Parallel lines do meet at infinity
While doing some geometry homework one day, my daughter asked, parallel lines don’t ever touch right, daddy? “Correct. Except at the point of infinity.” Then her brain exploded. What followed was an interesting discussion about what infinity is. What is definable and knowable. What is indefinable and what might be knowable in the future. I told her that more than three thousand years ago, people used to tell time by looking at the shadow they cast on a sunny day. That’s why the sundial was invented. Our relationship with time is much more advanced now. And in another three thousand years, we might even have the technology to explore unknown facets at the point of infinity itself.
She resumed her homework with renewed rigor knowing that sometimes, it’s easier to reframe the problem using real world experiences. It helped her significantly to know that the Pythagorean Theorem is just a fancy way of describing whether daddy’s ladder will reach the roof. By using different examples and situations that a child can relate, it can make math much more relevant to students.
The math class in my daughter’s school is fortunate enough to have a flexible curricula and to have faculty who looks for new ways to engage the student rather than just teaching the standard approach. In two simple examples, students in her school can tell time from an analog clock (there are kids who can’t!) and can easily recall the times table without too much trauma.
Bringing common sense to common problems demystifies mathematics. In effect, kids learn to use math to solve problems, rather than spending time solving math problems.
In addition to creative ways of teaching age old topics, the educators also show students to disregard irrelevant information. For example, the arrival time of a given length of a train travelling through a tunnel of fixed length at a particular speed is not impacted by the temperature of the day. All things being equal, the train’s arrival time will be the same whether it is sunny or not or whether there are four carriages or five. Bringing common sense to common problems demystifies mathematics. In effect, kids learn to use math to solve problems, rather than spending time solving math problems.
If nothing else, math helps the young mind to focus only on the important variables of concern; everything else is superfluous. I don’t want my daughter to be just tied down to the technicalities of finding a precise answer—not at this age. She’s learning to learn; she’s not attempting solve math’s toughest problems. And if she gets the wrong answer, then it could be one of two other reasons than not understanding the problem: not considering all the information or considering irrelevant information. But if we only teach based on whether she gets an answer right or wrong, then she’s taught that lessons must fall into only two categories.
Mathematics is merely an analytical method of describing what she already perceives: the natural world. It’s important to remember that math isn’t just about solving an equation. It’s about finding multiple solutions to problems. As in life, math sometimes may yield an indeterminate answer. And nothing in that statement is wrong.
