Paul Halmos on Mathematics

Today’s commonplace quote is from I Want to Be a Mathematician: An Automathography.

We do our students a disservice if we give them the idea that trial and error, experimentation, and guesswork aren’t allowed in math class.

Yes, math problem-solving involves methods and procedures our students can learn. But following the rules we supply is no replacement for reasoning things out for themselves.

Math shouldn’t be a “Do it because I said so” subject.

At least some of the time, kids need to be playing with ideas and trying stuff, exploring relationships, drawing their own conclusions about how things work. Because that sort of experimentation leads to deeper understanding.

Sometimes, such experimentation leads to discovering their own way to reason about a problem and get the right answer for themselves. Other times, getting stuck and floundering a bit provides the “headache” that our teacher-methods can be the “aspirin” for.

But either way, taking things into their own hands for awhile lets students develop a more solid, experiential knowledge of math relationships and connections.

• Math Game Monday: Decimal Product Game

• Introduction to the Science of Counting

• Thinking Thursday: Words Help Us Think

[If you’re reading this late, the “Math Game Monday” and “Thinking Thursday” posts have a time limit. Each one stays on my blog for about a month, and then falls away, replaced by new games and journaling prompts. You can always find the newest posts at DeniseGaskins.com/blog.]

More admin problems this week, so not a lot of writing.

A bit of progress on the journaling logbooks, collecting puzzles where children can apply the sort of “trial and error, experimentation, guesswork” that Halmos talks about in the quote above.

Oh, and I discovered a minor formatting error in Charlotte Mason’s Living Math: I forgot to add the “Also by” list to the front matter. Oops! It’s a little thing, but it’s traditional for a reason, so that readers who like the book know what other titles they might look for. So I’ll get it in there one of these days, when orders slow down enough to pause the printing for awhile.

Also, I spent most of one afternoon doing my own trial-and-error mathematics, attempting to recreate a simplified version of Hipparchus’s calculation of the distance from the Earth to the Moon for an upcoming Alexandria Jones post.

It’s a basic problem in trigonometry, but it’s been a long time since high school. Less time since my kids were in high school, but they studied precalculus at the local community college to get some dual credits on their transcript. Finally, I got the round-off error down into the ballpark, so I’m calling it good enough for now, even though I haven’t figured out why my first approach didn’t work.

Probably one of those basic beginner errors that will make me slap my forehead and feel stupid when I finally get it.