I wish it weren’t true.
But as a kid, I hated math.
I was that stereotypical third grader who scoffed at his times tables and said, “When will we ever use this when we grow up?”
My theory on why many kids have a poor attitude towards mathematics is that we’re subconsciously taught to avoid problems. Whereas Mathematics is all about embracing problems.
Math wants you to make friends with problems. Spend time with problems, not run from them.
Problems are there to be solved!
True enough, the Altitude-on-Hypotenuse Theorum has yet to be an agenda item on any of my zoom calls. But the skill of problem solving still punches the clock everyday.
And the strategies for solving a math problem, can also be applied to any real world problem.
Grant Sanderson’s 7 tips for solving hard problems are below.
My real-world application take is in italics.
Hopefully at the end, you’ll hate math less.
- Use the defining features of the setup
- What are the rules of the game your playing? What are the inherent limitations?
- Give things (meaningful) names
- Naming things helps your mind organize ideas and outline solutions.
- Leverage Symmetry
- Identify what is similar. Are there any patterns? Have we seen this before in a previous problem?
- Try describing one object two different ways
- This reminds me of a practice the economist Tyler Cowen has. To improve his understanding of an argument, he’ll write out the point of view of the argument he opposes. Try the opposite of whatever strategy your using.
- Draw a picture
- Drawing, like writing is a form of thinking. As maker Adam Savage has stated: “Drawing is your brain transferring your idea, your knowledge, your intentions, from the electrical storm cloud at its center, through the synapses and nerve endings, through the pencil in your hand, through your fingers, until it is captured in the permanence of the page, in physical space. It is, I have come to appreciate, a fundamental act of creation.” Doodle. Stickfigure. Sketch. Create a visual form of the problem.
- Ask a simpler version of the problem
- What’s the smallest part of the problem we can solve first?
- Read a lot, and think about problems a lot.
- A great excuse to buy more books.