A viral post on social media from an upset parent uploading his child’s assignment read: “make it make sense.” The problem on the associated picture asked the student to “make 10 while adding 8 and 5.” The student replied, “you cannot; the answer is 13,” and was marked as incorrect. The student is correct that 8+5=13, but this is not what the question was asking.
The question, given out of context in this post, was asking the student to perform a mental trick many clever students naturally intuit. (8+2)+3=13 or just as correct (5+5)+3=13. The trick is to reduce problems into more manageable chunks, which greatly assists doing more difficult calculations than 8+5. It also helps students view numbers as a more fluid object. 8 isn’t just 8, it’s 2 groups of 4, it’s 6 and 2, it’s 5 and 3, it’s . One of the most important identities in all of physics is rewriting 1 as 1=-e^ipi.
My explanation of this was poorly received by some. One commentor claimed you’re just overcomplicating things. Something like, “what is 8*9” is something you should just DO. How does one calculate 8*9 if they don’t already know the answer? The comments were filled with students who are very proud they excelled in the 3rd grade and managed to memorize their multiplication tables. Much like the original parent, they were upset that they were being asked to think about a problem they knew the answer to. Of course, the way to calculate this problem is not difficult, its sampling adding up 9 groups of 8. The “make ten” trick is useful here. 10 groups of 8 is easy to count, even if you don’t fully grasp multiplication. If you understand that 10 groups of 8 is 80, and that 9 groups of 8 is simply one group of 8 fewer, then the math is 80-8=72. This reduces nearly every problem down to something that can be done on your fingers.
As you learn this skill on problems you already know the answer to you can be confident in your answer, and your ability to implement the process for more difficult problems. What is 492*8? Using the same skills, we can break this down as (500*8)-(8*8)=4000-64=3936. Memorizing your times tables is not required to perform any multiplication, although it does help you save time. The purpose of this exercise to help students better understand the relation of numbers, to calculate problems more quickly, and to show some level of understanding beyond rote memory. If these tricks don’t make sense to you, or you don’t feel it’s worth changing the way you already perform these problems, that’s fine, but I was interested in a common response to these posts: “Just do it.”
Many responses seemed confused by question, “If I don’t already know the answer what is 8*9?” The most common response was, “but I do know the answer…” followed by a less than complimentary comment about my intelligence. This question is asking people to think about why their answer is correct. For these posters, math is simply memorizing answers to all possible combinations of numbers. They never learned the process, or they never really thought about it much. They don’t care about the process or what can be learned by studying it. They want the answer to the problem, nothing more.
This follows a broader trend. Spend any time listening to political debates or conversations and you’ll notice something right away. People who have never met nor interacted before are saying the exact same thing, often word for word. Once you start to hear it, you can’t stop hearing it. Millions of people speaking with a voice that is not their own. Ask them to explain what the phrases mean, most can’t beyond the superficial. Ask them why what they’re saying is good. Most can’t. They are using answers they were told were correct, and they thought no more on the matter.
Dionysus was the Greek god of alcohol, chaos, and actors. Just as the spirits (alcohol) inhabit us and change our personalities, so too does the actor take on a new persona and speaks with someone else’s words. This connection hints at the ancient world’s view of actors. In the social stack they were below prostitutes, who also let their body be used by others. There is an inherent degradation of the self in allowing your body to be used in such a way.
Richard Dawkins called religion, “virus of the mind.” An atheist and pragmatist he could not understand why religion was so readily accepted when it required, or so he thought, the abandonment of reason. I very much disagree with Dawkins’ contention that reason and faith are antithetical. However, he was correct in identifying why so many accept religion. It does fill a need, that need for certainty, that need for an answer. Christianity’s retreat from daily life has left a vacuum, an unfilled need. In its place something far worse is taking root.
Progressive’s new religion (which I outline in my essay The Progress of Virtue) offers its adherents a moral and ethical certainty that was being unmet. How should one act in the world? What is the purpose of life? What is the role of men and women in society? These are eternal questions that demand answers every generation. Traditional religions had thousands of years to pull evidence from for their answers. The progressive religion is trying to start from scratch. Wisdom of the ages replaced with the wisdom of the age.
Socrates simply asked people to explain their reasons for things. The citizens of Athens found this so annoying they put him to death. Socrates said, “the unexamined life is not worth living,” they executed him. It is an unnatural thing to challenge our own assumptions. Appeal to a higher authority is simply easier. Surly they, being a higher authority, must have done their due diligence to arrive at the correct answer. A serious problem emerges when you no longer believe in a higher power and also believe hierarchy is inherently evil. Where does one find these answers then? Provide a source during an online argument and see how much ground that wins.
The modern answer seems to be some variation of “my truth.” Like most modern theories it is centered around the self as a near blameless and faultless being. “My experience must be representative of the human condition, and so I can answer these eternal questions.” More often than not this ends up being an exercise in self-validating whatever choices the individual has made. For what it’s worth, 30% of Americans have been diagnosed with depression, and the nation’s suicide rate of 14 per 100K is a historic high.
A society that is both unwilling to examine its own beliefs and is confused about authority is not going to last in the long run. Take the time and examine what you believe. Really ask yourself why you think this is true. If you find yourself relying on someone else’s authority on the matter, question the legitimacy of that authority, vet it. You’ll likely find dozens of beliefs you don’t actually think are correct. Practice only saying things you truly believe. Speak only in your voice. An unexamined life is not worth living.
I’m 58 and I vividly remember multiplication sheets (and timed tests). I’m not a math guy but I still recall most single digit multiplication readily. That said, this “new” method is really eye-opening. Would have been a nice additional arrow in the quiver.