Children should be encouraged in their formative years, ages six to fourteen, to develop their intellectual and creative capacities by solving mathematical games and puzzles with minimal, yet supportive adult intervention. Mathematical games and puzzles prompt children to make a series of decisions in the perusal of a satisfactory outcome.
The habit of decision making develops skills such as problem-solving, logical thinking, strategic thinking and critical thinking. Solving the puzzle demands a certain combination of creative thinking and logical reasoning that utilizes these skills. Mathematical games and puzzles, enable children to develop alternative perspectives, expanding their thinking to form dynamic and open-minded approaches. It is through the skills from recreational mathematical games and puzzles that children learn to build their connections of and with the wider world through communication and collaborations (sharing solutions). Being exposed to perspectives different from their own, is where real learning takes place and forms new thinking patterns in the child’s brain.
What is critical thinking?
“Critical thinking is a desire to seek, patience to doubt, fondness to meditate, slowness to assert, readiness to consider, carefulness to dispose and set in order; and hatred for every kind of imposture” is a famous quote by Francis Bacon (1605). In simpler words, critical thinking involves evaluating the reliability of the sources of information and being able to discuss the meaning and the implications of the information from the source.
How are critical thinking and mathematical reasoning related?
According to a study by Alcantara and Basca, “The mathematics performance of the students is positively correlated to their level of critical thinking skills and to their level of problem solving skills.” Further analysis into the tools and tricks that can be employed to demonstrate this correlation include a solving method by George Polya that has four steps mentioned in his bestselling book, “How to Solve It” (Princeton University Press, 1945).
The first is by the teacher prompting students with questions such as “Do you understand all the words used in stating the problem? What are you asked to find or show? Can you restate the problem in your own words?” Secondly, students are asked to plan how they are to solve the given problem, they will have to critically evaluate which strategy they want to pursue. Thirdly, creating a strategy by themselves provides children with the self-confidence and skills for learning and thinking by themselves. Lastly, providing the children time to introspect and reflect upon their actions, see what worked for them and what didn’t work for them.
This will give children the experience to analyze similar problems in the future and develop strategies quicker. Like in all play, in math as well, it is worth letting children develop their own hypotheses. It is best to test them through experimentation as they seek to find out what the causes and effects are. The implication of this will be a positive problem-solving ability.
How can children apply critical thinking to coding?
Critical thinking can teach children to apply their minds to literally everything. It is the fundamental building block of making educated and informed decisions through the power of questioning. Asking “what”, “how” and “why” things occur and the implications of their occurrence gives them an insight into how the wider world works. It makes them aware of their thoughts and mental processes when analyzing problems. It makes children aware of their biases or reliance on heuristics (mental shortcuts) and makes them meta-cognitive, enabling them to think about their thinking capacity. Hence, it enables them to make decisions and problem-solve objectively.
According to Cambridge University, asking questions such as “What have you discovered? How did you find that out? Why do you think that? What made you decide to do it that way?” really probe your child’s thinking. It will also help them collect evidence and provide logical arguments, reasoning with themselves and peers when questioned as to how they problem-solved specific questions. In addition, as they grow up and are taught different academic perspectives and even come across different people with different backgrounds to them with different viewpoints, they will be able to logically form their own opinion on facts, rather than be influenced by fads.
To further boost coding and critical thinking in your child, use the following four-fold strategy.
1. Create mind maps or spider diagrams with technical tools.
Mindmup.com is a great free tool as opposed to lined paper (which encourages you to think laterally). But, with Mindmup, the screen is as vast as the ocean, encouraging your child to jot down all ideas. See if you can find other tools online, for example, on the Microsoft Office Suite or even encourage your child to build their own.
2. Out of the box thinking.
The best way to think critically and a format that is encouraged in other disciplines, particularly in design thinking is to think in other people’s shoes and empathize with them. This is not just a social skill, but also enables children to bypass their own cognitive biases, perceptions and experiences.
3. Consider the different interests of the users of the app/animation.
Not only are you going to help your child increase the usability of the application they are going to build, but also encourage them to adopt a multifaceted approach. This is usually a feature of modern technology and children can sharpen their critical thinking skills by brainstorming how to make these features work to achieve the same goal in a seamless way that might be more feasible to create.
4. Encourage children to ask questions.
The more questions children learn to ask, the more they will be able to unearth, frame and re-frame the knowns and unknowns in their mind in different logical structures, enabling them to come up with different perspectives of solving the same problems, mostly, by themselves. This will boost their confidence and give them a great sense of achievement. You can also encourage debates by proving them wrong, developing your own critical thinking and help them learn from flaws in their thinking. This exercise works well as both an excellent learning tool, but more importantly, also helps build your child’s confidence by being a positive validation method for their decision-making skills.
It is these principles upon which WhiteHat Jr teaches children coding. The application of mathematics to teach them algorithmic thinking and logical thinking and the usage of critical thinking to develop their applications and animations for a dynamic and social world. For example, mathematical puzzles allow children to train on different combinations of numbers to arrive at particular outcomes. These numbers and combinations are then applied to building code and creating the logic behind a computer’s functioning which will be used for the greater good of society and at the same time fulfilling your child’s potential.
It is rare for programmers to immediately look at a problem that they are trying to solve and start coding. Most of the time goes in bringing the separate modules of code together in creating a program that works. Hence, learning to think in a modular process with tools in logical and critical thinking echoes the coding process which in turn is built upon the foundations of mathematical reasoning.