Amelia, this is a deep question, and one that is vital to educators at all levels. A proper answer would require much more space than I have here, but I will try to outline an approach.
As Einstein once observed, “The value of education is not the learning of many facts, but the training of the mind to think.” By this, Einstein meant the acquisition of critical thinking skills. This is the ability to think independently, question current consensus, challenge beliefs that conflict with personal observations, and apply analytic reasoning in reaching conclusions.
In young children, we can begin the process of challenging our beliefs by exposing them to illusions that defy their perceptions. What animal do you see in the picture below?
On August 18, 2019, Dan Quintana, a scientist at Norway’s University of Oslo, posted a video with the caption: “Rabbits love getting stroked on the nose.” The video went viral with viewers asserting that this was not a rabbit, but rather a raven. Two years earlier, Paige Davis, a curator at the World Bird Sanctuary in Missouri had posted this video of a raven named Mischief, who lived up to its name. When asked how Mischief was responding to his new celebrity status, the Sanctuary reported that he’s ravin’ about it.
When young chldren are shown a variety of optical illusions they learn that what they think they see may not always be real. We need to challenge our perceptions and constantly question our basis of certainty. Such illusions can lead to questions about why a long pole inserted in a swimming pool appears to be bent. This is a natural segue into a discussion of diffraction.
As students move into their teens, they can become engaged in more sophisticated logical problems such as the one below that challenges the reliability of their instinctive first answer.
Read this problem and choose answer a, b, or c, within three minutes.
• Peter is looking at Mary, while Mary is looking at Paul.
• Peter is married. Paul is unmarried.
Is a married person looking at an unmarried person?
Answer: a) yes b) no c) cannot be determined
Are you confident that your answer is correct? Are you really sure?
Our initial pass at this problem usually involves a quick look, a judgment, and a response, known as the “fast and frugal” intuitional approach. However, when challenged to revisit the problem, your students will be more likely to move into a slower, more rational state that mathematicians call “problem solving mode.”
With my students at the university level, I introduced problems such as the Monte Hall dilemma. Based on the old quiz show, Let’s Make a Deal. It shows the counterintuitive nature of some probabilistic problems. When I shared this with my students, they would return to next class exclaiming how their family members refused to believe the result of the mathematical analysis.
Problems like those described above are vital in having people challenge their first intuition and move into rational mode when confronted with a conundrum. Sources of stimulating problems can be found in Jordan Ellenberg’s book, How not to be Wrong, and in Rob Dobelli’s book, The Art of Thinking Clearly. As Socrates recognized over 2000 years ago, the best way to stimulate thinking is through challenging questions. Socrates’ classic dialogue with Meno, reveals how we can help people discover things that we never thought we knew (unknown knowns) through the process of asking questions.
