I always struggle during the days spent going over differentiation rules. The mathematician in me says the students need to see where the rules come from so that they aren’t just a recipe. On the other hand, I see students glazing over a bit with notation and getting lost in the midst of the overall goal: how do we find shortcuts for finding derivative functions outside of using the limit definition every time?

I have also tried going through the derivations in class and having them just watch and see the progression on their own, without copying things down. Some compulsively copied despite my repeated requests not to do so – I think it was a situation of seeing copying notes down as an alternative to really digging in to what was actually going on. It’s mindless to copy down notes, a great alternative to actually going through the steps of understanding.

Last year I made videos of the derivations and asked students to watch them outside of class in a one-off attempt at flipping. That didn’t work – students said they watched but ‘didn’t get it’, so my attempt to quiz them when they arrived in class was a bust.

This is my compromise this year: for finding the derivative of a constant, a constant times a function, and the power rule, students will be guided through what has essentially my lesson plan for previous lessons. Sums of functions, products, and quotients will be given first as applications of the limit rules, but the details of getting from the start to the finish will be kept as an exercise for later.

See my handout for today here:

03 – CW – Differentiation Rules

Thank you to Patrick Honner and Dan Anderson for their comments pushing me on this.

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I totally agree, it’s so hard to find the balance between what you want to prove and what you need them to just accept. You can’t prove everything. Also, what do you have them try to discover is a challenge to figure out as well. I liked your worksheet, it has some problem types that reminded me I need to be intentional about teaching because they re not in my book.

I like the new approach, Evan. I hope it works for your students and you, and look forward to hearing how it went.

I do wish to address your point about copying notes.

As a learner, I can not understand most things I am taught – inside the class and out – unless I take notes. Oral learning really confuses me; I mute my computer unless I am watching a video which depends on audio. Watching an explanation or demonstration of a concept is useless for me as I forget what I watched. Experimentation and doing are just as bad. I learn by taking notes.

These notes don’t necessarily need to be copied, but, when you are hiking on an unfamiliar trail, it is best to follow precisely the map you are given until you become familiar enough with the trail to write notes that are more reflective and perceptive. I write these notes as well. Soon the notes drop away.

You are right. Most of your kids are likely copying notes as a substitute for reasoning. I would not be one of those students. The key here is that I review my notes when I have time to truly explore the concepts and skills they describe. Essentially, I do on my own what others try to get me to do during a lesson. I find the lesson overstimulating to do it then. Most of your kids who are copying notes probably don’t review their notes, at least not before they cram for tests.

Ironically, as a teacher, I try to teach without students copying notes. I strongly believe in reasoning and learning in the moment and through experimentation and exploration. I believe in inquiry and discussion and hands-on experience. I certainly feel that those of my students who spend their time taking notes instead of reasoning and participating are not learning. It is just that I would be one of those students.

Something to consider. Something to plan lessons around maybe.

Have fun with the new approach.