6 ms·

You have what appears to me a bias against teachers. I find this curious given one of your products. I personally think that bingo is a worthless activity but

You have what appears to me a bias against teachers. I find this curious given one of your products. I personally think that bingo is a worthless activity but I don't thrust this opinion on other teachers. Personalities come into play with teaching. I could never make a bingo activity work in my class because it is antithetical to my personality. But some people do make it work. And with 30 people in a class is it reasonable to believe that all 30 will enjoy the activity or find merit in it? I sometimes hide knowledge from my students because I want them to see it for themselves. Do you know how hard it is to get someone to understand that -4^2 is -16 and not 16? I can say this fact ad nauseam and it just doesn't click until a person sees it. They have to be guided into understanding this. Me telling them it is so and explaining it doesn't work. At any rate it seems you have a bias against teachers. Have you taught much? When was the last time you were in a classroom?

JacobAldridge 15y ago
Wait - I thought -4^2 was 16 not -16. But then the 2^3^4 discussion here lost me as well.
- m_myers 15y ago
  -4^2 is -16. (-4)^2 is 16.
- jhurliman 15y ago
  Order of operations. -4^2 is equivalent to -(4^2).
  - aaronblohowiak 15y ago
    heehee, programmer's error. -4 is assumed to be the value, and not seen as -1 * 4, which i believe is the interpretation. order of operations is a useless source of confusion -- we should just use parens always and avoid ambiguity. #toomuchcprogramminglately
    - patio11 15y ago
      I tend to agree, and always did explicit parens for that sort of thing. Then again I use parens in ruby code, too, so maybe I just like them a little too much. You could argue from consistency that the standard convention is more aesthetically appealing, though. I tried writing this in a HN post but it boiled my brain so I sketched it on the back of an envelope instead. http://images2.bingocardcreator.com/blog-images/hn/arithmetic-consistency.jpg http://images2.bingocardcreator.com/blog-images/hn/arithmeti... Basically, assume high school algebra works the way you think it works. If we treat unary negation like it magically grabs the nearest integer prior to the exponent happening, things we assume are equal in high school algebra start to break catastrophically. You'd have to invent a new and perhaps uglier way to do algebra which would lose properties like "moving terms around the same side of an equation on paper for clarity is allowed because it doesn't change what they sum to." Anyhow, if this ever comes up in my household, I'm going with "Yeah, that one's weird. Your dad didn't like it either, but convention is that -2^2 is -4. That's totally separate from math, it's just how we choose to represent math in squiggles, and this collection of squiggles is supposed to be read as -1 * (2^2) instead of (-1 * 2)^2 . Why did we pick that math-to-squiggles mapping? Long story and kind of boring, but it's sort of important that everyone read the squiggles the same way, for the same reason that we don't get into an argument over which side of a road should be called 'left' and then smash our cars into each other. Either way would have been a perfectly good 'left' because left is ultimately just squiggles, but now we're stuck with one of the squiggles."
      - aaronblohowiak 15y ago
        At the risk of getting off in the weeds, I'd rather re-frame the problem here as to wether unary negation makes sense as an operation, at all! In my ideal world, -EXPR would be a parse error, and it would only be valid to write -LITERAL * expr. (-1 * a.) So, you could have -4^2 is 16 because the - would not associate to the nearest constant, but rather be part of the 4-value. The reason for this is that -a^2 is super confusing, and I believe it should be treated as invalid. I do not think that promoting the order of precedence of unary - is the best solution because it leads to the common confusion of thinking "well, a is already negative, so there is nothing to do". if instead this was explicitly -1 * a ^ 2, then you can always "plug and chug" with simpler rules. Essentially, the confusion is because unary negation is the only operation that is confuse-able with the value definition. Final qualm against unary negation: what does --4 evaluate to in ruby? 3? No. 4. If I had my way, then --4 would clearly be invalid because the inner -4 could not receive the unary negation. In more programming stuff, I think that mixed-type operations should be illegal (no implicit casts!) adding an int64 to an int32 and storing the result in an int32 should be a compiler error!
patio11 15y ago
I am occasionally critical of every profession I've ever been a member of, including software developers (get me started on how well we understand the typical user someday), salarymen (get me started on... anything), translator (get me started on professional ethics), research assistant (get me started on code quality in an academic setting), and while I don't have a specific complaint about "seasonal order entry operator" if you give me a minute I can probably come up with one. I'm not even a very negative person -- I actually like teaching quite a lot. If it isn't obvious, pick a different set of two comments from me to generalize from and you'd assume that I'm a rabid fanatic about it. Do you really want to play the "you're only allowed to have opinions on pedagogy if you're a real teacher" game?
- yequalsx 15y ago
  The bias I perceive in you is not based solely on two comments you've made. It's just two comments that I've responded to. I'm not playing "you're only allowed to have opinions on pedagogy if you're a real teacher" game as you put it. Anyone is allowed to have opinions about anything. Some opinions have more merit than others. Some people have worthy opinions on topics that they don't have direct involved with. I've met lots of people with strong opinions on teaching. I've found that what superficially seems obvious to non-teachers often times miserably fails when you've got a class of 30 students with varying abilities and interest in learning. Anecdotally I'd say a majority of opinions from non-teachers about what would be great in the classroom only holds true if the classroom contains people desiring to learn. Well, I asked about your experience in the classroom because I wanted to know if the thoughts and ideas you've expressed about what is not useful in the classroom is based on your teaching experiences on your student experiences. I used to have strong feelings about k-12 teaching. Two years ago I was in a project that paired a college teacher with an 8th grade teacher at a local school. It took one day in the 8th grade class to realize that I don't know squat about k-12 teaching.
  - patio11 15y ago
    In that case, most of my teaching experience was at the K-12 level, in small groups and classes of 25 through 40. Some in a classroom, some outside. I also tutored college students for a bit. Many kids wanted to learn, some not so much. Your turn. Do your opinions come from actual experience or do you have a bias against elementary schoolteachers?
tptacek 15y ago
This is the second time in 2 weeks someone has chimed in on an HN thread to change a discussion from "something involving education" to "whether Patrick McKenzie has a bias against teachers". If you disagree with a thought someone expresses on HN, address a comment to the thought. Redirecting the discussion towards the motives of the commenters isn't simply uncivil; it's boring. No. Worse. Hygroscopically boring. It sucks all the juice out of the whole thread. I am partly irritated by this because I know Patrick does not have a vendetta against teachers. I am partly irritated because I know the "bias" Patrick is displaying here is a hacker trope: if you interviewed 100 hackers, 95 of them would say the same thing about secondary education. But I'm mostly irritated because it's a clear example of a superficial argument. "Hacker vs. teachers". Who could possibly care? He's not biased against teaching... but if he was, so what? In what sense would the thread possibly be different?
- yequalsx 15y ago
  He makes a product geared toward teachers. He made a comment about busywork in the classroom and, what appeared to me, to be against this and against activities that hold brighter students back. I find it interesting because using bingo cards in the classroom can easily fall into this category. My comment addressed this apparent disparity. There was nothing uncivil about making an inquiry into this. It's too bad you don't see something interesting in this. I do and hence made the comment I made. I strongly disagree with your view that my post was inappropriate or should not have been made. I'm not planning to change.
  - tptacek 15y ago
    You don't appear to understand how Bingo Card Creator works. Go visit the website. I'll wait. Back? Did you notice, on the website, the near total absence of advocacy for using bingo cards in lesson plans? Or even how classroom bingo works? Patrick sells BCC passively. His entire marketing system presumes a continuous feed of people who already wanted bingo cards. The pain point he solves isn't "how to automate classrooms with bingo cards". It's "how to automate the bingo cards for your classroom bingo day". There's exactly one argument you can make about Patrick's business that would even be germane to your argument: that classroom bingo is so radioactively evil that simply enabling teachers to do it is harmful. I don't think you believe that. Instead: you didn't like something someone said on a message board, so you went looking for reasons to discredit them. In this case, you failed. You should have more confidence in your own opinions. You have actual K-12 educational experience; it should be easy for you to use actual logic to refute things people say about it.
blacksmythe 15y ago
>> Have you taught much? When was the last time you were in a classroom? I have spend at least 20 years in classrooms as a student. I think this qualifies me to have an opinion on what teaching methods I found effective, and observed to be effective with others. I don't believe that having been a teacher is a requirement in order to have come to valid conclusions.
- yequalsx 15y ago
  It qualifies you to have a worthy opinion about what works for you. Are you sure that what works for you scales well? I don't remember much of day to day activities in elementary school. I did go to elementary school. But I don't think my opinions on elementary school teaching necessarily are accurate even when applied only to myself as a youngster. One doesn't have to be a teacher to come to valid conclusions. I think though that most conclusions that don't include an acknowledgement of the importance of the teacher's personality coupled with students' personalities is most likely not valid.
  - blacksmythe 15y ago
    >> One doesn't have to be a teacher to come to valid conclusions. I apologize if I misunderstood you, but your previous post gave the impression that that is precisely what you thought. >> Have you taught much? When was the last time you were in a classroom?
droithomme 15y ago
I must say your chosen example is a bit poor since the precedence of unary negation vis a vis the binary exponent operator is arbitrary and varies according to the arbitrarily selected rule system selected for the task at hand. Promoting one arbitrary choice over all others as if it is natural, obvious and correct is clearly the source of difficulties explaining to students. When I have taught this topic, I cover precedence rules as being arbitrary and show a chart of the rule system in play for western math textbooks. This clears up confusion, or rather prevents it from occurring in the first place.
- yequalsx 15y ago
  "This clears up confusion, or rather prevents it from occurring in the first place." Not in my experience and I venture to guess that you haven't taught developmental learners. Obviously one discusses the order of operations and the fact that the order is arbitrary. This does not prevent confusion from occurring in developmental learners.
  - droithomme 15y ago
    I don't know about these "developmental learners". I've taught students in college, high school, and elementary school. Mostly bright kids in elementary, and a wide range of skill levels in high school and college. Your responses to others here consistently dismiss others' personal experiences and knowledge while touting yourself as the only reliable expert. Frankly your responses here to others are so argumentative and belligerent I'm having a hard time imagining you're really such an expert in the things you claim.
    - yequalsx 15y ago
      You are incorrectly interpreting what I've written if you think it has been belligerent. I'm not an expert and have not claimed to be an expert. I do have extensive experience with developmental learners of mathematics. Think adults who are innumerate. I did preface my response to you with, "not in my experience". It is not a valid conclusion to say that my remarks have been belittling. Based on what you wrote above it looks like my guess that you haven't had much experience with developmental learners appears to be correct. I stated my experience was different than yours. What is there to be upset about?

JacobAldridge 15y ago

Wait - I thought -4^2 was 16 not -16. But then the 2^3^4 discussion here lost me as well.

m_myers 15y ago
-4^2 is -16. (-4)^2 is 16.
jhurliman 15y ago
Order of operations. -4^2 is equivalent to -(4^2).
- aaronblohowiak 15y ago
  heehee, programmer's error. -4 is assumed to be the value, and not seen as -1 * 4, which i believe is the interpretation. order of operations is a useless source of confusion -- we should just use parens always and avoid ambiguity. #toomuchcprogramminglately
  - patio11 15y ago
    I tend to agree, and always did explicit parens for that sort of thing. Then again I use parens in ruby code, too, so maybe I just like them a little too much. You could argue from consistency that the standard convention is more aesthetically appealing, though. I tried writing this in a HN post but it boiled my brain so I sketched it on the back of an envelope instead. http://images2.bingocardcreator.com/blog-images/hn/arithmetic-consistency.jpg http://images2.bingocardcreator.com/blog-images/hn/arithmeti... Basically, assume high school algebra works the way you think it works. If we treat unary negation like it magically grabs the nearest integer prior to the exponent happening, things we assume are equal in high school algebra start to break catastrophically. You'd have to invent a new and perhaps uglier way to do algebra which would lose properties like "moving terms around the same side of an equation on paper for clarity is allowed because it doesn't change what they sum to." Anyhow, if this ever comes up in my household, I'm going with "Yeah, that one's weird. Your dad didn't like it either, but convention is that -2^2 is -4. That's totally separate from math, it's just how we choose to represent math in squiggles, and this collection of squiggles is supposed to be read as -1 * (2^2) instead of (-1 * 2)^2 . Why did we pick that math-to-squiggles mapping? Long story and kind of boring, but it's sort of important that everyone read the squiggles the same way, for the same reason that we don't get into an argument over which side of a road should be called 'left' and then smash our cars into each other. Either way would have been a perfectly good 'left' because left is ultimately just squiggles, but now we're stuck with one of the squiggles."
    - aaronblohowiak 15y ago
      At the risk of getting off in the weeds, I'd rather re-frame the problem here as to wether unary negation makes sense as an operation, at all! In my ideal world, -EXPR would be a parse error, and it would only be valid to write -LITERAL * expr. (-1 * a.) So, you could have -4^2 is 16 because the - would not associate to the nearest constant, but rather be part of the 4-value. The reason for this is that -a^2 is super confusing, and I believe it should be treated as invalid. I do not think that promoting the order of precedence of unary - is the best solution because it leads to the common confusion of thinking "well, a is already negative, so there is nothing to do". if instead this was explicitly -1 * a ^ 2, then you can always "plug and chug" with simpler rules. Essentially, the confusion is because unary negation is the only operation that is confuse-able with the value definition. Final qualm against unary negation: what does --4 evaluate to in ruby? 3? No. 4. If I had my way, then --4 would clearly be invalid because the inner -4 could not receive the unary negation. In more programming stuff, I think that mixed-type operations should be illegal (no implicit casts!) adding an int64 to an int32 and storing the result in an int32 should be a compiler error!

patio11 15y ago

I am occasionally critical of every profession I've ever been a member of, including software developers (get me started on how well we understand the typical user someday), salarymen (get me started on... anything), translator (get me started on professional ethics), research assistant (get me started on code quality in an academic setting), and while I don't have a specific complaint about "seasonal order entry operator" if you give me a minute I can probably come up with one. I'm not even a very negative person -- I actually like teaching quite a lot. If it isn't obvious, pick a different set of two comments from me to generalize from and you'd assume that I'm a rabid fanatic about it. Do you really want to play the "you're only allowed to have opinions on pedagogy if you're a real teacher" game?

yequalsx 15y ago
The bias I perceive in you is not based solely on two comments you've made. It's just two comments that I've responded to. I'm not playing "you're only allowed to have opinions on pedagogy if you're a real teacher" game as you put it. Anyone is allowed to have opinions about anything. Some opinions have more merit than others. Some people have worthy opinions on topics that they don't have direct involved with. I've met lots of people with strong opinions on teaching. I've found that what superficially seems obvious to non-teachers often times miserably fails when you've got a class of 30 students with varying abilities and interest in learning. Anecdotally I'd say a majority of opinions from non-teachers about what would be great in the classroom only holds true if the classroom contains people desiring to learn. Well, I asked about your experience in the classroom because I wanted to know if the thoughts and ideas you've expressed about what is not useful in the classroom is based on your teaching experiences on your student experiences. I used to have strong feelings about k-12 teaching. Two years ago I was in a project that paired a college teacher with an 8th grade teacher at a local school. It took one day in the 8th grade class to realize that I don't know squat about k-12 teaching.
- patio11 15y ago
  In that case, most of my teaching experience was at the K-12 level, in small groups and classes of 25 through 40. Some in a classroom, some outside. I also tutored college students for a bit. Many kids wanted to learn, some not so much. Your turn. Do your opinions come from actual experience or do you have a bias against elementary schoolteachers?

tptacek 15y ago

This is the second time in 2 weeks someone has chimed in on an HN thread to change a discussion from "something involving education" to "whether Patrick McKenzie has a bias against teachers". If you disagree with a thought someone expresses on HN, address a comment to the thought. Redirecting the discussion towards the motives of the commenters isn't simply uncivil; it's boring. No. Worse. Hygroscopically boring. It sucks all the juice out of the whole thread. I am partly irritated by this because I know Patrick does not have a vendetta against teachers. I am partly irritated because I know the "bias" Patrick is displaying here is a hacker trope: if you interviewed 100 hackers, 95 of them would say the same thing about secondary education. But I'm mostly irritated because it's a clear example of a superficial argument. "Hacker vs. teachers". Who could possibly care? He's not biased against teaching... but if he was, so what? In what sense would the thread possibly be different?

yequalsx 15y ago
He makes a product geared toward teachers. He made a comment about busywork in the classroom and, what appeared to me, to be against this and against activities that hold brighter students back. I find it interesting because using bingo cards in the classroom can easily fall into this category. My comment addressed this apparent disparity. There was nothing uncivil about making an inquiry into this. It's too bad you don't see something interesting in this. I do and hence made the comment I made. I strongly disagree with your view that my post was inappropriate or should not have been made. I'm not planning to change.
- tptacek 15y ago
  You don't appear to understand how Bingo Card Creator works. Go visit the website. I'll wait. Back? Did you notice, on the website, the near total absence of advocacy for using bingo cards in lesson plans? Or even how classroom bingo works? Patrick sells BCC passively. His entire marketing system presumes a continuous feed of people who already wanted bingo cards. The pain point he solves isn't "how to automate classrooms with bingo cards". It's "how to automate the bingo cards for your classroom bingo day". There's exactly one argument you can make about Patrick's business that would even be germane to your argument: that classroom bingo is so radioactively evil that simply enabling teachers to do it is harmful. I don't think you believe that. Instead: you didn't like something someone said on a message board, so you went looking for reasons to discredit them. In this case, you failed. You should have more confidence in your own opinions. You have actual K-12 educational experience; it should be easy for you to use actual logic to refute things people say about it.

blacksmythe 15y ago

>> Have you taught much? When was the last time you were in a classroom? I have spend at least 20 years in classrooms as a student. I think this qualifies me to have an opinion on what teaching methods I found effective, and observed to be effective with others. I don't believe that having been a teacher is a requirement in order to have come to valid conclusions.

yequalsx 15y ago
It qualifies you to have a worthy opinion about what works for you. Are you sure that what works for you scales well? I don't remember much of day to day activities in elementary school. I did go to elementary school. But I don't think my opinions on elementary school teaching necessarily are accurate even when applied only to myself as a youngster. One doesn't have to be a teacher to come to valid conclusions. I think though that most conclusions that don't include an acknowledgement of the importance of the teacher's personality coupled with students' personalities is most likely not valid.
- blacksmythe 15y ago
  >> One doesn't have to be a teacher to come to valid conclusions. I apologize if I misunderstood you, but your previous post gave the impression that that is precisely what you thought. >> Have you taught much? When was the last time you were in a classroom?

droithomme 15y ago

I must say your chosen example is a bit poor since the precedence of unary negation vis a vis the binary exponent operator is arbitrary and varies according to the arbitrarily selected rule system selected for the task at hand. Promoting one arbitrary choice over all others as if it is natural, obvious and correct is clearly the source of difficulties explaining to students. When I have taught this topic, I cover precedence rules as being arbitrary and show a chart of the rule system in play for western math textbooks. This clears up confusion, or rather prevents it from occurring in the first place.

yequalsx 15y ago
"This clears up confusion, or rather prevents it from occurring in the first place." Not in my experience and I venture to guess that you haven't taught developmental learners. Obviously one discusses the order of operations and the fact that the order is arbitrary. This does not prevent confusion from occurring in developmental learners.
- droithomme 15y ago
  I don't know about these "developmental learners". I've taught students in college, high school, and elementary school. Mostly bright kids in elementary, and a wide range of skill levels in high school and college. Your responses to others here consistently dismiss others' personal experiences and knowledge while touting yourself as the only reliable expert. Frankly your responses here to others are so argumentative and belligerent I'm having a hard time imagining you're really such an expert in the things you claim.
  - yequalsx 15y ago
    You are incorrectly interpreting what I've written if you think it has been belligerent. I'm not an expert and have not claimed to be an expert. I do have extensive experience with developmental learners of mathematics. Think adults who are innumerate. I did preface my response to you with, "not in my experience". It is not a valid conclusion to say that my remarks have been belittling. Based on what you wrote above it looks like my guess that you haven't had much experience with developmental learners appears to be correct. I stated my experience was different than yours. What is there to be upset about?