Month: June 2019

Exit 246. A memorial service for someone I didn’t know.

Today I attended a memorial service for someone I didn’t know.

Now, before you get creeped out, this isn’t some story about wedding crashing, except for funerals instead.  Do people do that?  It seems wrong.

The deceased was my pastor’s father.  I knew him in the sense that I saw him at church every week.  He wasn’t a stranger.  I said hi to him every week, and we exchanged pleasantries.

But at the service today, looking at pictures of him in childhood, in the Army, at his wedding, and with family, I realized that I never knew who he really was.  I only met him a couple years ago, late in his life, after Alzheimer’s disease had greatly affected his mind and his personality.

Please don’t wait until it’s too late to spend time with your loved ones and tell them how you feel.  Get to know the people around you before it’s too late.  I know there was nothing I could have done differently in this situation; it isn’t like I knew at some point in the past that there would be a man out there somewhere who would become part of my life later on, but he would have Alzheimer’s before I would meet him unless I did something about it.  I don’t have a time machine.

All of this kind of sounds like a cliche.  But it’s true.  And this isn’t the first time that someone passed before I got a chance to really know him, and that other time I could have done something about it.  In that case, it was someone I knew from dancing, who was well known in many of the partner dance communities in the area.  He was an innocent bystander in a drive-by shooting in 2012, and no suspect was ever caught, as far as I know.  We were acquaintances and surface-level friends, but I didn’t know him well.  Part of this was because his lifestyle was very different from mine.  Part of this was because another much closer friend of mine had a falling out with this guy before I knew either one of them, so I had heard stories about that guy colored by that perspective.  At his memorial service, I heard a lot of stories from people who had known him better than I had, and I realized that there were many sides to this man that I never knew or would have expected.

Of course, it’s hard to get to know everyone.  There are many people I cross paths with every day.  Some of them are toxic personalities that I’m better off not being in regular contact with.  But maybe there is someone out there whom I need to reach out to before it’s too late.  And maybe there’s someone like that for you too.  Until then, I can know that my pastor’s father is with Jesus, and someday I’ll see him again and get to know who he really is.

Exit 245. Intentionally written to be confusing.

Every few months, a meme circulates asking people to solve this math problem (or one like it):

6 ÷ 2(1 + 2)

People begin arguing over what the answer actually is, with most people saying (for this problem) either 1 or 9. They insult people with the other answer, because apparently that’s what people do on the Internet. And several of my friends tag me every time this goes around, either to resolve an argument or just to read what people are saying.

The correct answer is 9, but I’ll come back to that later. The issue is that this problem is intentionally written to be confusing.

I find the whole thing annoying. For one thing, this is something that we were supposed to learn somewhere around sixth grade. Apparently, we as teachers and educators aren’t doing our job if adults’ mathematics skills have atrophied to the point that no one can do a simple yet fundamental problem from sixth grade. So, naturally, everyone tags their friend with the college degree in mathematics (me) to resolve a sixth grade problem. I wonder, do these same people tag their friends with degrees in English when they forget to spell a word? Do they tag their friends with degrees in music theory when they don’t remember the name of a song? I’m writing this so that when this meme goes around again, I won’t have to type a long response; I can just share this link.

Anyway, Order of Operations says this (paraphrased, my own words): First, resolve expressions in parentheses and other grouping symbols. Then resolve exponents. Then evaluate multiplication and division from left to right. Then evaluate addition and subtraction from left to right. This was somewhat of an arbitrary distinction, but mathematicians and others in related fields have done it this way for centuries, and an organized set of rules needs to exist in order for most problems to have a well-defined solution (for example, whether you follow these rules or not determines whether the answer to the above problem is 9 or 1 or something else entirely). Math books and teachers often abbreviate this rule with the acronym “PEMDAS,” which stands for Parentheses, Exponents, Multiply and Divide, Add and Subtract.

So, the correct answer as written is 9, and this is why:

6 ÷ 2(1 + 2)
Do what is in parentheses first: 6 ÷ 2(3)
Multiply and divide from left to right. As you read from left to right, 6 divided by 2 comes first, and that equals 3, so now the problem is 3(3).
This equals 9.

There are several common incorrect interpretations of these rules which lead to the arguments. Before I continue, it should be pointed out that the disagreement has nothing to do with “Common Core” or “new math” or anything like that. The Common Core State Standards say nothing about changing the order of operations from what it has been for centuries.

Misinterpretation #1:

6 ÷ 2(1 + 2)
Do what is in parentheses first: 6 ÷ 2(3)
2(3) still has parentheses in it, so do it before the division: 6 ÷ 6
This equals 1.
The rule, and the fundamental concept of what parentheses are, is that what is INSIDE the parentheses is done first. Parentheses go AROUND the operation that needs to be done first (or out of order). The parentheses are not AROUND the multiplying by 2, so the fact that 2 is next to the parentheses has nothing to do with changing the usual order.

Misinterpretation #2: “I typed it into my calculator and it said 1.” Your calculator was programmed by a human being who apparently interpreted the rules differently from someone who got 9 as the answer. I have actually seen photographic evidence that some calculators give 1 as the answer and some give 9. Calculators will do whatever their users and programmers tell them to.

Misinterpretation #3: In my observations, this one is the most common. The issue here is a lack of understanding of the acronym PEMDAS:

6 ÷ 2(1 + 2)
P: Parentheses first: 6 ÷ 2(3)
E: there are no exponents.
M: Multiplication comes next, so do 2 times 3. 6 ÷ 6
D: Division comes next, and 6 divided by 6 is 1.
A, S: there is no addition or subtraction, so the problem is done, and the answer is 1.

As I explained above, multiplication and division are evaluated on the same step; it is not correct to evaluate all of the multiplication and then all of the division. Addition and subtraction work the same way. Evaluating all of the multiplication, then all of the division, then all of the addition, and finally all of the subtraction introduces other problems as well. Multiplication and division have to be evaluated on the same step, because every division can be changed to a multiplication using fractions (e.g., 6 divided by 2 is the same as 6 times ½). Addition and subtraction have to be evaluated on the same step, because every subtraction can be changed to an addition using negative numbers (e.g., 6 minus 4 is the same as 6 plus -4).

More than once, I have pointed out this error to people, and the response is something like “then my teacher/textbook/etc. taught it wrong, because I’m doing what I learned.” Now that is possible; I have seen teachers inadvertently teach incorrect subject matter. A more likely explanation, however, is that the person making this statement either never learned it properly or remembered it wrong. One who only remembers the acronym PEMDAS and what the letters stand for, with no context, would be very likely to make this error, because they follow the order of the letters. The rules for order of operations written as complete English sentences say something very different.

For this reason, I have often encouraged students to write “P-E-MD-AS” to emphasize that some of the operations have equal predence. I have also started to hear some students in middle school say that their elementary teachers told them not to just memorize “PEMDAS,” probably for this reason. And that is what good teachers should be doing, teaching students to understand rather than just memorize out of context.

Misinterpretation #4: “Multiplication without a times sign, just writing two numbers or letters next to each other, creates an ‘implied grouping,'” which would then make the work identical to misinterpretation #1 above. In a simpler example of this thinking, these people would say that “10 ÷ xy” would mean to divide 10 by whatever you get when you multiply x by y, instead of to follow PEMDAS strictly and divide 10 by x first, then multiply this answer by y.

I find this hardest to argue against. Although the order of operations rules say nothing of this implied grouping, it doesn’t always look right. I read “10 ÷ xy,” and my first thought would be to find out what xy is, and then divide 10 by this answer. This violates PEMDAS, but maybe it looks right because x and y are written more closely together. There is mathematical precedent for this implied grouping as well; to find the cosine of 3x, one usually writes “cos 3x,” and this is almost universally interpreted as the cosine of 3x, rather than whatever the cosine of 3 is, multiplied by x.

Ultimately, there is a simple solution to this issue of implied grouping: be like every mathematician ever, and every high school and college textbook, and don’t use the ÷ symbol in the first place. Many people don’t remember math beyond elementary school and buttons on a calculator, so they may have forgotten that in more advanced math, division is usually written as a fraction. So now, if division is written as a fraction, it can be made extremely clear which order of operations the author of the problem intended, and the so-called implied grouping becomes an expression within the numerator or denominator, which is grouped explicitly by the fraction bar.

And if you are typing instead of writing by hand, use an extra set of parentheses to make sure that your intended order is clear. In other words, even though the answer to the original problem is 9, it is written in a way as to be intentionally ambiguous. So stop arguing about it and do something more productive with your time.

Exit 244. Sunshine blogger award.

I had nothing to write about this week. Conveniently enough, Charlene at Curiosity & Confession nominated me for the Sunshine Blogger Award. Thank you! That means I get to answer a bunch of questions about myself, and then nominate people to answer different questions about themselves.  I know I’ve gotten nominated for a few of these before.  I don’t remember if I’ve done this exact one, but the questions are different every time, so it doesn’t matter.

  • Thank the blogger who nominated you.
  • Answer the 11 questions the blogger asked you.
  • Nominate new blogs to receive the award and write them 11 new questions.
  • List the rules and display the Sunshine Blogger Award in your post/or on your blog.
  • Notify the nominees about it by commenting on one of their blog posts.
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These are the questions I got from Charlene. There were 12 of them, even though there were supposed to be 11, so you get a bonus question.

Where do you get your news? Mostly from the website for the major newspaper in my area.

If your job gave you a surprise paid three days off, what would you do those three days? I’m a teacher, so I have long periods of not having to go to work on a regular basis. But if it happened unexpectedly, I’d spend at least one day sitting around the house being lazy and catching up on cleaning. And if my friends were doing anything spontaneous, I’d be a lot more likely to go along with it than I normally am on a weeknight. Maybe I’d take a day trip to eat at an In-N-Out Burger I’ve never been to before (I’ve been to 116 different locations). But anything more adventurous would require a lot of advance planning and mentally getting myself ready, not something I can handle in three days.

What is something that you resent paying for? Other people’s abortions, via my tax dollars. (Please don’t argue about abortion or politics in my comments. A question was asked, and I answered it.)

What is the most expensive thing you have broken? A few women’s hearts. I’m not good at having the conversation when someone is into me and I’m not really into them like that. However, I’ve been on the receiving end of those conversations far more often than the giving end.

What was cool when you were younger, but is not cool now? Vanilla Ice. When I was 14 years and 2 months old, he was the coolest thing I had ever seen. I had outgrown him and his music by the time I was 14 years and 3 months old.

What is something that no matter how evolved we become will always be popular? Breathing. Breathing has been in style since prehistoric times. Either that or the Rolling Stones, since they’ve already been popular for over half a century.

Who do you go out of your way to be nice to? Going out of my way to be nice is kind of my default. However, if you’re openly angry about how much you hate people with my beliefs and opinions, then I’m going to go out of my way to ignore you as much as possible.

Who was your craziest/ most interesting teacher? What grade did they teach? I’ve had a lot of crazy and interesting teachers.  And this is a hard one to answer, because I’ve had a lot of favorite teachers for reasons that “crazy” and “interesting” don’t describe.  (I could say that I’m my own craziest teacher, because I’m sure a lot of my students would say I’m crazy and interesting, but that’s a cop-out.)  The first one who comes to mind was my PE teacher in 9th grade, because of the nicknames he would give some students (for example, there was a kid who always wore a blue hoodie, not sure if it was gang related or not, but this teacher always called him “Little Blue Riding Hood”).  He also made up names for some of the activities we would play; the flag football class championship was called the Toilet Bowl, and when we would have to run two miles on the day before a long holiday, it was called the Turkey Trot (Thanksgiving), the Reindeer Romp (Christmas), and the Bunny Hop (spring break, which included Easter).  I think those are the right names.  I wrote more about him, including a hilarious quote, a few years ago when he passed away.

What are some red flags to watch out for in your daily life? People who say they care about you but are always too busy for you, especially if said people are significant others.

If you could move one character to play in a different movie, what character would it been and to what movie/show? Barry Goldberg on Beavis and Butthead. That could be interesting…
Barry: “And so I pass into Hyperspace, Maybe you can follow me
Where I will be starting my own rap colony”
Butthead: ” “Uhhhh… this guy sucks.”

What actor/actress plays the same role in almost every movie or show they do? Jack Black comes to mind. He’s really good at that one role.

What protagonist from book or movie would make the worst roommate or spouse? There was this one character, I don’t remember what movie he was from, where he would interrogate his roommate every time his roommate had a new woman in his life, and lecture him about Christian purity and how great it is not to kiss until your wedding day (the roommates were both adults, it should be pointed out). And sometimes he would wander around the house talking to himself about how messy and immature his roommate is (the roommate found out because the guy didn’t realize his roommate was home). He told his roommate on numerous occasions that he was immature and weak in his Christian faith because he played video games, and how he was wasting his time by having friends who weren’t Christians and not was actively trying to convert them. I can’t remember… what movie was that from?… oh wait, it wasn’t a movie, IT WAS REAL LIFE.

I don’t like nominating people for these, so if you want to be nominated, go ahead and do this. 🙂 And if you are nominated, leave a comment below so people can go check out your blog. The rest of you, go check out some new blogs in the comments.  Seriously, don’t forget that part, because that’s the point of these blog awards.

My questions for you:

  • What place would you most like to visit right now, if neither time nor money were a factor?
  • What is the farthest away from home you’ve ever been?
  • What is the longest you’ve ever waited in line, and what was it for?
  • What is the weirdest or most noteworthy story you have about how you met one of your friends?
  • What is something you liked to eat as a kid, but you don’t like anymore?
  • If you could bring back one discontinued product, what would it be?
  • What was your least favorite thing about school?
  • If you could change one law/rule/etc. that applies to you, what would it be?
  • Who is your celebrity crush?
  • If you could change your name, what would you change it to?  And if you like your name the way it is, why?
  • What’s that band/singer/musician that you’re a fan of, but you’re kind of embarrassed to admit it? Come on, everyone has one.