The Brain Station and little Italian Conductors
An Essay of the Mind
by: A.Z.K.R.
The “Train of Thought” is a very common expression, that I’ve discovered is (at least for me) very helpful in visualizing and understanding my AuDHD mind, as long as you remember, it’s a whole train station and not just one train.
“The Brain Station” first came to mind when I was trying to explain why (I think) I tend to repeat myself and have the same kind of conversations over and over.
I picture a topic like a train car. When several topics/stories/memories/thoughts or ideas are connected in a way, probably not by one grand picture, but like how Spot It cards all have one thing that they share with each other Spot It card, they get hitched together on the same train, and most likely stay on that train together for a while—or indefinitely—so that if something gets brought up that triggers a need for one of these cars, the little conductor just brings the whole train in and unloads the information accordingly.
This idea came back to me when I was getting stuck in logic puzzles and geometric proofs. My mom said that based off of how I described “The information just being there or not” (and how she observed me staring off into space until an answer came to me) it seemed that, as opposed to just being incredibly stupid (my conclusion) I was just so smart that I was used to having answers come to me and not using my thinking muscles. So when I actually needed to think, those thinking muscles had atrophied. Now I understood what she said, but it didn’t quite ‘click’ in the right way until a specific proof in my geometry book about parallel lines. I was able to articulate that I understood the proof just fine, but on my own, I would have never been able to come up with and break down the steps to explain why the given was true, because it just obviously was true based on the definitions on the previous page. (Now the reasons for the proof were all, ‘because of this definition’ but I wouldn’t have realized I was supposed to write that.) Mom connected this scenario to the proofs and logic puzzles I had been doing and I was able to understand my struggle, which I explained to myself first through how reading works, and from there, to train cars.
I realized that my problem was like learning to read. In the early stages you learn phonics and sounding out. But once you’ve learned to read proficiently, you don’t need to sound out every word anymore. So, in my case, if for some reason I needed to sound a word out now, it would be as if I have completely lost the information of how because I haven’t in so long. (I can sound out words, but not with a very high success rate. I can read at a college level… and spell like a fifth grader. I might be being generous with myself on the spelling part.) Now we bring in the Italian Conductor.
You’ve learned to read, or maybe you can come up with a more suitable example, but you no longer need the basic, rudimentary, information for your topic of choice.
It is tedious to the little conductor to have the “phonics” and “sounding out” train car on the train of information responsible for every time you read. There are probably several of these reading trains depending on how much you compartmentalize school subjects; so to be more accurate, it is tedious to the little conductor to move these cars back and forth from each needed train. There’s probably a more useful car he needs to put in that spot, like word definitions that keep getting lost. (Let’s face it, if the words are in a bin like a coal car, the new ones will fly off the top anyway.) So, he unhooks the “phonics,” and “sounding out” train cars, and leaves them in the “Graveyard of Information” to rust.
Then, inexplicably, one day, you need that information. But it isn’t on the train. The little conductor goes to the graveyard, but he cannot find the lone rusted train car among many similarly rusted train cars he had thought wouldn’t be need anymore. On top of that, they’ve accumulated even more things that he’s forgotten for you, as you were learning more things. So, it’s lost. He’s missplaced this outdated information. He scratches his head.
“Eet-a ees-a not-a here.” (This is why he’s Italian.) So he shrugs and moves on. He has better things to do than check the faded label of every rusted train car to find one among thousands.
But, “Eet-a ees-a not-a here” obviously isn’t enough for your parents, or teachers, or what have you.
(No, for real, it’s not enough. My mother made me look up the translation for “It’s not here” in Italian. So, my little Italian Conductor cartoon in my head should be saying: “Non è qui.” Thank you Google translate.)
“But we taught you this! It has to be there!”
And they’re right, of course, it is there. You just don’t know how to remember it. You can’t talk to the conductor as far as you know. His telegraph machine is probably broken.
The even more irksome part is that if the memory of actively learning the information is connected to the information itself, (who am I kidding? it absolutely is!) then when Mr. Italian Conductor unlatches ‘unnecessary’ information he probably left the memory of learning it in the first place, also in the “Graveyard of Information,” still hooked to “phonics” and “sounding out.” Which means that you might only remember the parts of learning that are actively connected to still-relevant information. Which could just be a funny story you like to tell, or a particular lesson you loved for any given reason, which leaves huge gaps in your memory that annoys everyone. Especially your mom.
Sir Arthur Conan Doyle has a quote he wrote for Sherlock Holmes, along the lines of this: Everyone’s brain is an attic that must be furnished with the necessary information of getting through life. He says that this attic does not have rubber walls and can’t be stretched to accommodate information you don’t need. Which is why, he argues to Watson, that as a detective, facts about the solar system are a clutter to him, and he doesn’t need to know who orbits what, or how many planets there are, in order to solve crimes.
I think Sherlock is wrong on the part about not stretching our attic walls. We can, he’s just lazy. The answers come to him.
Maybe people have different consistencies of rubber, but I think you can stretch it. Like my mom said, it’s like a muscle. The part he is right about is clutter and furniture. While we work on stretching the rubber attic muscles, we still have a lot of crap to sort through and keep track of. That’s what the train station is for, to bring information in and out of the crowded attic, or across parts of it, you pick. Our problem? It’s this: The person in charge of maintaining and organizing the attic? He’s just as confused as your are, because he’s a just little cartoon Italian Train Conductor. And his English ees’a not’a too good.
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Beauty in the Math
As a homeschool mom, I’ve been teaching math every day since 2017 when my oldest officially started first grade. We did Math-U-See Alpha through Pre-Algebra with steady diligence. When we finished the curriculum for the school year, we often used another to review. For years we had colorful, used copies of Singapore (1A-6B) to ensure there were no gaps in our learning. It wasn’t necessary, we just liked it. My oldest also loved reading Life of Fred books for fun until about a year ago when she grew as impatient with them as I have always been. We feel they make great supplements if your kid is into them, but they aren’t really a complete curriculum. (My husband and I honestly don’t understand how anyone learns anything from them at all.) With all this math drilling, I have always passionately felt like I needed to have books that kept that spark–the love of the beauty of math–alive in our home. It’s easy to get lost in crunching numbers and forget that it’s fun to play with numbers, to entertain ideas, and to marvel at the patterns.
Books that have helped me maintain that in the younger years were things like Swirl by Swirl, Blockhead, the Sir Cumference series, The Lion’s Share, and many more. I collect math picture books and biographies of mathematicians for kids like Michael Phelps collects Olympic medals. I love them and I love reading them to my kids. We enjoy Penrose the Cat and Bedtime Math: A Fun Excuse to Stay Up Late. I have a more MathStart picture books than I can count. Not really, Anno taught us to count pretty high. But as my oldest got older, I realized I needed to have more than just picture books to keep that love for math alive.
We started in middle school with books on fractals. She had already read Mysterious Patterns: Finding Fractals in Nature by Sarah C. Campbell, but we needed more. A friend recommended Lisle’s Fractals: The Secret Code of Creation and we ate that up. It’s so beautiful. I even bought and read Mandelbrot’s The Fractal Geometry of Nature from the 70’s, for my own personal amusement.
Then I became even more devoted to being purposeful in adding math books to our history and science reading. Zero: the Biography of a Dangerous Idea by Charles Seife was a fun one, and I recommend it for 7th and 8th graders tackling Algebra I for the first time. Learning about the beginnings of things, when the world wasn’t quite sure what to make of a concept, is always exciting. Adding living books to a student’s math studies is what I think is greatly missing from the public school system’s approach to math education in the upper grades. As a society we’re helping elementary students get excited with great picture books like The Boy Who Loved Math and then we leave them hanging once they hit Algebra. Books like Derbyshire’s Unknown Quantity aren’t being touched until college, if at all.
Just this week we finished A History of Pi. Beckmann’s writing isn’t as thrilling as Siefe’s, and he often goes on tangents about governments he doesn’t like, showing some interesting biases that made my 9th grader roll her eyes, but I’ll still take his passionate sometimes wrong hot takes over a boring textbook that never mentions the history of 3.14 and how it came to be what it is today.
Once you dive into the world of living math books, it’s actually more difficult to find someone dispassionate about their topic. Francis Su in Mathematics for Human Flourishing also has several political asides while arguing for math bringing virtue to those who study it. While it wasn’t my favorite of the math books I’ve read and I won’t be assigning it, it helped me identify and articulate some of my goals as a math teacher.
What math or math history books have you read that have inspired you as a teacher or student? Books that made the beauty of math shine for you?
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