Learning from Mistakes (And, teaching percents)

We try to teach our students the benefits of mistakes. 

And I like to talk about brains and neuroscience, so “someone did this study…”  is a thing I say a lot in class. My favorite one: guessing wrong helps you learn things. 

This is wonderfully useful to cite in class. It can encourage participation, free up guessing, or encourage resilience (“Got it wrong? No worries, now your brain is ready to remember it right”

It’s a little less fun, but still useful to live in our own practice.

Last time I taught percents, I guessed wrong about some mental math.

Context: There are always multiple practice options in my class (a post for another time). When I guessed wrong, I included a new exercise among these options, thinking it would be an easy add  and some welcome variety. 

 It was not. 

It was confusing and most of my students gave up and used their calculators to practice the approach they already knew. Which is fine as far as it goes, practice is practice, but doesn’t help you calculate a tip in a restaurant without a phone app.

But, guessing wrong helps you (ermm, me) remember. 

Without going back to my lesson plan, I don’t really remember what else we were doing that day, but I remember G., an older guy, with a settledness about him that I liked, looking at that paper like it was written in a foreign language. 

Ouch. 

Mistakes help you learn 
Practicing what we preach, and learning from teaching mistakes
mathacognitive. 
Background picture of a hand writing with pencil on a lined notebook

It’s a good reminder, as we’re celebrating the value of mistakes, that they still sting. Even when we believe they’re beneficial, even when we are actually benefiting from them.

And it’s a good reminder, that ( maybe because) they sting, they help us learn, too.

So, months later, I sat down to plan a new percents unit, and, I remembered G., remembered the sting,  and remembered my mistake.

But I also remembered I wanted to do better, remembered the changes I wanted to make (more intentional introduction, more time, more structure etc.) and designed a whole lesson about using mental math to find common percents using my mistakes as inspiration.


I probably made more mistakes when I first started teaching.

But I think I learn more from them now.

I suspect that’s true for many experienced teachers….?

I think, as veteran teachers, we can ….

… Recognize a mistake for a mistake. You have to know something about what your best teaching looks like to recognize when you fall short of it.

…. Feel the sting, but have the confidence in our abilities to respond productively (and not go into a shame spiral/avoidance)

…. Diagnose what actually happened (not just that something wasn’t good), and analyze why the mistake was a mistake.

… Have enough perspective to sort out the signal from the noise. What mistakes are important? What are about us? What are not actually ‘mistakes’ , but rather the randomness of the universe or factors beyond our control.

… Respond, because we are not constantly ping-ponging from one mistake/learning to the other, trying to grow in all the ways at once, so we have some time between mistakes to process them.

… Respond, because we have skills and mental resources to do better.

This fall, a lot of us, are feeling like beginners again, as we’re figuring out how to teach in new physically-distanced, virally-safe ways.

And, we’re going to make mistakes. I’m just hoping I can keep my head clear enough to learn from mine.

What I *AM* emailing myself, distance learning edition.

Ok.

So.

We’re doing this.

For at least the next couple of weeks (and for at least the rest of the semester for some of my classes) we’re figuring out distance learning. My inbox is full of tips and resources. It’s a little daunting. These are a few I’m actually bookmarking.

What I'm emailing myself: Social distancing edition
Educational resource roundup from mathacognitive
Picture of a computer on a desk with plants

Comparison Cards

When I rounded up all my various links about some of my favorite, go to activities I made a discovery.

I had posts about equivalence cards, and error correction, and my write/shuffle/share routine (although it could use expanding, tbh)

I had two different activities with comparison cards in my Teachers Pay Teachers shop. (Scientific notation, and probability for the curious)

But, somehow I had never written about how I actually use them.

Oops.

Clearly, I have been taking Comparison Card activities for granted. Also, clearly, I am attempting to rectify the situation


Why: 

They make for natural pair or group activities, so students are talking and figuring together (*cough* Mathematical Practice 3*cough*) 

They ask students to stop and think and reason about the meaning and values of the numbers, instead of jumping straight into computation.

Content:

Super-flexible, but they’re particularly well suited for formats that students tend to struggle to read/understand. So decimal values with multiple places, or scientific notation, in my class.

Materials:

Make cards by hand (half of a 3×5 index card works well) or use my Google slides tutorial.

Each card should have a single value, but mixing the number formats raises the critical thinking level (For example: my exponents set uses whole numbers, exponent notation, expanded notation, and words) 

Make enough for each student to have a set.

Facilitation options: 

Number line: Sort the values from smallest to largest, arranging in a line on the table.

Further option: Give students benchmarks to compare their number line, or construct parallel numberlines with two formats (one line with fractions, for example, and another with decimals)

War: Each student gets a set of cards, shuffled and face down. Play the classic card game, War, where the player who turns over the card with the higher value takes both

Inequalities | Number Sentences: Add inequality cards to the mix. (I have a full on set in my store, or make your own). Students should arrange two value cards and a comparison symbol to create sentences

(Note: If students are comfortable with inequalities, this is a less challenging activity since students can pick values that are easy to compare) 

Extensions: 

Add reflection/discussion questions (I always like to start by asking which were hard? which were easy? and why?)

Students create their own cards to add to the mix. This might be open or more structured (e.g. add a card that is smaller, larger, in the middle…) 

Subscribe to access my PDF Comparison Card Planning Tips (and other subscriber-only resources!)