Goodbye, U-Substitution. Hello, Anti-Chain

This summer I decided I was done with u-substitution. I’m just over it. My kids tend not to see the connection to chain rule. Instead, they see it as a formulaic set of steps that they follow, oftentimes incorrectly. By the time we’ve finally “mastered” (I use that term very loosely) the steps, it’s a whole other battle to get them to understand when to use this tool.

Now, when it comes to deriving, my kids are masters. They always ask themselves what rules they need to use or if they need to rewrite a term before diving in.

Going forwards, we are experts.

So, why not going backwards too? Especially when there really aren’t that many kinds of functions you’re asked to anti-derive in Calc 1.

So, that’s the background story. I’ve decided to ditch u-sub and teach an “anti-chain rule” instead. Sorry to every calculus author ever.

Today, we dipped our toes into anti-chain by practicing only when the inside function is linear. This is Step 1 of my 4-step plan.

And—Step 1 was a success!

Kids rotated in groups as I asked them to both derive and anti-derive compositions of functions. They were forced to do some serious mental gymnastics and they did not disappoint. I adore these double-sided white boards I got with a grant last year. Students rotate so they work with different people throughout the hour. Plus, as we’ve all learned, they talk more when they stand up. ❤️

Next week, Steps 2-4!

*****

If you want to watch Step 2, here’s how I plan to teach it.

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