A 26-century old fable becomes part of a new fable on more effective math instruction.
In ancient Greece around the 6th century BC, there was a storyteller named Aesop who formulated a collection of stories titled Aesop’s Fables. In one of the most famous fables, a tortoise challenges a speedy hare to a race. As the race begins, the hare jumps out to an incredible lead. The hare is so confident that he will inevitably win the race that he decides to take a nap. All the while, the tortoise moves along at a slow and consistent pace, and eventually passes the hare. When the hare finally wakes from the nap, he sprints to the finish line, only to find that the tortoise has already beat him. In an effort to make sure the reader has a clear takeaway, the story ends with the punchline: Slow and steady wins the race.
Why did Aesop waste all this time and energy to tell a story about a tortoise and a hare when the concept to be learned is so simple? Let’s consider the alternative. What if Aesop had instead published a book that only contained the punchline. No story. Just the punchline. Alone on a blank page.
Slow and steady wins the race.
By itself, this statement doesn’t have much depth. It is only because we have all engaged with the story of the tortoise and the hare that this statement has real meaning. With the experience of being in the story, a person is much more likely to truly understand and appreciate the meaning, and then be able to apply this lesson in real life.
Much like Aesop, mathematics teachers also have a clear goal for what they want students to learn by the end of the lesson. But all too often, we start the lesson with the punchline:
The Pythagorean Theorem for right triangles is a2 + b2 = c2
What if instead we taught every math lesson like Aesop? We could start each lesson with a story that students could engage with and think about:
We could help students interact with the story, by asking them to do something as part of an investigation, like breaking spaghetti into pieces to represent the distances in the story.
Let's model the two different paths using pieces of spaghetti. Measure one piece of spaghetti to be exactly 3 inches and another to be exactly 4 inches. Then break a third piece of spaghetti to be the shortcut path measure its length.
Use spaghetti pieces to find the distance of the shortcut for a walk on each day.
UP OVER SHORTCUT Day 1 3 4 Day 2 6 8 Day 3 5 12
Then through a series of carefully scaffolded questions, we could help students arrive at the meaning of the story.
Now take each number in the table above and multiply it by itself.
UP x UP OVER x OVER SHORTCUT x SHORTCUT Day 1 Day 2 Day 3 - What pattern do you notice with the numbers in this table?
- Write an equation that goes with the pattern.
And then at the very end, and only after students have discussed and debated patterns they noticed, would the teacher help them to see the punchline:
The Pythagorean Theorem for right triangles is a2 + b2 = c2
When learning in this way, students know much more than simply memorizing a new formula. They know that the hypotenuse is longer than either of the two legs of a right triangle. They know that the sum of the two legs is always going to be greater than the hypotenuse. They know that the dad should listen to the daughter because the shortcut will save them time!
Because we know the story of the tortoise and the hare, the saying “slow and steady wins the race” has much deeper meaning, and we can remind ourselves of the meaning by recalling the story. Similarly, a math student who knows the story of a dad and his daughter out for a walk has a much deeper and longer-lasting understanding of a2 + b2 = c2 because it is attached to a memorable experience.
I like to think of the story that introduces the lesson as the experience of doing mathematics. At the end, the teacher helps the students to see the clear meaning of the lesson, by formalizing the learning from the experience. In short, I believe that mathematics should be taught in an Experience First, Formalize Later approach…just like Aesop did 26 centuries ago.
Lesson adapted from https://blog.mathmedic.com/post/pythagorean