How Anime Changed My Perspective On Math

Fractions…Were you good at them growing up? I certainly wasn’t, especially dividing them. I never understood the concept of dividing one part of a whole with another part of a whole – and the further I tried to comprehend it, the further I would fall into an abyss of confusion. Many years passed since elementary school and I have gone about much more complex problems than the simple division of fractions (ironic, right?). I have come to realise that, even now, I often struggle to figure out the ‘why’ behind solving fractions and just stick to the by-heart method taught to divide them. 

The good thing that came out of this struggle was the fact that I realised I wasn’t alone. When I first watched the Studio Ghibli masterpiece, Only Yesterday, and saw that a young woman – Taeko – was also recounting her struggles on dividing fractions when she was a kid, I finally felt recognized.

Image courtesy of Studio Ghibli

One poignant scene in the film left an everlasting impression on me. It was when Taeko remembered coming home from school one day after she had gotten a ‘D’ on her test about fractions. Apart from her entire family being incredibly disappointed in her, they even managed to call her “abnormal”. When her older sister was assigned the duty of teaching her how to divide fractions, Taeko took the example of an apple to illustrate the perplexities of dividing ⅔ by ¼ . Her older sister was baffled by the question and failed to answer it; instead like many others, Taeko was taught to memorise the steps when solving questions on dividing fractions. 

Image courtesy of Canva (Fractions through apples)

This singular scene is what reignited my, previously dead, inquisitiveness regarding math. I had now come to the conclusion that fractions was a concept that confused kids and adults alike, but why? Was there something deeper causing this universal perplexity? Interestingly, Taeko's bewilderment wasn’t just a personal experience – it is a well-documented phenomenon in math education. A study done by Frontiers in Psychology discusses the whole numbers bias. According to the study, children who are not yet familiar with the idea of fractions assume that the rules of whole numbers are applicable to rational numbers as well. This leads to confusion in conceptualizing whole numbers as decomposable units (Gabriel et al., 2013). In addition, the research paper, along with another study from the European Journal of Social & Behavioural Sciences, points out that children have difficulties when learning fractions due their widening gap between conceptual and procedural knowledge. The current educational system focuses on procedural knowledge – leading to techniques like rote memorization when solving math problems. This fundamental error in understanding carries over when solving more complex operations, such as multiplying and dividing fractions (Singh et al., 2021). All of this makes perfect sense to me now – my disconnect between logic behind the ‘why’ and methodology when solving questions is what led me to detest fractions growing up. Nowadays, I enjoy learning tricky mathematical concepts. Although the process may feel like a dead end, and often times take a lot of work to reap even the tiniest of results, nothing can beat the internal sense of satisfaction after cracking a difficult concept.

My attempt at visually explaining the mind-boggling division of ⅔ by ¼:

Using an apple to visualize 2/3 divided by 1/4

The absurdity about math is that one day you’re able to comprehend all that’s going on and the  next day, you are back at square one. These boulders in the way are what bring out the beauty in math, and I have come to appreciate its tough love. Through this often infuriating process, we come to learn a lot about ourselves and how we think – this journey of self-discovery is something people spend decades trying to figure out, math might just get you one step closer; and prove incredibly handy when faced with challenges. 

Now, to the Curious Quirks out there, I urge you all to ask questions. The silliest, most dumb and childish questions you can think of – because when times get tough, these blatant questions might just lead you to the answer you are looking for.

Final Thoughts: Like I learnt from Taeko, even the most complex ideas can be simmered down into simpler notions. 

So, can you figure out how to visualize fractions?