Part 1: when it all began
Homeschooled at a young age, one of the most effective learning methods for me is to learn ahead of many peers, like going over the concepts, formulas, and practice questions for high school math before going to high school.(would elaborate on this method in another article later)
This method is particular useful as it allows me to make mistakes, remember that, correct the mistakes made, and eventually learn from them.
Thus, when the school has end-of-semester exams—ministry exams that I do take while being homeschooled, most of the math questions are already types I’ve encountered and reflected on or remembered (yes, a great way to make people think you’re smart even though it’s just hard work)
So the fun memory I’m going to share today is a bit related to the above mentioned method—just in case people question why I was doing exponents in primary school
Part 2: what started it
Yes, exponents.
It all started with this famous story: Once upon a time, there was a king and his trusted advisor. The king’s advisor helped him a lot, so the king said he would grant him a wish as award for his work. The advisor replied that he only wanted some grains, but they have to be placed in a certain order: as there are 64 squares/places on a chess board (totally unrelated, but I personally find that people who like math seem to like chess a lot too), he said that he would like 2 grains in the first square, 2*2 grains in the second, 2*2*2 grains in the third, and so on.
The king tried to fulfill his promise, but from what I remember, he did not succeed
I was curious, how could it be possible that a king, with all the riches of a whole kingdom, cannot even get some grains to fill a chessboard… in my mind, it wasn’t that big of a number, so I thought it’d be cool to prove that the king just wants to go back on his own promise.
And of course, the easiest way to prove that was to find how many grains he’ll need for the 64th square on the chessboard
Part 3: what actually happened, not much really
I can’t remember the exact age I was at back then (already in primary school and definitely before grade 3 though), because I’d just learned multiplication a little while ago
Homeschooled means I had time, lots of time, to focus on one single question. In my daily life then, aside from poetry and ancient Chinese, some sports and English novels, I was totally free.
And one thing in my personality has been my tenacity (should probably relate on that part later too)—once started, I’ve always been stubborn to get things finished; if interested by a game or rule or something, I’d be sure to learn or master it with passion; when obstacles occur as they often do, I use means that looks to be contradictory to stubbornness, adaptivity and creativity, to reach my goals.
In this case, no creativity was needed though
It was just multiplication, the ones you write vertically instead of horizontally, as pictured.
It was just a week or so of time needed, not much when you really think about it.
And it just took about a dozen notebooks, of the horizontal multiplications.
The result was super long, even after all these years, I still remember it started with 18……(just double-checked while writing this article, seems like I should be congratulating my childhood self for accuracy)
After that week, I stopped doubting the king’s wallet, and was instead, shocked by the advisor’s avarice and ‘courage’ (look, imagine what happens if the king decides he doesn’t want to owe any living human being…)
However, I was even more shocked to learn that this huge number I discovered, could be written as easily as three simple ones: 2^64.
Part 4: fun memory, what to get out of it
So the question comes, as always, at the end of every article, what’s the purpose? What did I learn? What can I use from this?
Sure, that kings are not all-powerful, can’t even fulfill a promise; that the numerical answer of 2^64=18…(something); It is true that I discovered the symbol of exponents and started my interest in them, making the next steps of math learning fun and memorable.
Yet as a teacher, I feel it’s not just that, all the above answers are correct, and all are important.
But in my own teaching, I find that the time and process is very valuable, especially in terms of the discovery moment, the sensation of « wow, I found this », the realization that « ohh, so this is how… »
These feelings entwine, and in term, inspire students’ self-confidence in their academic ability and interest in the subject area. It turns passive learners into proactive ones, and leads to the question: how can we, as teachers, make our class activities creative enough to attract student interest, plan our lessons/units/semesters in a way that guides students to that discovery moment, and with effective management, stay in alignment with the provincial curriculum and ensure students' academic fulfilment
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