I took notice that our 5⅔-year-old was using the word ‘half’ and the word ‘part’ interchangeably and decided that the time had come to set her straight on the matter. She’s quite bright and loves learning new concepts so it wasn’t at all challenging to pique her curiosity. However, she hadn’t yet encountered fractions so, for simplicity’s sake, I suggested that we should consider only the even numbers, which she knows about. On a piece of paper, we wrote down 2, 4, 6, and 8. And then:
2 = _ + _ 4 = _ + _ 6 = _ + _ 8 = _ + _
Unsurprisingly, she caught on quickly. After filling in the blanks together, I drew a circle for each of the four equations: one circle divided into two, one divided into four, and so on. How many slices do we need for half of a circle if there are eight slices? Four! What if there are six slices, like in this circle? Three! And over here, with four slices? Two! Wonderful! Good job! You’ve got it.
I also drew a 5th circle and divided it into two unequal pieces – one noticeably larger than the other. See? Here we have two pieces – but these are not halves. You can say that these are parts of the circle, or sections of the circle, but it would be inaccurate to call them ‘halves’. Do you know why? Because they’re not the same size? Exactly!
At that point, I decided to push the lesson a bit further. After all, she had just recently crossed the threshold from 5½ to 5⅔, right? My intention was to show her that the twelve months of the year (which she knows) could be divided into half (6) and also into thirds (4), thereby explaining why I had just recently started calling her a 5⅔-year-old.
So I began by explaining that we would first write down the number 3, and then add another 3 for the next number, which she said should be 6. And then? 9? Yep. And then? 12! After we’d written those numbers down, I jotted down:
3 = _ + _ + _ 6 = _ + _ + _ 9 = _ + _ + _ 12 = _ + _ + _
At this point, she began to noticeably tune out due to mental exertion. We managed to fill in the equations, but by the time I had drawn four circles (for 3, 6, 9, and 12) and divided them into the corresponding numbers of slices, I realized that I was pretty much doing the math exercise on my own. Then, even when I attempted to close out the activity by reinforcing that two 1’s gives us 2, whereas three 1’s give us 3, meaning that 1 is both ½ of 2 and ⅓ of 3, her mind had already wandered, and she was off to another activity.
I’m pretty sure that she still doesn’t understand what one-third is.
* * *
I enjoy speaking, writing, reading, typing, watching movies, and playing various word and story games with my daughter. We are raising a trilingual child, and I am both fascinated by and very proud of her language development. It’s incredibly rewarding for me to know that I am shaping her development and giving her an invaluable gift in this way. Never before have I been so invested in any project.
As it happens, I have an engineering degree, but most of what I learned back in college has long since faded from my memory banks for lack of any application. To the extent that I am good at math, it’s almost entirely due to the comfort with numbers that Papa inculcated in me from a very young age, and, of course, I wasn’t the only son who benefited from his tutelage. My brother, not long after Papa died, reflected upon his appreciation that Papa had been around to help him with his university math studies, which led him to receive a minor in mathematics.
My wife and I can both teach our daughter essential math skills, and I can even pass down many of the same math tricks that Papa once taught me, but… math isn’t enjoyable for me and it doesn’t come naturally. I’d rather be teaching her to write poetry. I’d rather be… I’d rather be… teaching her about mythical creatures of legends native to various world cultures. Perhaps some of those same colorful, magical creatures were good at mathematics themselves, but it has never excited me.
* * *
Not so long ago, on the 2nd anniversary of Papa’s death, I lit a 24 hour memorial candle in his memory. Lighting such a yahrzeit candle is a universal Jewish custom but not a requirement of religious law. Many people also light yahrzeit candles on those Jewish holidays when we traditionally recite the Yizkor prayer for our deceased loved ones, including Yom Kippur and Shemini Atzeret, both of which we celebrated just recently. I did not attend communal prayer services at shul for the holidays (COVID-19 is my excuse), and so I did not recite the Yizkor prayer, but I did light candles on all of the holidays… even including the recent holiday of Sukkot, which has no associated memorial prayers for the dead.
I’ve been attracted to candles and to fire for longer than I remember, but I never made a point of lighting them until the time came to commemorate my Papa, and, unexpectedly, I found it comforting.
Now, I don’t put much stock in belief in the supernatural. I believe that it is possible (and even likely) that some supernatural, omnipotent Force exists that created everything… but that’s about the extent of it. If somebody somehow proved that such a Force doesn’t exist (which I don’t believe to be possible), this wouldn’t be particularly disconcerting to me. It’s okay with me if God’s existence is disproven because I don’t believe that God or any other supernatural Force actually cares about us.
Still, the candle flame does excite my imagination in how it licks at the air around it. It’s soothing to imagine my Papa’s neshamah flickering in its flame, and I’m hardly the first human being to relate emotionally to fire as a living thing. In fact, as I now write about this, I find myself stirred to write some poetry about it… perhaps I’ll do that later. [addendum: here’s the poem I wrote later]
And so I’ve taken it upon myself to light a yahrzeit candle for Papa every Friday evening before Shabbat starts. For me, this has nothing to do with religious obligation, nor anything to do with faith. Rather, it’s simply comforting. It feels nice to spend a minute focused on remembering Papa. It feels nice to wake up on Saturday morning and see his candle still burning.
Of course, if I continue lighting a candle every week, I suppose I’ll have to come up with something else to do for Papa’s yahrzeit… but, unlike math, imagination has always been my strong suit.