopener"><span data-preserver-spaces="true">connections between chess and mathematics</span></a><span data-preserver-spaces="true">. Both are philosophical, require tactics, strategy, creativity, and complete analysis, and revolve around proof and proving.</span></span></p>
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<p><span style="font-size: 11pt;" data-preserver-spaces="true">Dr Leicha Bragg, a senior lecturer in mathematics education at Deakin University in Australia, says: "Games may have the potential to provide students with a mathematically focused activity while engaging them through a perception of fun."</span></p>
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<p><span style="font-size: 11pt;"><span data-preserver-spaces="true">So, if you want to help your child improve his mathematical skills, consider joining a </span><a class="editor-rtfLink" href="https://chessa.co.za/" target="_blank" rel="noopener"><span data-preserver-spaces="true">chess club</span></a><span data-preserver-spaces="true"> in your area.</span></span></p>