I think professor/youtuber Po-Shen Loh is extremely clear when he explains math problems, using the perfect combination of intuition and logic, by that I mean no redundant information and sparking synapses in students' minds, active thinking is a effective way of learning because it connects to other previously built connections and remaining relevant in the mind.
It's entirely cool how Po-Shen Loh has a handfull of shortcuts here and there, and more intuitive prospectives! As a superficial example, we normally think of solving systems of two equations by adding up the two equations, divide algebraically. Po-Shen Loh translates this as taking "the average", one variable has opposite signs and gets averaged to zero, the other gets added twice so we just find the averages of the numbers! This is a much time saving explaination for beginning students of algebra to give the realization branches of math is indeed connected.
It's also amazing how concisely the divisibility by 8 rule is explained, let me try to explain it (in feeble attempts to practice logic).
We know that 1000 is divisible by 8 (1000 = 125 * 8), and adding another eight to 1000 is still divisible to 8, so why bother taking redundant information, just only look at the sum of the last 3 digits. this is like setting your stopwatch to zero at 1000. If we examine the hundreds, we notice 200 is divisible by 8. (200 = 25 * 8), and for any multiple of 200 meaning an even hundred, we set our counter to zero again. We ignore the hundreds as we did with the thousands. This way, we only need to consider two digits. Much faster for timed math competitions.
Even for non timed math practice this is a clearer perspective. Practice optimization, fellow geeks, if you have trouble managing time, I guess you could make the radical move of joining a excessive amount of clubs(that you also love), see how your week changes, and focus like crazy on homework. This sets the habit of entering flow state quickly, and when clubs are over, hopefully you would've gained personalized strategies for managing time and time would seem more rewarding - principle of scarity.
YOU ARE READING
Unending hypotheses (2020)
Non-FictionSome of my hypotheses on subjectivity, perfectionism, thinking skills etc. Mostly unedited. For fiction, please see "Unending experiments" Written in grade 9/10 days.
