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Why playing with algebraic and calculus concepts—rather than doing arithmetic drills—may be a better way to introduce children t
The familiar, hierarchical sequence of math instruction starts with counting, followed by addition and subtraction, then multiplication and division. The computational set expands to include bigger and bigger numbers, and at some point, fractions enter the picture, too. Then in early adolescence, students are introduced to patterns of numbers and letters, in the entirely new subject of algebra. A minority of students then wend their way through geometry, trigonometry and, finally, calculus, which is considered the pinnacle of high-school-level math.
But this progression actually “has nothing to do with how people think, how children grow and learn, or how mathematics is built,” says pioneering math educator and curriculum designer Maria Droujkova. She echoes a number of voices from around the world that want to revolutionize the way math is taught, bringing it more in line with these principles.
The current sequence is merely an entrenched historical accident that strips much of the fun out of what she describes as the “playful universe” of mathematics, with its more than 60 top-level disciplines, and its manifestations in everything from weaving to building, nature, music and art. Worse, the standard curriculum starts with arithmetic, which Droujkova says is much harder for young children than playful activities based on supposedly more advanced fields of mathematics.
“Calculations kids are forced to do are often so developmentally inappropriate, the experience amounts to torture,” she says. They also miss the essential point—that mathematics is fundamentally about patterns and structures, rather than “little manipulations of numbers,” as she puts it. It’s akin to budding filmmakers learning first about costumes, lighting and other technical aspects, rather than about crafting meaningful stories.
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“It is in our relations with other people that we gain a sense of ourselves; it’s that, pretty much, that makes relations with other people unbearable.”
Every summer I panic because I know everything will happen so fast I tumble through time and can't stop it I just have to resign myself to the endless overwhelming bustle of life. I just want space and time for myself
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Leaving a party like "Now for the part of the night where my mind claws and bites and pulls at every minor moment of tension throughout the night and tries to get me to hate myself because of them." But just naming that that is happening helps... Because why do you hate me so much? Why do you berate me for every little thing, why is nothing I do good enough for you? Why can't you just let me live my life and be happy?
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An acquaintance of mine invited me to the housewarming dinner party for her new roommate last night and I thought it was sweet to be invited, I've encountered this acquaintance every so often for a few years now and she has a chill vibe but we've never really clicked. But I'm on the remote outer edges of her friend group and get invited to that group's events every so often and that friend group seems out of my league, maybe I shouldn't say that but they're so cool and whimsical and vulnerable and I do love to be around them when the opportunity presents itself so I was happy to go to this dinner party.
So this acquaintance who invited me ended up sitting next to me at the party -- there were four little tables set in a circle facing each other, so we had our own table between the two of us. I thought it was slightly awkward to be sitting next to her actually as like I said, we've never quite clicked, but that means we've never really talked at length so I took the opportunity to try to learn more about her.
So I asked her what her work is like, and she's a dog trainer and just got certified to teach dog training classes to others and she was talking about the upcoming class she's going to teach and she completely lit up while talking about it like you could tell her smile was coming free from its containment uncontrollably and I told her that she was lighting up talking about it and she laughed and thanked me. But also while noticing her lighting up I was thinking, "wow, she is so cute, I've never noticed before."
And then later in the evening people had moved around and she was sitting across the room and I was sort of zoning out pleasantly but then noticed her noticing me zoning out and she smiled and waved at me from across the room and I smiled and waved back and could feel myself blushing afterwards.
And then when I was leaving I went outside to the burgeoning bonfire to say goodbye to the hosts and she said "it was so fucking good to see you" and she had never expressed such enthusiasm to see me before and I walked away wondering if a spark had been ignited.
But shhh we can't talk too much about these things
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