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Imaginary Numbers Is Where Math Lost Me. And Now I’m An Editor!

, , , , , , | Learning | March 22, 2024

My geometry teacher would offer what he called IOUs to students who answered difficult questions or otherwise impressed him. After we collected enough, we could trade them in for various perks such as removing the usual penalty that came with turning in homework late.

Pretty early in the year, he offered up a flawed postulate: “Multiplying a number by another number always results in a larger number.” He offered out IOUs to anyone who could disprove him. He got all the obvious answers from various kids: zero, negative numbers, decimals, etc. After they were all used up, I decided to try a shot in the dark for a second IOU.

Me: “I’m not sure if it works, but what about imaginary numbers?”

Teacher: “How do you know about imaginary numbers?”

Me: “Our science teacher rambled a lot last year. He told us he wouldn’t have trouble giving us negative points because he learned to do far more complicated math like imaginary numbers once.”

Teacher: “Do you know what imaginary numbers are?”

Me: “Not really, but would they make a number bigger?”

Teacher: “I don’t know if they would make it bigger or not, but I’ll give you an IOU just for thinking to try imaginary numbers.”

I got my coveted IOU, but I was still disappointed. This was a math teacher. How could a math teacher not know what happened to the size of a number if you multiplied it by another number? Math teachers should understand imaginary numbers, shouldn’t they? The fact that he wasn’t able to answer what should be such a simple question frustrated me so much that I set out to find out the answer myself.

First, I asked my sister, who was two years older and had learned about imaginary numbers already, but she couldn’t answer whether multiplying by one made a number bigger. I tried my mother, an accountant and presumed master in math, and she couldn’t answer me. I didn’t try my father as I knew his skills didn’t reside in math, but a week later, when my uncle came to eat out with us, I tried him. He was a smart programmer, and programmers were supposed to know math, right? He couldn’t tell me, either.

Every single adult I tried could not answer my question. Most of them seemed to not fully remember what imaginary numbers were. With each failed answer, I grew more frustrated, but also more committed to solving this conundrum once and for all.

Eventually, I gave up on asking adults and decided to research the question online. This was back when the Internet was new and search engines were abysmal, so it wasn’t as easy a feat as it would be today. I partially taught myself what imaginary numbers were by reading an online encyclopedia about them, though I was still confused about some things, such as why everyone insisted on charting them on graphs.

Finally, I thought I might understand the problem, so I caught my geometry teacher after class to verify if I was right.

Me: “Do imaginary numbers not have a size?”

Teacher: “What do you mean?”

Me: “Like, if you have a normal number and an i-number added together, you can’t combine them to get a single size from them?”

Teacher: “Not really. You can calculate a magnitude by treating the two parts as points on a plane and using Pythagorean’s theorem, but that’s not really the same as a size.”

I had no clue what he meant about calculating magnitude, but all I cared about was that he had confirmed that complex numbers didn’t have a size.

Me: “Why didn’t you say that the first time?!”

Teacher: “First time?”

Me: “When I asked if you could multiply a number by an imaginary number to make it smaller.”

Teacher: “Oh, that. I gave you the IOU so we wouldn’t have to discuss the various ways you could handle the size of a complex number.”

Me: “But you said you didn’t know what would happen!”

Teacher: “Have you been trying to figure out if imaginary numbers made things smaller for the last month?”

Me: “No one was able to tell me what would happen.”

Teacher: “You could have just asked me.”

Me: “You said you didn’t know!”

My teacher was clearly a bit amused by my frustration but trying to keep a straight face at that point.

Teacher: “And did you learn what imaginary numbers were in that time?”

Me: “Sort of.”

Teacher: “Well, what do you know?”

Me: “The ‘i’ means the square root of negative one, which shouldn’t exist, but if you keep it around as an ‘i’, you can still solve problems with it anyway. But there was a lot of other math for using it that I didn’t understand.”

Teacher: “There is lots of math using imaginary numbers that math majors in college don’t fully understand. You still learned about imaginary and complex numbers well enough to answer your own question. If you ask me, that’s impressive enough to be worth two IOUs. But next time, just ask me after class if you want to know something like that.”

I was then sent to run off to try to make gym class in time. I was still slightly frustrated that my teacher hadn’t just told me that from the start, but I admit that managing to earn not just one but two IOUs at once seemed an impressive enough feat to mostly appease me.

If You Could Grade Teachers, An F Would Be More Than She Deserves

, , , , , , , | Learning | March 21, 2024

A similar thing to this story happened to me in high school. It was highly annoying, and, to be honest, it still infuriates me thirty years later that anyone can be this ill-equipped for their job.

For whatever reason, my science teacher didn’t like me. Mostly, she seemed annoyed to meet me outside of school, and I get that she didn’t want to mix her work life and personal life, but it wasn’t my fault that her children’s daycare provider was my next-door neighbour. ([Teacher] lived one street over from us.) Thus, I met her or her children almost daily after school.

[Teacher] sucked at math. If we had a weekly test and I had 12 points on one page and 14 points on the other, she would add it together and conclude that my total point was 10 out of 26. It never made any sense. I would point out her error, and she’d tell me that she’d correct it in her notes and it wouldn’t affect my grade. Hah. Suuuuuuuuuure.

She never made these errors on other students’ tests, just mine. It was weird. Oh, well.

Then, we had the major exam for the semester. The day before, a Thursday, I was in massive pain and went to the school nurse, who sent me to the hospital, where I was booked for urgent surgery during said exam.

So, I went back to school to talk to [Teacher] as I had missed her class for the hospital visit.

Teacher: “Come straight after surgery to take your exam.”

I showed up on Friday, almost unconscious from the massive pain as the anesthesia from the surgery was fading off. [Teacher] just looked at me and told me:

Teacher: “Just take the exam during class on Monday.”

Me: “You could take my books to make sure I can’t study during the weekend.”

Teacher: “Go home.”

And she closed the door in my face.

[Teacher] was sick that Monday, but I still got to take the exam. And then, I fell ill and missed a couple of weeks, so when I finally was back in school, the grades were final. [Teacher] threw my exam at me. The score was mediocre, and I knew I had done better than that, so as she began berating me for my poor results, I quickly checked the test. Then, I heard her yammer about my poor results on our weekly exams. 

Darling, I have the weekly exams right here. Let’s take a look at them. Oh, yes, she hadn’t corrected her stupid errors and still had those abhorrent “results” she had somehow conjured up by failing first-grade math. And THIS exam? She had outdone herself.

As usual, she was unable to add two sums together (13 + 26 = 12), AND she had missed grading the major task, worth a whopping 25 points. I don’t remember the exact numbers, but I think her original result was that I had 21 out of 50, whilst the actual result was 49 out of 50. As I said, infuriating. She had given me a grade THREE STEPS below what I had actually achieved, and she told me that she couldn’t possibly change it nor raise it more than one step the next (and final) semester.

[Teacher]’s solution was that I was relieved from attending class. I could skip the entire semester and she would still raise my grade. She had effed up that badly. But I like school. I like to learn stuff. So, I attended class, did all the assignments, got top scores (she still never calculated the results correctly because she was a moron), and graduated with a grade two steps below what I had achieved.

Yup, I’m still pissed about that.

[Teacher] also had to start the semester by telling my extremely ambitious classmates that no one would be able to get top grades because I was the top student and I couldn’t get it, and thus, no one else could, either. They really hated me because of it — like it was my fault [Teacher] was such a moron. Oh, and she actually could raise grades more than one step as she did it for one of my classmates, so she was a LYING moron.

One of my priorities as a teacher was to make sure I NEVER missed grading anything. And that my calculations were correct. It is my duty as a teacher to ensure that the students get the grades they deserve.

There was no way for me to dispute my grade. As a teacher, I always make sure that the students know how to dispute grades, and if they want to dispute another teacher’s exam, I listen to their complaints and support them however possible. That only happened once, but it was not a pleasant battle. However, the students who asked for my assistance were students I was mentoring, so I was the obvious go-to person for help. In the case of [Teacher], this would have been an issue, because, well, [Teacher] WAS my mentor.

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The Dreadful Doodle Dilemma

, , , , , | Learning | March 20, 2024

One of the comments on this story reminded me of one of my teachers and his… distracted approach to teaching. He would talk to you about something you did that he didn’t like, you’d tell him why you did it and/or apologize, he’d agree with you, and then, he’d completely forget that the conversation ever happened.

For example, I liked doodling. It helped me focus, which was dearly needed because [Teacher]’s teaching style could be pretty boring. But every time he called on me in class, I could answer his question or at least explain why I didn’t know the answer, so it was obvious that I was actually listening, even if I wasn’t looking. Even then, I often raised my hand without him prompting me, and I always did most of the work in all group projects.

One day, [Teacher] asked all of us individually to come outside so he could talk with us about our grades, especially how we behaved during class and how much we participated.

Teacher: “Sorry, I can only give you a C.”

That’s eight points, for the German readers.

Teacher: “You are not paying enough attention.”

Me: “But I am.”

Teacher: “No, you’re doodling the whole time. It doesn’t look like you’re listening to anything I say.”

Me: “But… I am? I can answer your questions every time. Doodling actually helps me listen and focus. I’m sorry if it seems like I’m ignoring you, but I promise you, I’m not. You can test me if you want.”

As if he hadn’t been doing that already…

Teacher: “Well, okay. I think I understand what you mean. I’ll definitely keep it in mind.”

A couple of months later, he talked to us again about our participation grade. I had tried to look more attentive, and I was sure that I’d get a better grade. But alas…

Teacher: “I’m sorry, but it’s just a C again. I thought you wanted to improve?”

Me: “I… have improved. I thought I had.”

Teacher: “You’re still doodling!”

Me: “But I told you why, and you said you understood. And I still participate, answer questions, and do every task you give to us, most of the time even faster than the rest of the class.”

Teacher: “Sorry, but you really need to stop being distracted.”

The best part is that he taught “pedagogy”, which is not very common in Germany. In our case, it was basically how kids learn and how to best educate them and stuff like that. None of us ever found out how he got to teach this specific class, but it couldn’t have been his amazing skills or understanding nature.

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Computers Are Cool, But They Don’t Know Everything (Nor Do Teachers)

, , , , , , , , | Learning | March 9, 2024

As part of a career change, I once took an online university course. When I got a paper back from the instructor, I was dismayed to see several grammar and spelling errors indicated. In my existing career, I’m a language professional and have been for twenty years, so I was puzzled by this to say the least.

On closer inspection, it turned out that the instructor had accepted all of the suggested “corrections” from Microsoft Word, marking them as though each had represented an actual error. Of course, they hadn’t, given how the spelling and grammar check works: the corrections are merely suggested, and it’s up to the user to decide whether the change makes sense or not.

In fact, in some cases accepting the suggested change introduced an error. For example, it corrected “assuming that” to “if” in a sentence, for “concision”. But I wasn’t using “assuming that” to mean “if”; I was literally referring to the act of assuming (e.g. “Client-centered care can include not assuming that the therapist understands the client’s background,” etc.), so replacing it by “if” made the sentence gibberish.

Never mind, of course, that I had obviously typed the thing in Word, so I had seen all the same suggested corrections she had and decided that they weren’t appropriate. 

It’s hard to describe how personally and professionally indignant I felt about this, especially because she had docked me marks for each of these “corrections” and left a little comment about “paying more attention” to spelling and grammar!

I still got above a ninety (out of 100) on both the paper and the course, so I decided it wasn’t worth the hassle to complain about, but it still rankles me.

Dad Really Didn’t Make The Grade On Parenting

, , , , , , | Learning | March 8, 2024

Around twenty years ago, my parents were looking to sell their home as we were moving abroad. There was one middle-aged couple who looked at the house. The wife seemed interested but the husband not so much. During this time, my parents mentioned that I was due to do my GCSEs (General Certificate of Secondary Education exams) very soon. The gentleman said he was a secondary school teacher and proceeded to tell us a rather unbelievable story about a previous student of his.

Several years ago, he had a student in his class who was extremely smart and capable but made next to no effort to apply himself. This was partly because his father was very vocally anti-school, and during many parent-teacher evenings, he had been vocal about what a waste of time this whole thing was and that his son should be out in the world working, not wasting time learning. Sadly, his son had taken the advice to heart, and despite being very capable and producing some good work, he still believed his dad was right.

Come GCSE time, they noticed that for the first exam, [Student] was not present! They immediately called him, and his father answered. It’s been twenty years since I heard this story, so my memory is a little fuzzy, but it went something like this.

Father: “Hello?”

Teacher: “Hello, Mr. [Father], It’s Mr. [Teacher] at [School].”

Father: “What the f*** do you want?”

Teacher: “Can you tell where [Student] is today?”

Father: “He’s on holiday with his mother! “

Teacher: “Sir… why is he on holiday? His GCSEs started today. He missed an exam this morning!”

Father: “So?”

Teacher: “Sir, he is not supposed to be absent. These exams are extremely important!”

Father: “Well, we’ve had this holiday planned for ages. It’s not our fault you idiots scheduled these exams at the same time!”

Teacher: “Mr. [Father], he cannot miss these exams. These are vital for his future plans—”

Father: *Interrupting* “Oh, so bloody what?! School never did nothing for me, and it won’t do nothing for him, either! The whole thing is just a f****** waste of time! I left school with nothing, and I turned out all right! He’s not coming back from holiday, and that’s final!”

Teacher: “This is his future we are talking about. It’s a very different society from when you left school. Having zero qualifications is going to affect him! He needs to do his exams!”

Father: “He knows his a**ehole from his elbow. That’s more than you idiots know! Now f*** off and don’t call again!” *Click* 

Sadly, the gentleman never heard what happened to [Student] in later years. He failed all his exams as he never showed up. The gentleman only hoped that [Student] wised up a little and was able to have a good future.

I appreciate that school isn’t for everyone, but to try and deliberately ruin your kid’s future is pretty awful!