Copy already solved math problem solutions
Learn the thinking pattern of mathematical problem solving by writing by hand.
Copy already solved math problem solutions
One helpful practice we have found is to find solved math problems that are almost pedantic in doing one step at a time and copying them.
Learning mathematics is not only about learning the techniques and “tricks” but also about learning a thinking pattern to apply to solving a question using said techniques.
Learning the thinking pattern is difficult when you have an exercise and the answer but not the steps in between.
This is where copying already solved solutions comes into play.
I got this idea from learning about writing.
Great writers copy other great writers to learn what it takes
Jack London, Robert Louis Stevenson, Hunter S. Thompson, and Benjamin Franklin are all noted for copying other people’s written work.
From the Art of Manliness1:
A large part of the self-improvement program Jack London set out for himself involved studying the work of other great writers. Of these literary mentors, London most admired the style of Rudyard Kipling. For hours at a time, and days on end, he would make it his assignment to copy page after page of Kipling’s works in longhand. Through such feverish effort, he hoped to absorb his hero’s rhythmic musicality and energetic cadence, along with the master’s ability to produce what one contemporary critic called “throat-grabbing phrase".
From an interview with Johnny Depp (the actor) about Hunter S. Thompson (the writer, whom Johnny Depp portrayed in a movie):
“You know Hunter typed The Great Gatsby? He’d look at each page Fitzgerald wrote, and he copied it. The entire book. And more than once. Because he wanted to know what it felt like to write a masterpiece.”
Even in copywriting for advertisement and direct sales, the same idea comes up
Find ads that have worked, and write them by hand.
I learned English this way
When my family moved to the United States from South America, I spoke no English.
My parents tried to have me enter the “correct” school year I was supposed to be in, but the American school held me back a year (I did 1st grade twice!) because of my lack of English.
My mom had me (and my sister) copy articles from Reader's Digest, an American general-interest family magazine.
For months, we had to write out an article in long hand.
I never had issues with English again.
Generate solutions with steps with AI
Finding math exercise solutions with each step delineated is time consuming if the textbook the kid uses in school (or at home) isn’t made for that express purpose (which few are).
We live in the age of AI now, and you can have an LLM of your choice (OpenAI, Claude, Grok, Gemini, etc.) generate these solutions for you.
An example from ChatGPT for how to think about using the fact that 20 squared is 400 to figure out what 19 squared is:
Great - we figured out 19 squared is 361.
We now have written instructions for our kids to copy, guiding them through each step of the problem and how to approach it.
Having the ability to generate written instructions like this is fantastic, as you don’t have to rely on books or worksheets for them.
You can load up an LLM and have it generate these walk-throughs for you.
Copying these things by hand takes time, so it’s not an everyday thing or a do multiples of these things everyday thing.
It’s a “when the kid struggles with a line of thinking” tool.
Start copying today
Grab a piece of paper and a problem, then start writing by hand.
Good luck!
That’s all for today :) For more Kids Who Love Math treats, check out our archives.
Stay Mathy!
All the best,
Sebastian Gutierrez
I know.
That aligns well with the “make thinking visible” school. Learning math or other problem solving techniques is so difficult, because no one knows how other people are thinking. So, we need to make thinking visible by articulate clearly every step, our reasoning, even our mistakes.