Murphy set a few questions to test Hermione Granger's and Tom's mathematical abilities. As expected, both were roughly at the level of an ordinary fourth- or fifth-grader. Tom was slightly better, but he was still only at an elementary-school level.
Even that put them among the best children in Britain. If Harry and Ron Weasley had been there, they probably would have gotten even multiplication with numbers under ten wrong.
"You two will need to brush up on your mathematics. At the very least, you need to understand some simple analytical tools," Murphy said. "Quantification is the first step in research. Without it, it's very difficult to analyze anything in depth."
Hermione felt a little stung. She rarely disappointed a teacher academically. "But, Professor, we haven't even finished learning some of the simple spells yet. Isn't it too early to start researching advanced magic...?"
This was how many of the young witches and wizards felt. After all, having first- and second-year children conduct magical research was decidedly strange.
"I'm not asking you to achieve any particular results," Murphy said. "But I hope that, by exploring the unknown, you can learn how to approach understanding and researching magic, rather than simply repeating what others say and following textbooks by rote."
That was also why Murphy had chosen to teach children in their first through fourth years, while leaving those in fifth year and above entirely alone.
Children who had studied magic at Hogwarts for four or five years were already accustomed to the school's spoon-fed approach to education. Their ways of thinking were probably set by then, and changing them would be too much trouble.
"All right, you two, come over here."
As he spoke, Murphy led the two children over to a stand.
It was a tripod with a wand