The Learning Curve
Welcome to The Learning Curve - insightful educational commentary from Dr. Bob Bowman, Assistant Head of School for Upper School.
Riddle Me This...
What is the beginning of eternity, the end of time and space, the beginning of every end and the end of every race? (From the Riddler on the Batman TV series, 1966 - 68)
I have always loved riddles. The answer to the one above is the letter “E.” As a kid I would buy books and magazines filled with logic problems and puzzles, poring over them, trying to find the solutions. I was often rather impatient and would peek at the hints and answers but still took great joy in the process. Little did I know how important solving these riddles was for my intellectual development.
One that I still remember and use with my students to this day goes like this:
You are walking on a path on an island inhabited by two tribes: one tribe always tells the truth, the other one always lies. Another peculiarity of this island is that each islander will only answer one question. You come to a fork in the road. One path leads to great fortune and the other to your demise, and you are running out of time. A person is standing at the fork; you do not know which tribe they are from. What one question do you ask to assure you find the road to great fortune in time?
This type of puzzle has many incarnations in the world of logic and mathematics (and the movie Labyrinth for those 1980’s movie nerds out there). In fact, if you take a deep dive into this class of problems you will find direct connections to geometry, genetics and computer science, to name a few fields. In fact, over the past several decades research has shown that deductive/inductive reasoning is an essential skill for everyone.
Below (taken from the website maxilliant.org) are brief definitions of three forms of reasoning:
Deductive reasoning starts from the general (rules, laws, etc.) and then moves to the particular (or from cause to effect). This leads to logical conclusions.
Inductive reasoning starts from detailed empirical reality and moves to general plausible principles.
Abductive reasoning starts with (incomplete) observations and moves to possible hypotheses (“guessing”).
Now, the term analytical thinking refers to mostly deductive reasoning and some inductive reasoning but no abductive reasoning. Design thinking emphasizes mostly abductive reasoning, and it focuses on exploration and on outcomes meeting desired objectives. At Wardlaw+Hartridge, we emphasize all three forms of reasoning across disciplines and strongly believe these are essential habits of mind. Three-year-olds to high school seniors are taught the ability to utilize all forms of reasoning; they are introduced and emphasized in an age-appropriate fashion throughout the curriculum. From building functional robots to crafting research papers applying critical analysis of primary sources to performing current, authentic research in biostatistics, our Upper School students are developing the intellectual capacity to think analytically. Providing Upper Schoolers, the opportunity to practice and to hone their reasoning throughout their time at W+H, across disciplines, is one of our most important educational emphases.
In no time in history have these skills been as important as they are now. It is essential that we teach and model for students the fundamental differences between analyzing data followed by drawing conclusions as compared to using one’s intuition to make important decisions. Global warming is an excellent and timely example. While there is unanimity around the observation that temperatures on the planet are rising, there are people, a few scientists included, who doubt the major contributions are man-made. Analytical thinkers reach data-based conclusions, while intuition might lead you to a different conclusion if you just experienced a historically cold winter. When the ultimate cost of making the wrong choice could be calamitous to the Earth, the ability to use sound reasoning to reach a factually supported understanding and future plan of action is not only imperative but possibly life-altering.
From light-hearted riddles to serious scholarship, students at W+H develop the ability to meet challenging material head-on with confidence in their methodology and in their conclusions. Their firm grasp of this process is not only an educational priority, it is an absolute necessity for our future.
For those intrepid souls who made it to the end of my blog, the riddle answer: Ask the person at the fork in the road what path would a member of the other tribe tell you to take. Then, take the path not chosen. Use your analytical thinking skills to prove this works!
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