Experiencing True Inquiry:
Things Lost & Locked up in my “Question Box”
In parallel with my fight against fractions, I was also fighting against another formidable foe called ZERO. My teacher asked, “What is 4 minus 6?” I knew that the correct answer that the teacher was looking for was “minus 2”. But I didn’t want to give that to the teacher because I thought that what the “correct” answer was would depend on the context in which the question was being asked. For example, I could not subtract 6 apples from 4 apples. In this case, 4 minus 6 would be zero. As it can be imagined, my teacher thought I was being deliberately obstinate to disrupt the lesson. My sense of justice was greatly injured because I believed I was right in my reasoning.
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In other words, I understood zero to mean “nothing” and had a very hard time thinking in other terms. Thankfully, my Mum stepped in by guiding me to the idea that ZERO does not necessarily signify “nothing” but it is a point of reference in some cases. I was finally able to wrap my head around this concept after she drew a thermometer and showed me how the temperature change which was the equivalent of 4 – 6 can be represented on a paper. She pointed out how temperature did not disappear when it hit ZERO but the point where ZERO “sat” showed an important point of reference within a particular measurement system.
Despite my triumph over ZERO, I never did manage to concur fractions. So after crying in frustration for a week and realizing that I just couldn’t get the whys and the hows of fractions, I reasoned with myself that I still had to find a way to go forward. My solution? Put this kind of big questions in my mind’s “question box” and lock it up. I was a “smart” kid. Manipulation of formulas and memorization of mechanics (“plugging things in”) were easy for me. I could do that, I thought. I could “solve” all the problems and I would get hanamaru (literal translation is “a flower circle”) – this was what teachers put on students’ exam papers when they got a 100%.
When I started reading Jo Boaler’s book, I just couldn’t put the book down because she was talking about 9-year old me and giving a voice to the feelings that I could not quite describe myself. I started to wonder and examine just how many questions I locked up in my “question box” just so that I could successfully navigate through the school system. What kind of unnatural behaviours and thinking patterns did I develop in order to survive an educational system that did not value critical thinking skills and problem solving strategies? How did I adapt to the reality that students’ success was entirely dependent on their ability to memorize facts? Well, I survived by developing my ability to memorize facts. I am not saying that ability to memorize is useless because it does come in handy whenever you might not wish to whip out your mobile to fact-check. I believe that there are some elements of recognizing patterns and making connections when you are trying to memorize seemingly random pieces of information. The issue that I have with memorization is that when it is valued out of proportion, it stifles practices of inquiry, penalizes curiosity and inquisitiveness, and eradicates whys and the hows out of our lives.
Jo Boaler (2015) is quite right in her argument that “the standardized questions test language as much as they do mathematics” (p. 88) and “the best thing that multiple-choice tests show is a student’s ability to complete multiple-choice tests” (p. 86). It is quite interesting that she mentions this because on my college entrance examination in Japan, I scored 80% in math because when I realized that I could not figure out how to go about solving the final geometry problem, I “measured” my answer with a protractor instead of solving the problem. The problem involved calculating one of the internal angles of a triangle, which was partially overlaid on a circle. I was vaguely aware that trigonometry (the concept I never understood) was involved somehow. This was the last complex problem on the exam sheet and I had just about 10 minutes left on the clock to solve this problem. Knowing that I was running out of time, I made a calculated (pun intended) decision that the remaining time was better spent reviewing all the other questions one last time than tackling and most likely failing to correctly answer this last question. I thought that I had a 25% chance of getting the answer right and I could probably increase the probability by actually measuring the internal angle of the said triangle on the exam sheet with a protractor. The measurement was 60 degrees and 60 degrees was one of the options on the answer sheet, so I marked out this option as my answer, which turned out to be correct! I cheated the system. I did not have to show how I solved the problem, so I landed on the correct answer by deducing that if there was a diagram on the exam sheet, it was usually to scale. In a way, my language and literacy skills were what helped me “solve” the problem.
At present, I am starting to slowly unlock my “question box”. For example, when a thunderstorm hit, instead of compartmentalizing the phenomenon as a change in weather, I let my mind wander for once, which prompted me to ask my “science” spouse (I am the “arts” partner), “how does lightening occur?” My spouse gave me a crash course explaining how electrons behave and how they create currents (my spouse is an electrical engineer – this is his speciality) but he also got stuck trying to explain how air gets “charged” in the first place. After whipping out our respective mobile phones, we have discovered that this question is still somewhat of a mystery even to scientists. When you start asking questions, the world seems to be a lot more magical place than when you thought you had it all figured out.
References:
Boaler, Jo. (2015) What’s Math Got To Do With It? (Rev. ed.). New York, NY: Penguin Books.