“Welcome to your first supplemental course in mathematics,” Twilight Sparkle chirped, giving a broad, sincere smile. She was in her element, wearing a pair of purple-rimmed half-glasses on a chain and a blue-and-purple plaid skirt and jacket combo, with a plain white blouse on her upper body. She stood before a blackboard covered in various simple equations, along with her name, which was written in the upper right corner.
“Umm, Twilight. I know your name. You didn't need to write it on the board,” Pinkie said, with a bemused expression. She was in her work apron, still stained with flour and fruit juices, and sitting on the floor of her bedroom, which had been turned into a small, makeshift schoolhouse.
“Sorry, I wanted the whole experience. I guess I got a bit carried away,” Twilight said with a blush, her magic lifting the blackboard eraser and slowly wiping her name off. “But still, this is something just for you. I know you never went to university, or college. I'm certain your education was complete but you're not required to learn mathematics past a certain level. This is a supplement to help that.”
“This is really neat! I never knew I needed to know really advanced math. How did I get along without it all this time?” Pinkie asked.
“Err... well... you don't... don't quite need it, really. I mean, you won't need the math that a Diamond Dog scout does or that a thaumatic engineer does. But I... I like teaching, you know that. And I figured... we have fun doing what you like. Maybe we could have fun doing... this too?” Twilight said, growing more and more nervous.
Pinkie considered the question for a moment then broke out in another giant smile. “Sounds good! You know how much I love it when we play those dice-rolling games. Maybe learning something might be fun too!”
“Yes, yes it is! Didactic play is the best kind of play, though I hope we can maintain seriousness and not get too playful. N-not that I don't intend for us to try and have some fun!” Twilight said quickly. “Math is fun. You can do fun little tricks with it, and find that it helps you out in your life. I think even the Cakes will like you doing this.”
“Oh? Why would the Cakes be so happy about this?” Pinkie inquired, tilting her head.
“You do well enough on the register, and in the back. But imagine if you could help them out with the accounting, or with more complicated ordering of raw material or shipping of things. You'd really be taking the pressure off of them,” Twilight replied.
“Oh... of course! Mister Cake hates doing all the accounting, it's boring. I don't like boring stuff either but I can take it because I know how to have fun,” Pinkie said eagerly.
“There are elements that you likely heard about but never used in the math you already learned,” Twilight said, lifting a piece of chalk and tapping on the board.
“Like Laughter and Magic?” Pinkie asked with a smile and pucker of her lips.
“Oh you...” Twilight said with a blush, clearing her throat and tapping the board again. “You know the normal operations and I see you use them all the time. Addition, subtraction, division and multiplication. You also work with fractions, quite a lot. I'm honestly impressed the way you can perform all the fractional equivalent calculation for recipe modifications and for changes between different scales.”
“Thanks! I used to use a lot of that for the rock growth calculating and for getting the right timing on turning the rocks and moving the harvest around the fields,” Pinkie said, with a bit of pride.
“I already love you, you don't need to keep trying,” Twilight said, blushing a bit. “Did I do that right? I saw it in a book and I thought I'd try...”
“It was cute. I like when you try things like that,” Pinkie said, sitting back a bit. “So what other elements are there?”
“Right! Elements! The use of parentheses to segregate arithmetic functions, exponents, and the various mathematical properties, including the order of operations. Plus algebraic use of unknown quantities,” Twilight said, tapping the board with the chalk pointing to examples of all the things she mentioned.
“I saw a lot of that. I used to think someone sneezed while they were using a keyboard, or something. Can you really teach me all that?” Pinkie asked.
“Of course! I'm an excellent teacher. But remember, if you ever need supplemental help you can get tutoring from Smarty Pants. She knows about as much about math as I do,” Twilight noted.
“Okie-dokie-okie!” Pinkie cried cheerfully. “But I totally won't need Miss Smarty Pants to help me. I'll be able to get all my education from you. This'll be easy.”
- - -
“This isn't easy. This isn't easy at all!” Pinkie wailed, looking over her 'completely not homework' homework. Her marks on the in-class work weren't that great, and her homework tended to be more graphite smudges than right answers by the time she turned it in.
She was trying. She was really, really trying hard. But Twilight... she wasn't quite the teacher she imagined herself to be. She was very good about relaying information and demonstrating the hard technical theories behind the concepts but she couldn't seem to express examples well or break down the theories into simpler ideas.
Despite her distress, Pinkie had to laugh at that. Her sweetie-sweet sweetie pie was so super-smart she couldn't figure out how to be not-smart. She wasn't being mean about things. She was just better at being a teacher for big-time eggheads.
It wasn't that she couldn't teach if she tried. Twilight had been the one to teach Pinkie how to play roleplaying games, and they both found that the best thing ever. She could be educational but she molded herself to the... feeling of the subject. Roleplaying games were not that smarty, so she could explain it easily, even if Pinkie had to read through the book a few times to understand what Twilight was saying, and get more examples than just the first few. But math was something super-smarty, and Twilight had studied the highest levels of it. She had to give it all her brains.
Looking at her homework again, Pinkie decided to do what she had said would not be necessary. She had intended to let Twilight's teaching carry the day, but the realization that Twilight's methods were above her level sent her out of Sugarcube Corner and out past the edge of town to Sweet Apple Acres.
Her knock at the door was answered by the winkled and pleasant face of Granny Smith, who gave a smile to Pinkie. “Well hello there, young'un. Ya here ta see Applejack fer some matter?”
“No ma'am, Granny Smith. I need to see Miss Smarty Pants,” Pinkie chirped.
A dark cast passed over Granny Smith's face at the sound of the name, followed by a sudden shifting of her eyes and a pointed look towards a side-table. She increased the size of her smile, without adding to the sincerity and replied, “Y-yes, mah new... future granddaughter-in-law. She's out with Big Macintosh checkin' trees an' buckin' fruit. You'll find 'em in the east orchard. Be a dear and make sure they ain't makin' mu-” Her eyes darted around again and she cleared her throat, “M-makin' music together, as we old folks sometimes say. Ain't right ta do 'til they is hitched, ya unnerstand.”
Pinkie tilted her head a little bit. That was an unusual way of saying 'playing procreation', which Twilight often said. But she just smiled and nodded. Old folks were weird. “Okie-dokie-lokie! I'll make sure they're being good.” With that she hopped happily away, never seeing the smile drop from Granny's face, replaced with a look of nervous paranoia.
It took some hopping through the orchard but Pinkie eventually followed the sounds of grunting and thumping to the pair. Both strong-bodied figures were engaged in a vigorous session of apple-bucking. Big Mac's considerable strength was brought to bear against the largest and heaviest of the trees, while Smarty Pants chose those that were slightly thinner. She was an intellectual, after all, not a farmer. But her natural donkey strength did not put her much below a well-muscled earth pony.
Smarty Pants still looked as she had the day she had been brought to flesh and blood life by The Granter. She was a thin, light gray donkey with her long ears both half-flopped forward. Her mane and tail tip were still a mess of tightly-bound hair bundles and she still wore her polka dot pants. Her eyes, too, remained as they had been, a heterochromatic red and blue.
Neither Mac nor Smarty noticed that Pinkie had arrived. They simply moved buckets of apples onto a cart and sat down beside one another wide a sigh, unashamedly leaning their bodies together, both shining with sweat. Big Mac leaned over and gave Smarty a kiss on the cheek. “Mm, ya taste like apples an' hard work. Yer gonna be a boon ta the family, darlin'.”
Smarty blushed lightly and nuzzled at Big Mac's neck. “Thank you. I want to do all I can to prove it and keep proving it. I enjoy all of you. But, of course, some more than others...” She giggled softly and lipped at Big Mac's throat.
“Eeyup, ah know ya do,” Big Mac Said, standing a little more proudly and lifting his chin just a bit.
Pinkie suddenly leaped into view and blew a whistle she kept hidden in her mane. “Hold it! Granny Smith told me to make sure you two weren't out here 'making music.' Looks like you were just getting warmed up.”
Big Mac and Smarty both pulled away, blushes burning on their cheeks while guilty looks rested on their features. “I-it weren't nothin' like that!” Big mac insisted.
“I promise you, we are loving but chaste, very much so,” Smarty stated.
Pinkie peered at the two for a moment and broke into a smile. “Just doing a favor. I really just needed to find you, Smarty.”
“Me? Does Twilight wish to have tea again?” Smarty asked. “It's always lovely to have some more reminiscing time. My memories always benefit from repetition. I can apply my new senses to what I recall and make them richer.”
“Oh, maybe! She always likes that. But I need your help first,” Pinkie said.
“My help? Well now, what sort of help do you need?” Smarty inquired.
“Well, Twilight says you're really good at math. She's been trying to teach me math and... she's a really, really good teacher sometimes. But, um, I still don't...” Pinkie said, her words fading to a whispered mumble.
Smarty regarded Pinkie with a slight smile and slowly nodded her head. “I understand. I've known Twilight for years. She loves learning, and wants to know the deepest, most basic ideas, the theoretical underpinnings of a subject. This is great for a researcher like her... but bad for imparting learning to a neophyte. She tries to jump right in and build, not from the ground up, but from the bedrock up, little realizing that there is actually a process of learning both up and down.”
“That's what I thought. I think,” Pinkie said, softly scratching her head. “She tries to teach me like a super-duper super-smarty but I don't understand what she's talking about when she tries to tell me about all the math-y things. I tried to understand but...”
“It's understandable,” Smarty said. “She's not a Doctor of Mathematics but she certainly had enough research time to get a degree if she wanted. Being an autodidact allows situations like that. But the tragedy is she can no longer think on the level of one who does not understand.”
Pinkie slumped a little bit. “So does that mean... I'm not going to learn math from her?”
“No, you will. I can help you learn some of the basic facts that you need in order to do well with her lessons. But eventually, you have to tell her right out that she can't teach the way you need to be taught,” Smarty said, cutting off a comment from Pinkie with a soft bray and the wave of a hoof. “I know what you're going to say, you don't want to hurt her feelings. But this is essential information. She must be told that her methods need tweaking. You'll be teaching her, which she should appreciate.”
Pinkie brightened a little bit. “Oh! I like the sound of that. She loves learning, so she'll love me even more! When can we get to learning?”
“In a moment. Once we haul these apples back to the farmhouse I'll wash off and start your supplemental lessons,” Smarty said, gently nudging Big Mac. “Come along, Mac.”
“Eeyup,” Big Mac said, attaching himself and Smarty to the cart and walking placidly off with her, Pinkie bounding happily in the lead.
- - -
“Twilight?” Pinkie inquired softly, lifting her hoof as was proper in a school setting.
“Yes? What is it Pinkie?” Twilight inquired back, halting in her explanation of how to derive the quadratic formula.
Pinkie hesitated a bit, tapping on her desk and looking shiftily around the room. “I... I talked to Miss Smarty pants, and got a little help with some of my work.”
“I noticed that your independent assignments had gotten a lot more polished. I told you she could help if you needed it,” Twilight said with a smile.
“Yeah... well... she gave me some advice...” Pinkie said, trailing her words off.
“Practice constantly? Work on your long division? Constantly complete the square?” Twilight guessed.
“No, she told me to tell you... you're not a good teacher,” Pinkie admitted, with her head turned to the side.
Twilight looked stunned by the statement, dropping the chalk from her magical grip. “O-oh... I... I don't... that doesn't seem like Smarty. She's been so nice since she came to life and got engaged...”
“Oh! I don't mean that you're not trying hard! You are, and you're really, really super smart and know everything,” Pinkie said.
“Not everything, but I hold my own in mathematics...” Twilight said with some humility.
“But Smarty told me you know so much everything that you don't know how to not know anything. You don't know how to teach somepony like me, who didn't learn all this before,” Pinkie said.
“Don't know... how to not know...” Twilight repeated, feeling the statement over her tongue for a moment and looking thoughtful. “She said that?”
“Mm-hmm,” Pinkie replied with a nod. “She said something about bedrocks, and the ground. I understood that part a little, I know the difference. That you build from the bedrock and somepony like me builds from the-”
“Ground,” Twilight said, finishing the statement, comprehension crossing her features. She glanced a side at the incomplete derivation and smirked a little. “Here I am... trying to teach you like a graduate student, when you're still on your undergrad path. I'm so sorry, Pinkie...” She trotted up and gave Pinkie a warm, soft hug.
Pinkie returned the hug with a little extra strength, squeezing her unicorn lover so tight she forced out a puff of breath. “It's okay, Twilight. You didn't know. Now you do. So I got to teach you something! I'm a teacher too!”
Twilight chuckled breathlessly, and nodded her head. “Yes Pinkie, you are. You teach me something new almost every day. I never knew love could be such a didactic experience until I met you.”
Pinkie blushed a touch, though she was largely unclear on what that meant. She nuzzled softly at Twilight's chin and planted a soft kiss on her lips. “So... maybe Smarty should teach me. She said that she wouldn't mind because it would probably take too much of your time from big research...”
Twilight winced a bit, kissing Pinkie back. “I never intended for it to seem like I saw this as a burden. I had a problem with teaching you because I never took courses in proper pedagogy. I was always destined to be a researcher, not an educator. But, if Professor Sliver taught me anything it was how to reach a student, to draw out their potential by touching their level of skill, not arrogantly displaying my own. I can teach you. I will teach you. Exactly as you need.”
Pinkie squeezed Twilight again, then moved back to her seat. “Great!”
Twilight quickly erased the board and picked up a piece of chalk. “So... did Smarty teach you elementary issues like the standard order of operations?”
“'Proper Education Makes Dreams Awake Sooner!'” Pinkie recited from memory. She took a moment to think about it and added, “Parentheses, exponents, multiplication, division, addition, subtraction.”
Twilight nodded and smiled. “Great. And you know about working with both sides of an equation?”
“It was a little tricky. But she said I could do anything as long as I did it to both sides. I'm supposed to get all the letters on one side,” Pinkie said.
“Getting the same letters on the same side is generally the idea if there's more than one. And you remember about these?” Twilight asked, drawing on the symbols for inequalities and variants.
“Yup! They remind me of Gummy going after cake. So I know that they go to the bigger side, even the ones that could be bigger or equal,” Pinkie said.
Twilight thought for a moment, her chalk softly tapping the board. A sudden idea came to her and she began scrawling an inequality on the board. “Come up here and reduce this inequality. If you need help I'll be right here. I'll always be right here to support you...”
9x-7i < 3(3x-7u)