Primary students’ mathematical problem-solving skills and the relationship to chess practice

Introduction
Chess is a popular primary school activity for students.  What was once seen as an activity for only those students who had shown a natural strength or interest in the area, has sometimes been replaced with all classroom chess lessons.  It appears those students who would naturally gravitate towards such problem solving, competitive game playing tasks, are often those who show an aptitude towards mathematics.  As well as those students who have higher cognitive capacity, and therefore may be natural problem solvers, many students who have experienced learning chess, may also develop a good sense of problem-solving tactics and these may be applied in Mathematics and general problem-solving thinking.

Learning chess appears to have a positive impact on students, when tackling unknown problem-solving tasks.  Students who have experienced thinking through the many facets of a chess game have used a variety of critical thinking tools along the way.  These students demonstrate the ability to collect the data mentally throughout the different positions in the chess game.  The information is then mentally analysed and examined, while they look at the many alternatives for the next move.  A very considered approach is necessary for the students, to not only just look at the one piece on one square of a chess board, but more importantly draw upon the knowledge of the whole game and decipher through the many possibilities in order to anticipate and examine the options for the next move.  Considering the many combinations of their own approach and the multiple option combination possibilities of their opponent, it is evident that chess offers a context with which students can develop their meta-cognitive ability.  This ability for students to ‘think about thinking’ and to then become aware of ways of examining the options and analysing decisions are important skills, of which can be applied to other curriculum areas such as mathematics and problem solving. 

“It suggests that chess teaching to students at different educational levels, improves significantly their mathematical problem-solving ability”. (Farhad Kazemia, Mozafar Yektayarb, Ali Mohammadi Bolban Abada, 2011)

The Program / Practice
Chess taught in isolation as a ‘subject’ one period a week can ignite an interest or passion area for students. The general foundational teaching of the rules and how pieces move on a chess board is beneficial for many students. Teaching the game essentials is a starting point but does not demonstrate any further complex real problem-solving techniques, "the mere knowledge of chess basic rules as the movement of the pieces, is by far insufficient to train cognitive skill". (Giovanni Sala, Alessandra Gorini, and Gabriella Pravettoni, 2015)

Once the fundamentals of the game and the rules and regulations are covered, a more complex approach to learn the game at a higher level is necessary, thus students can draw on analysing and abstract skills with the effect of playing at a stronger, more competitive level. Students who show success with the game of chess are often observed as strong confident problem solvers. Such students are efficient at observing and mentally sorting through complex data. They are determined with focus and have an ability to analyse, think ahead, look for multiple options, make appropriate decisions, weigh up decisions and options for sequences of moves. The ability to think abstractly throughout the chess game at a higher level, can be transferred to mathematics problem solving.  ‘The game of chess is a powerful tool to build children’s problem-solving competence in the mathematical domain’ (Giovanni Sala, Alessandra Gorini, and Gabriella Pravettoni, 2015)

Outcomes
Students who demonstrated effective problem-solving skills and strategies when tackling mathematical problems, prior to instruction, were also chess players, who had experience with playing chess beyond introductory level. These students found meaningful links that occurred naturally between the thinking skills learnt and engaged while playing chess and transferred these when working on Mathematical problem-solving tasks. Students who demonstrate having the strength and confidence to tackle higher order problem solving are often the stronger chess playing students. 

A calm approach to problem solving could be seen by the students who had played in multiple chess competitions and tournaments. The skill of taking appropriate considered time, although under a restricted ‘against the clock’ framework, and to consider the multiple options without becoming defeated and irritated is necessary when playing chess.  Optimism could be seen by these students, as they had previous experience with winning or loosing chess games, they remained focussed and persistent when facing a difficult problem. 

The chess playing students were able to tackle problems by looking at the larger context. They were quick to summarise and relate only the appropriate data from one part of the problem to the broader context.  These students were able to strongly sort through irrelevant information and decipher the valued important links necessary to solving the problem. When looking at ideas and initial concepts, the chess playing students were efficient at fully comprehending what the question was asking. They were able to tune into the inquiry and seek further clarification when necessary. This layered questioning and thinking was very considered before tackling the actual problem. It was evident that preparation to completely comprehend the question was an initial stage for these problem solvers.  Other students, who had not been previously exposed to playing chess beyond foundational level, were quick to make unrelated trial and error ‘estimations’, which were predominately superficial and lacked deeper understanding of the whole problem and broader context. Throughout solving the Mathematical problems, the chess playing students showed an increased ability to view and analyse abstract information. They displayed a strength in connecting of ideas to seeing the links between all aspects of the problem.

Conclusion
Through authentic engagement with both the game of chess and Mathematics problem solving tasks, the students were able to demonstrate a more complex and purposeful approach to solving problems pre-instruction.  Students who had previous experience in not only chess instruction, but extensive experience in managing themselves within chess competitions and tournaments at different levels were able to approach problem solving tasks using more complex and effective thinking abilities.  Successful students employed higher order thinking skills that would determine logic and overall approach where the entire complexity of the problem was examined as a whole.  Re-visiting the procedure and processes and making excellent informed decisions was demonstrated by the stronger chess playing students.  They had success in solving mathematical problem tasks and investigations, demonstrating excellent efficiency and mastery of using thinking strategies and sophisticated links.