What a nightmare you have described here! That teacher is an excellent example of one who will surely turn students off from mathematics. And she promotes bad attitudes about mathematics by penalizing preciseness and stressing memorization and following her directions for approaching problems over understanding and creativity. She seems to fail to recognize that any method is correct as long as it can be shown to be mathematically valid (though this logic alone does not tell us which of two or more methods is "best"). She also seems to fail to see that mathematics is supposed to be about finding patterns and classifying mathematical objects (among other things) because she wants the students to see all these area formulas as having no relationship with each other.
I applaud your son for using basic formulas and logic for finding the area of polygons instead of appealing to a memorized formula (though the latter is not wrong per se nor necessarily bad in itself but does become a bad sign when the student has little or no clue as to where the formula comes from or when the student prefers memorization over understanding and logic). I see far too many students in my college classes who would rather memorize and use formulas than use logic. I would tell your son that he thinks a lot more like a mathematician ought to think than his teacher does and that the "math" his teacher promotes is phony and helps no one to learn a darn thing.
I do find this story to be ironic in several ways:
1. This teacher is very precise on how students show work. She goes way too far in this direction. Most teachers make the mistake of taking the other extreme: not requiring students to show any work at all. In fact, those teachers often use just multiple-choice exams or other exams in which they look at just the "final" answers to grade them. I recognize many of my own students who most likely have had teachers like that because they gripe that I ask them to show some of their work in discussions or other assignments. Others gripe that they got the "correct answer" but had lost points for an error or significant gap in their reasoning or a computational error (but for some odd reason still managed to get the "correct answer"): "I got the right answer, didn't I? So how come I didn't get full credit?"
2. Though you didn't explictly say so, I suspect that this teacher is more attentive to grammar and spelling and other aspects of English usage than most math teachers are. In fact, most math teachers seem to ignore English usage entirely or almost entirely so that students end up thinking that grammar and spelling and English usage plays no role in a math class. And I believe that is one reason why my students are sloppy with such matters in discussions--in fact, "sloppy" is putting it lightly; their English is bad enough that many of my college students' posts look like their third grade kids wrote them! And I swear that students' spelling is getting worse over time because I have noticed significantly more spelling errors in recent terms than I did early last year and in previous years.
Some students are so bad with writing that they struggle to write even one coherent sentence. However, at least most of them can be understood (except in many cases of severe vagueness), but the grammar and spelling is still bad enough that they pass themselves off as kids instead of as adults. I now recall seeing a message the other night from a student that I could not answer because I could not figure out what she said; not only was she vague, but her writing was quite incoherent. I do wonder how many of them manage to get jobs because I'm sure that if they wrote their resumes and job applications using the same garbage they use in class, their materials would be trashed immediately because employers would question if a child and not an adult had written them.
In short, it is a shame that many math teachers teach math in ways they had learned it and cannot seem to recognize any other ways to teach math. According to them, the way they were taught to do that problem is the only right way to do it.
--- In firstname.lastname@example.org, "Julie Living Math" <julie@...> wrote: > > Busywork projects are common enough unfortunately in my daughter's class. > The last one was a Pi Day project. It could have been a decent project but > the grading was far more geared toward dotting i's and crossing t's, so > there was no learning. > > The grading has so much to do with how students approach a project. She had > a scaling project a couple months ago. She was docked points because she did > her measurements including fractions, so when she converted the scale, she > had long decimal numbers that she rounded off one place too short; never > mind the fact that I had her do the project in such a way that she actually > learned something, and it should have been obvious to the teacher that real, > substantive work was put into it above and beyond what was required. Had she > used sloppy, rounded measurements, the conversions would have been simple > and she wouldn't have been docked, so her reality is that being thorough > cost her a grade, and this isn't the first time. This is the same teacher > that just marked a diligently completed, carefully labeled homework > assignment down a full 25% for the sole reason she stapled two sections > separately and turned them in, rather than staple the two sections together. > She's paranoid now about how she labels, formats and packages her homework > because the cost of a tiny misstep is so steep. When she had a stock market > project, she had a great deal of anxiety about whether she could generate > her graphs in Excel vs. hand draw them, because it wasn't stated on the > rubric. I knew she learned more by generating them in Excel, shoot, she's > been graphing for years, but would the teacher agree, or dock her 25% for > being creative? So what does she do? She does them both ways hoping that she > wouldn't be docked for doing too much work. > > Now I constantly fight her attitude of looking for what she should do on > paper to please the teacher for the grade, vs. being interested in actually > learning something. My son has figuratively had his "knuckles rapped" for > calculating the areas of polygons using a couple basic equations and logic > vs. memorizing dozens of separate equations for each and every polygon. I > mean really, teaching that A=bh is the formula for rectangles, and A=s^2 is > the formula for squares? This is what my daughter is being taught now, and > she is terrified of getting a grade knocked down if she recognizes that the > A=bh formula works for a square as well, or if she recognizes that all you > do for a trapezoid is average the bases and you're back to base times > height, oh no, she has to know the official formula in the proper format. > This also occurred in her chapters on percents, discounts and interest - > they were treated like two totally different subjects, when they use exactly > the same kind of thinking and process. She begins to lose the ability to > recognize basic underlying concepts in a sea of terms and formulas to > memorize. When my son used his logic vs. rote memory, the fact he didn't > write out all the formulas cost him a grade. By the end of last school year > he was trained to memorize and not think about why things work, and with it, > he lost all interest in math. What a shame. > > I am quite happy with the school's English, history and science classes, my > daughter is learning heaps. I just have to work very heavily with her every > week to try and reverse the mindset from her time in math classes to try to > protect her from my son's experience. > > Julie Brennan >