Misleading graphs

[Myriad]

Ignore the brighter students, if they're bright and interested enough then they'll push each other and themselves forward. Focus your energy on those who actually need your help, ie the ones who struggle with it.

In my 3rd and 4th year (in Belgium high school is 6 years, 1st to 6th, and for every pair of years you get to choose increasing specialization) I had a math teacher who had this "everyone must go at the speed of the slowest" thing. It felt like being forced to solve mind-numbing things like "1 + 1" and "1 + 2" over and over and over again, it almost destroyed my interest in math altogether.

Then in 5th and 6th year I had a different math teacher (who was also more mathematically inclined, probably given that she taught the math specialization class). After about two weeks into the 5th year I had read the full textbooks for that year so I was getting bored again. So I started immediately shouting the right answer to every question she asked (someone in) the class. By that time she was annoying me by forcing me to participate so I started annoying her. After a bit of this she put me in her 6th year class instead.

Somewhat later she gave in to my refusal to make my homework as well. I had explained that it was a mindnumbing waste of time (it was always of the sort of "solve these integrals" or "solve these equations" etc, something a computer could do just as well) but she didn't go along with that at first, but at least she wasn't putting me in detention all the time for refusing, like that previous teacher did.

One time homework consisted of solving a bunch of integrals, which I of course didn't do, and which she had noticed I didn't do. So she wrote the most difficult one on the blackboard and then called me to show my solution. Normally in those situations the guy who sat next to me would just give me his homework and the teacher wouldn't know, but he had been unable to solve that particular one. So I was in a bit of a problematic situation, so I got up from my chair and started walking towards the blackboard, trying to solve that integral in my head. After a couple of steps the teacher said "well you obviously didn't make your homework again, did you?" to which I replied "wait, I didn't get to the blackboard yet." A couple of steps further I saw the solution, so I smiled, increased my pace, and wrote the solution on the blackboard. After which she said "fine, you win, you don't have to make your homework."

After a couple of weeks in the 6th year class I had fully read the textbooks for that year as well, after which I didn't have to participate at all anymore (this actually took another round of annoying her by immediately shouting the answer to every question she asked the class). In the end I spent the last 3 years of highschool (I had to do the 6th year twice) being 8 hours per week out of 32 (I picked maximum math specialization, hence 8/32 hours) completely free to do whatever I wanted (just as long as I didn't bother her teaching the rest of the class). She even put a computer with Mathematica on it in class just for me to experiment with.

My point is, trying to teach everyone at the same level is a fool's errand. See who it is you're actually helping and who it is you're actually holding back, and put your energy into those who actually need your help and just ignore the ones who you're holding back.

I'm impressed by your talent (I find solving integrals quite difficult, despite it often being a mechanical process).

But, if you wanted the teacher to just ignore you, why did you show off by shouting out the answers? And of course she didn't ignore you; she made concessions and provided you with special educational equipment. Your earlier boredom and frustration that you expressed by not doing the homework and by shouting out the answers suggests that you would have found it preferable had she made those adjustments sooner.

Your own story shows that "just ignore" is not an adequate recipe for dealing with the more advanced students.

 

[caveman1917]

I'm impressed by your talent (I find solving integrals quite difficult, despite it often being a mechanical process).

There was a good amount of luck involved there as well. It usually would've taken me more time than the couple of seconds required to walk to the blackboard. And they were highschool integrals, not exactly trivial (there were some trig functions and such in there) but not advanced either.

But, if you wanted the teacher to just ignore you, why did you show off by shouting out the answers?

Because she didn't ignore me at first. She still went like "open your textbooks on page whatever" and went round the class and such, forcing me to participate in that. Hence I wasn't free to do what I wanted.

And of course she didn't ignore you; she made concessions and provided you with special educational equipment.

I mean ignore as in "not forced to participate in the lessons in class". The concessions were all, from my perspective, so as to stop me being forced to participate in a particular (intellectual) activity. And yes, she didn't ignore me, for example when I proved some theorem she'd check the proof etc. But I was free to do whatever I wanted (I didn't have to use that computer for example, just whenever I thought it was useful for whatever I was doing I'd get up and go sit at it and use it). I read a lot of Marxist works during those classes as well, for example.

Your earlier boredom and frustration that you expressed by not doing the homework and by shouting out the answers suggests that you would have found it preferable had she made those adjustments sooner.

Well duh. But she didn't.

Your own story shows that "just ignore" is not an adequate recipe for dealing with the more advanced students.

I can't speak for any other students of course, but for me, yes it was.

 

[Minoosh]

I'm looking at the "post-test" which students are supposed to take for data-gathering purposes (even though there was no "pre-test," so no baseline has been established). Teaching to that test offers another interpretation of what the actual "curriculum" is. But IMO that test is a mess. It does not align with *anything*. Just another avenue to paralyze myself. I don't think it's for a grade, and I don't think students' performance is going to be used against me, but I can be very literal-minded. And that test is all over the place:
piecewise functions, translations to quadratic functions, an inordinate number of questions on complex numbers, exponential functions, solving systems of equations in three variables ... if I try to teach to that test, I'll lose everyone. I'm not sure I'm even meant to cover all that stuff in the next 5-6 weeks. Many students won't have the vocabulary to even understand what is being asked of them.

I hate giving students a test that is simply going to make them feel ignorant.

And there is almost nothing on this test that will do them any good for testing into college algebra. Nothing that they really need to know in life. But they are used to taking absurd tests; it may be there biggest takeaway from their high school careers. I probably need to just put my head down, settle on a realistic sequencing scheme and then toward the end coach them on test-taking strategies. It seems to be my call as to what I'll actually teach, my call on how easy or difficult to make the tests and quizzes and my call on their final grades, as long as it's based on quantitative data.

If I get caught up on my gradebook, come up with a general game plan for the week and a specific plan for tomorrow I'll be in OK shape to start the week. But that post-test. Grrrr.

 

[Minoosh]

And most teachers in HS math/science classes will probably just roll their eyes and say welcome to the club. But it's a disservice to students, IMO. They'd probably be better off with a heavy emphasis on basic skills that they need to break down some of these problems, and a crash course on vocabulary so they understand what's being asked. The post-test is almost completely abstract, nothing much related to concrete situations they can relate to.

Believe it or not I hate to complain, and in a way it just gets me more wound up.