Miranda was a tutor for high school students. She loved working one on one with adolescents and there is no greater high, she thought, than watching the light bulb go off in the mind and eyes of a student. Today Miranda worked with two very different students and each was a real joy. First there was Ralph, very bright and quick with math, but doing it on his own without a classroom environment. Miranda watched as Ralph looked over the marked papers she had returned to him. “Any questions, Ralph,” Miranda asked.
“You said this proof was brilliant–I want to go back and look at that and see why you liked it,” said Ralph.
“Sure thing,” answered Miranda. “There are frequently multiple approaches that can be taken to solve a geometry problem and that is what makes them such fun, or so I think.”
“Yeah, I like that also,” answered Ralph, “but this seemed very easy. What was different about my approach?”
“You took it beyond what you had to do,” answered Miranda. “You didn’t just quote the theorem you’d been given in this chapter. You actually proved the theorem in your solution, and believe me, not many would do that!”
Ralph beamed! He really liked working with Miranda because she had a way of always making you feel good about yourself. “Ok,” said Ralph, “but what about this one–did I goof?”
Miranda smiled as she prepared her answer. “You didn’t goof really, but you made an assumption which turns out to be true, but which you did intuitively, making a major shall we call it ‘leap of faith.’ In geometry you need to take it step by step and even though you know something is true, you have to prove it step by step using the building blocks you have. Once something is proven, then it becomes another building block to be used down the line.”
Ralph nodded, and then looked more closely at the corrections Miranda had put in. All of a sudden his face lit up and he said, “Got it! I needed two more steps in here, didn’t I.”
Miranda congratulated him just as the bell rang for lunch and off Ralph went, happy and excited.
Later in the day Miranda tutored Steve, and while Steve and Ralph had a lot in common, both high school juniors, both really sweet boys, both really smart, Steve was a writer and a poet, and he struggled with math. It wasn’t that he didn’t work at it. He did, in fact he worked very hard, but he just couldn’t grasp the abstract concepts of math for more than a few seconds at a time. But today, when Steve arrived, he exclaimed, “Hey, guess what! I got 100% on my matrices math quiz! I like matrices!”
Miranda grinned and said “Way to go, Steve! That is fantastic!”
The two of them then settled down to work on today’s homework and sure enough, as long as things stayed with matrices and numbers, Steve got everything perfect. When it moved into solving for variables, Steve was lost again. But Miranda refused to let that get him down.
“Steve, you can do this. What steps do we set up to solve an equation? What do you do first?” Miranda asked.
Pretty soon Steve answered, “I get this a little. I think I understand. Let’s try another just to be sure.”
By the end of the session Steve left, confident, and feeling good about what he had learned. As he went through the door he commented, “Sure is more fun when it actually comes together and makes sense!”
Miranda smiled and answered, “Yes, it is, for sure! And you have come a long way since your freshman year! Good work! See you next week.”
Miranda was tired after her long day, but her encounters with Ralph and Steve made it all worthwhile.