Would you mind posting a link to whatever you came up with regarding factoring trinomials?
One comment: in a sense, you are describing motivating student learning by raising the stakes in a kid-centered way: “I want to learn this because it’ll help me __”. Something I love about the Beast Academy curriculum is that it takes the opposite tack of lowering the stakes. It introduces big topics within little games and puzzles that have the flavor of, “This is just a fun little game, wanna play?”
I remember when you first wrote that, because then and now I disagreed with the premise--math isn't aspirin. But then, I always disagreed with your concept of selling math, too! Not how I approach it.
However, I find that teaching students that you can add functions, specifically lines, and then ask what happens when you multiply lines does a pretty good job of introducing both binomial multiplication and then factoring--what lines made this parabola? What parabola can't be the product of two lines? Works pretty well as glue tying everything together.
What a great metaphor. Related to no pain no gain. In physical exercise you get used to the idea that if you're exercising correctly, your body will experience a certain level of invigorating pain. Same with learning.
The corresponding phenomenon I study in product design is that if you want to find potential customers to interview who can give you useful feedback on a product you are developing, you like for the people who have an acute problem that they are actively trying to solve — people with a headache. The common wisdom is to convene focus groups of random consumers, but if you ask people that don't have a headache to speculate on what they might need, they will give you vague, wildly inaccurate speculation. AND only people with headaches have the motivation to put in the effort to solve their problem.
Taking it further, imagine interviewing students to understand what headaches they already have, then shaping a math curriculum around that, rather than force-fitting a predetermined curriculum to the students. Where would that lead?
In Florida they are forbidding teachers to give students headaches. So there will be no more learning in Florida. The aspirins will pile up without any reasons to use them. Sad.
Would you mind posting a link to whatever you came up with regarding factoring trinomials?
One comment: in a sense, you are describing motivating student learning by raising the stakes in a kid-centered way: “I want to learn this because it’ll help me __”. Something I love about the Beast Academy curriculum is that it takes the opposite tack of lowering the stakes. It introduces big topics within little games and puzzles that have the flavor of, “This is just a fun little game, wanna play?”
Gotcha: https://blog.mrmeyer.com/2015/if-factoring-trinomials-is-aspirin-then-how-do-you-create-the-headache/
I like how that integrates the low-stakes “this -is-just-a-puzzle” approach and the “this-has-depth-and-power” high-stakes approach.
I remember when you first wrote that, because then and now I disagreed with the premise--math isn't aspirin. But then, I always disagreed with your concept of selling math, too! Not how I approach it.
However, I find that teaching students that you can add functions, specifically lines, and then ask what happens when you multiply lines does a pretty good job of introducing both binomial multiplication and then factoring--what lines made this parabola? What parabola can't be the product of two lines? Works pretty well as glue tying everything together.
What a great metaphor. Related to no pain no gain. In physical exercise you get used to the idea that if you're exercising correctly, your body will experience a certain level of invigorating pain. Same with learning.
The corresponding phenomenon I study in product design is that if you want to find potential customers to interview who can give you useful feedback on a product you are developing, you like for the people who have an acute problem that they are actively trying to solve — people with a headache. The common wisdom is to convene focus groups of random consumers, but if you ask people that don't have a headache to speculate on what they might need, they will give you vague, wildly inaccurate speculation. AND only people with headaches have the motivation to put in the effort to solve their problem.
Taking it further, imagine interviewing students to understand what headaches they already have, then shaping a math curriculum around that, rather than force-fitting a predetermined curriculum to the students. Where would that lead?
In Florida they are forbidding teachers to give students headaches. So there will be no more learning in Florida. The aspirins will pile up without any reasons to use them. Sad.