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I know Twitter’s reputation: it’s a cross between a skull, a mushroom cloud, and a swamp fire. But dang if I don’t love math teacher Twitter! So many friendly people. So many great questions. So many array photos.
I got a lasting reminder of this awesomeness in June, when I tweeted this:
I expected to hear two dominant kinds of memory: happy recollections of a teacher’s validation, and traumatic ones of a teacher’s censure. The actual flood of memories that filled my notifications were richer, weirder, and far more diverse.
Backseat revelations on car trips.
Games with parents and grandparents.
The endlessness of counting.
And—coolest of all—strong emotions excited not by a teacher, not by a peer, not by a parent, but by the mathematics itself. More than I’d have guessed, people remember early encounters with mathematical truth, with the deep persistence of pattern. It made them feel angry, joyous, fearful, awestruck.
I offer up these stories with a minimum of curation. Each is a vivid little window into one of the strangest symbioses on planet earth: the relationship of a human being to mathematical reality.
“I Knew the Best Secret in the World, Because I Could Count Forever”:
The Endlessness of Number
Several folks recalled glimpses of infinity, or (equivalently) the idea that there’s always a next number. I’m still reeling from this, and I am objectively growing old and dusty.
“We’ll Get There in One Episode of Sesame Street”:
The quantification of time is one of the more peculiar achievements of civilization – and one with immediate importance to kids, who are always being made to wait for stuff.
(Interestingly, this “multiply by 10 then divide by 2” trick showed up in several people’s earliest memories!)
“For a Six-Year-Old, It Was a Big Revelation”:
It will surprise few of my math teacher colleagues that people remember the intellectual breakthroughs that felt like their own.
Your teacher tells you a thing? Fine.
You uncover a universal truth with nothing but your mind? More than fine!
“Minus Three Blocks North”:
The Allure of Negatives
Several folks remembered early encounters with negative numbers. Makes sense! They’re as weird as anything in Dr. Seuss or Lewis Carroll.
“They Seemed Arbitrary to Me”:
Those conversant in mathematics don’t think much about the symbols. They take a backseat to the thing symbolized.
But kids – just learning to shape symbols with their hands and to discern them with their eyes – put a bigger emphasis on the marks on paper. What shape is an 8? A 9?
“I Still Think I Was Right”:
Conflict with a Teacher
As a teacher, I half-dreaded and fully expected these answers. I know that disagreeing with a teacher burns a moment in memory far better than any mnemonic.
(As the follow-up tweet explains, Erick’s teacher couldn’t find one, and the vindicated Erick repeated the exercise the next day – this time with five colors.)
(I’m with the student on this one! 2-1 games at halftime rarely end 4-2.)
“Feeling Ecstatic That I Could Stack Two Odds”:
Odds and Evens
These recollections bolster my sense that “odd” and “even” are the best conceptual playground for the young mathematician. They’re abstract yet easy to visualize, rich yet elementary, not to mention a natural place to make the leap from specific (what’s 6 + 7?) to general (what’s an odd plus an even?).
“A Half of What?”:
Given how fractions dominate the upper-elementary curriculum (and the laments of secondary teachers), it’s no surprise that they surfaced often in folks’ memories.
These memories also point towards a meaningful context that stuck with people: coinage. “A quarter” = 1/4.
“Just Couldn’t Figure Out How My Dad Was Younger Than Me”:
Confusion & Clicking
Two emotions predominated: the feeling of “WHAT THE HECK IS GOING ON” and its successor, the sweet relief of “oh THAT’S what the heck is going on.”
“We Were Now Properly Going to Start Mathematics”:
Visions of Things to Come
Given the hierarchical structure of math education (year-by-year advancement, a sense of cumulative build-up, the sorting of topics as “beginning” or “advanced”), I’m not surprised that many folks remembered occasions when they got to glimpse around the corner, to see what lay ahead on their educational path.
“This Makes the Patterns in My House Better”:
Sorting and Arranging
I have a conjecture for why there weren’t more memories like this: because people don’t necessarily think of this work as mathematical!
It is, of course – pattern and classification are deep, essential mathematical tasks. But I wouldn’t be surprised if some folks’ minds’ skipped past similar memories, and latched onto something arithmetical, i.e., something more quintessentially “mathematical.”
“I Could Break the Ice and Scrape the Fragments into Triangles”:
Shape & Geometry
I was surprised to find so little geometry among these memories. The few that did surface were notably beautiful.
“What Did That Little x Do?”:
From Addition to Multiplication
Most folks have a sense of autobiographical memory that kicks into high gear around age 7 – right when they’re starting to encounter multiplication.
Apparently, meditating on the meaning of “2 x 3” is a very common activity for mathematicians at this age!
“I Am Still So Satisfied and Delighted By This”:
Whether self-discovered or not, clever numerical tricks and patterns have a way of sticking in the brain.
“By the Teens I Was Struggling”:
Some memories concerned not just the endlessness of number, but the peculiar nature of our numeral system itself, with place value and positional notation.
This is, after all, a pretty fancy technology, one that took centuries to develop, and which then swept the globe. The early experience of students often recapitulates historical development, in one fashion or another.
“I Am Five! How Should I Know?”:
Memorization and Drill
These early memories of drill and memorization aren’t all negative. But it’s striking, I think, how few of the memories overall concern drill!
Perhaps it’s because drill isn’t as common as we think.
Perhaps it’s because repeated events, by nature, are hard to pluck out as a “first” memory.
Or perhaps it’s because drill doesn’t stick in the mind quite the way other experiences do.
“Using This Little Guy”:
Only three of the memories dealt with calculators, and none with computers. A generational thing? Or – as I suspect – do technological experiences (e.g., playing with a calculator) stick in memory less than social (e.g., conversing with a parent) or interior experiences (e.g., sitting in the back of a car, dreaming mathematical thoughts) do?
“A Puzzle To Be Solved:
Learning Through Games
Again, given how much kids love games, I was surprised how few adults remembered playing them!
“I Always Wanted the Book with the Counting Monkey”:
Falling in Love with Math
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