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Think Like Da Vinci…If Only….

If we desire to revive the practice of critical thinking in our classrooms, we need to have a place to start, a ground floor, so to speak, of what we want to develop in our students. When you peruse available materials on teaching critical thinking, you can find dozens of manuals of workbook/worksheet pages…just what we don’t need.

One consequence I have noticed since the passage of No Child Left Behind (2002–2015) during the second Bush administration is that we have created a generation (at least) of young people who are looking for the “right” answer and not questioning the actual material they are learning. Worksheets that are composed of material to practice for standardized state tests dominate what teachers have to do…and if we don’t —

  • if we are bold enough to ask “why” an answer could be right or wrong,
  • and do it in front of an administrator,
  • but it was important to not pass over the chance to get students to think through a potential problem —

then we run the risk of a poor evaluation…and nowadays salaries for teachers are directly tied to the testing results of our students.

Sometimes the best technique and learning tool in developing critical thinking for our students is to say:
…and then practice WAIT — Why Am I Talking? Or my personal favorite — WAIST — Why Am I Still talking?

Students are flummoxed that they need to go beyond the single answer for the test. Before standards and teaching to the tests took hold, one of the best experiences I ever had in my math classroom was to shut up and listen to my class arguing, divided over the correct answer to an open-ended math problem. I had to bite my tongue because I wanted to tell them they were both right, that both answers and how they arrived at them were valid means of solving a problem. There was shouting. By the time both sides were willing to agree that each was valid, one student said, “But what would be correct for the test if we have to show our work?” And yes, my administrator was evaluating me…but she was wise enough to know something very important had happened in the 30 minutes in both math education and critical thinking.

Another great example again involves math — specifically Pythagoras (NOW DON’T STOP READING BECAUSE THIS IS MATH — and yes, I’m shouting), because it is the process that is important.

First, we had practiced finding areas through drawing various size squares and how you could easily then find the area of right triangles, all necessary before we could move to any type of formula and have it be meaningful — and not just some letters.

The lesson plan from Connected Math 2 (Michigan State University - Hi, Glenda!) has the teacher ask students to determine in their own words how to find the hypotenuse — the longest side of a right triangle — which builds on their work with area of squares.

From my students:

“Take the length of the first side of the triangle and multiply it by itself. Then do the same process to the second side of the triangle, being sure not to use the long side. Add the two sides together and make an equation that makes them equal to the long side, which is our unknown.”

Okay, now it’s time to begin using mathematical terminology.
From my students:

“Take the length of the first side of the triangle called a and square it by itself. Then do the same thing to the second side b, and add a and b together and set them equal to c, which also needs to be multiplied by itself.”

Okay, somewhat shorter, and my task at this point was to remind them that math folks can be very lazy and save themselves lots of work by using shortcuts which they already knew.
From my students:

Take side a of the triangle and square it. Do the same thing to the second side. Add them together and set it equal to c, the hypotenuse, which needs to be squared.”

Can you see where I am taking them? Now, let’s shorten it more.
From my students:

Side a of triangle squared + side b of triangle = c hypotenuse squared

And finally: a² + b² = c²

I was so excited that they got there, that everyone participated, and EVERYONE understood it. In fact, one of the fun things in math class is when students say, “Well, why didn’t you just tell us that, it’s so much easier.”

Well, yes, it is, but now you understand where it comes from and why it works.

So how do we move from having students ask questions and pursue additional avenues to solve problems to Leonardo da Vinci?

Years ago I bought a book called How To Think Like Leonardo Da Vinci, but I never got past the first few pages. I started to reread it as I prepared this article, and several things popped up: 1998 copyright, rarely was a woman mentioned, Columbus and Magellan didn’t prove the world was round, and NO MENTION was made of any other area of the world beyond Europe where scientific and artistic advances were being made. Having read Noah Gordon’s amazing book The Physician, I came away with a new, deep appreciation for Islamic teaching in science and medicine. And as I had read 1421: The Year China Discovered America, about Chinese exploration throughout the world LONG before the Portuguese, I was amazed at the civilization that flourished in Middle Ages China.

That’s not to say there aren’t some helpful bits in How to Think — there are good checklists (in fact, the “senses” have a checklist for each sense), 7 traits of da Vinci, a seven-day personal challenge, and a “beginners’ da Vinci drawing course.” Not a worksheet to be had, but interesting exercises to try.

While there will never be another da Vinci, we can foster the skills Leonardo developed in our students. Imagine a student who observes, writes, draws, reads voraciously, experiments, and keeps at it. Here’s a snapshot of da Vinci from Walter Isaacson’s amazing book, Leonardo da Vinci:

“Leonardo’s genius was a human one, wrought by his own will and ambition. It did not come from being the divine recipient, like Newton or Einstein, of a mind with so much processing power that we mere mortals cannot fathom it. Leonardo had almost no schooling and could barely read Latin or do long division. His genius was of the type we can understand, even take lessons from it. It was based on skills we can aspire to improve in ourselves, such as curiosity and intense observation. He had an imagination so excitable that it flirted with the edges of fantasy, which is also something we can try to preserve on ourselves and indulge in our children.” (p. 3)

Tune in next time as we explore bringing Leonardo and critical thinking front and center in our classrooms, especially in our under-valued history classes.

This story is published in The Startup, Medium’s largest entrepreneurship publication followed by + 381,862 people.

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