Grandpa decided to wait to start school until Samantha woke up on her own. He didn’t want to start off on the wrong foot, and he knew Sam would need some time to adjust to the transition. Sam — this is what he always called her, rather than Samantha. When Samantha finally came out of her room to ask Grandpa when they would start, she found him squirreled away in his office, peering through a telescope at the forest scene out his window.
Seeing her come into his office, he quickly changed the angle of his telescope and switched tasks to pretend he was looking for a book on his shelf and not finding it. “Sam,” he said. “So glad you’re here. Are you ready to begin?”
Grandpa said he had a philosophy about school, one that she was destined to like. Rather than dictating to her what she would read and study, he decided to let her formulate the curriculum — within reason. She could choose the books she would read and study. She could choose the real-world scenarios they would apply to math problems. She could choose the hours she would study — as long as she put in 8 hours a day. She would also teach every other lesson to grandpa, since you learn best when you’re teaching yourself.
It was clear he wanted her to take charge of her own education. He wanted to kindle an inner desire for learning, and he would do it by giving her latitude to be her own person, to choose what and how she learns. He was more of a coach than a teacher, one who could help when she got stuck, or who could motivate her when she needed motivating.
“Well,” Samantha said, “if we’re going to use real scenarios, how about this one: let’s figure out the area of the forest.”
“Excellent,” Grandpa said, and he pulled out a large topographical map. Samantha had thought calculating this would involve walking around the forest somewhere, but instead Grandpa proceeded to spread out a three foot map on a large wooden table. Given how convenient the map was, and how familiar Grandpa with the folds of the map, he must have unfolded it on this table many times.
Samantha knew how to calculate the area of a rectangle or square. But the forest wasn’t a perfect rectangle or square, so she didn’t quite know what to do. Grandpa let her think about a solution for a good hour. The forest was shaped somewhat like a rounded trapezoid or rhombus, with multiple edges following different contours and terrain edges, such as a river.
While Samantha worked on the problem, Grandpa stole onto the deck and looked at the forest through his large telescope. Samantha thought most people used telescopes at night to examine the stars, but Grandpa used it to peer into the depths of the forest. As he looked and turned the focusing ring to adjust the view, he often pulled away and would jot a few notes down in a notebook. Sometimes he would laugh as he wrote the notes, and then return his gaze to the telescope, change the angle a bit, zoom in, and then chuckle a bit. “Perfect,” he said, and then made a few more notes.
Samantha wished she could read inside Grandpa’s notebook, but he was too secretive about his research to let others know what he was up to. Whenever Samantha would ask him, he would say, “All in due time, Sam. Be patient, and observant for now.”
Samantha decided to divide up the forest into a series of squares, rectangles, and triangles. She knew the formulas for calculating the area for these shapes, and she began making her own notes, jotting down dimensions. As she made notes of the dimensions, the forest song began to rise gradually in her mind, growing louder and louder the more dimensions she wrote down. The music pulsated with almost a controlling rhythm, mixing her emotions inside her, almost making her dizzy.
Given the distraction of the music, which she kept to herself, it took her a while to add up all the sides, and then plug them into the formulas. When she finished, she told Grandpa her answer.”37 square miles,” she told him.
Grandpa consulted his notebook, which he carried in his hand. “36.74 miles,” he said. “But close enough.”
Samantha thought it was strange that he had already calculated the area of the forest, and she wanted to press him about his research. But as this was the first day, she thought it best to maintain a little respect. Having finished calculating the forest area, the music in her mind softened again and died out.
“Now how about the next scenario,” Grandpa said. “What do you want to know, Samantha? What is it inside you that you really want to know? That’s what you should study next.”
She thought for a minute. She wanted to understand the music she kept hearing in her head, but telling Grandpa about it would make her sound crazy. She would save this for later, another time.
“I want to know the average diameter of the forest trees,” she said.
Grandpa paused and looked at her a minute. “And why do you want to know what?” he asked.
“Oh, I don’t know,” she said. “Just curious, I guess. I’d like to compare the diameters of trees in the Wabash with the same trees elsewhere, and then maybe check the diameters against a few other things, like rainfall, to see if there’s a connection.” Samantha was sure Grandpa wouldn’t be able to produce trees from his pocket. She would have to venture into the forest to gather this information.
“Are you sure you’re ready?” Grandpa asked. He seemed to know more than he was letting on. Ready for what? Samantha thought. What kind of notes are you making in your book, she wondered. Grandpa himself didn’t venture out much. His bum leg — an old war injury, he said — held him back from real exploration.
Grandpa looked around for a minute. He gazed out at the forest, and then looked at his watch. “You’ll be back in a couple of hours?” he said.
“Sure,” Samantha said. “I’m just going to measure a few trees. Two hour tops.”
Grandpa consulted his notebook again, and then seemed satisfied. “Two hours tops, and you have to stay on the edges of the forest. Don’t go too far in. If you don’t come back in 2 hours, I’ll send in the cavalry for you,” Grandpa said.
He set the notebook down on the table and went to retrieve a few items for her diameter-measuring excursion. From the other room Grandpa asked if she had a compass or whistle. “How about a water bottle?” he asked. He returned after a few minutes with a fanny pack full of a few essential items — a compass, signal mirror, fire-starting kit, whistle, and a water bottle.
“Here you go, Sam,” Grandpa said. “Just in case.” Samantha adjusted the fanny pack around her waist and headed toward the forest. She did not tell Grandpa that, inside her shirt, without his knowing it, she had tucked away his special research notebook.