Happy St. Patrick’s Day to anyone who celebrates! (Any Irish followers out there?)
I recently got a job at Mathnasium, which is a US franchise that functions as a math tutoring center for kids who are both behind in math and passionate about the subject. As a teenager, I work with the youngest kids who come into the center, generally from 2nd-5th grade.
Most of the students I’ve worked with are struggling with their math classes at school, and I often have to work with them through problems of simple addition and subtraction. These are skills I internalized about 10-11 years ago, and are the most basic arithmetic taught to elementary school children.
Yet, when I work with a struggling child, it often eludes me how on Earth to teach them to add two numbers together. How do you explain the ideas of mental math to a child? How do you transition them from counting laboriously on fingers to recognizing simple facts like 7+7? One girl I work with has immense difficulty adding 10 to other numbers half the time, and half the time she knows instantly. How do I teach her, when sometimes she knows the material perfectly, and other times she appears completely lost in the sea of numbers swirling around in her head?
I’m learning techniques, of course- subtracting or adding ten, then adjusting from there- but it’s left quite an impression on me that I am sometimes incapable of transmitting the basics of arithmetic from my mind to that of a child.
This is a post about first impressions, and surely I’ll have a much deeper understanding of pedagogy as it relates to math in the coming months. Right now, all I can think about is how strange it is that there are people, albeit young people, who can look at an equation like 10+7 and be lost. That’s not to criticize these children, or make them inferior, or put myself on any kind of pedestal. Really, I just feel baffled: how is it that these equations come so automatically to us after only a year or two of practice? How is it that once I see 10+7, 17 immediately pops into my head? I literally cannot look at 10+7 without seeing 17 in my mind’s eye. The knowledge is just there, appearing before me, without even having to think about it.
The same applies to reading, of course. I cannot look at a word in English without immediately knowing what it is and thinking about it. There is no way for me to separate myself from the knowledge of English, no way to interpret letters as mere sketches without meaning and phonetic principles. Put me before a page of words and I am a slave to it. I will read it because that is what my eyes and brain do.
It is this quality of the human mind that amazes me so much, working with these children. In a relatively short amount of time, we go from conscious thinking about math and reading to an entirely unconscious process. We accumulate knowledge so deep in our minds that it is literally ingrained in us. Each of us carries in us the English language and the laws of mathematics, the names of famous people and the ability to match spoken language with objects and words. These bits of knowledge are just as much a part of us as our personalities and preferences, and perhaps even more so- they simply exist, unaltered, always immediate and full of meaning.
I know how often I end posts with messages of gratitude, but I truly feel so grateful to be so automatically receptive to thoughts, language, math, and people. People especially; we are so fortunate as a species to have a built-in ability to detect emotion and thought in other people (which is such a broad topic that I will not even begin to delve into it here). I’m constantly astounded that we as human beings have become such advanced creatures that to read, write, and listen to words requires nothing more than presence.
I hope the kids I work with internalize math in such a way that they may seamlessly match answers to their addition and subtraction problems, and I am confident that they will. In the meantime, it is fascinating to watch the processes which occur unconsciously for me happen consciously for them. It makes me realize how much is going on in my head every time I open a book, turn on the radio, or do something as simple as read my alarm clock every morning. The things that happen each instant in a human brain…