Continuation of my previous quick take about teachers.
Long ago I read a thing claiming that some types of anecdotes can be hard to remember because of their absurdity. Things that do not make sense are funny specifically because they do not match correctly into your knowledge. I think that is also why it is difficult to recollect confusions in education: at least one side of the conversation was having a wrong model, which cannot be remembered by just a natural association. It takes more space in memory to remember other person’s incorrect image of the world.
I am trying to recollect as many confusions as i can. I had an mechanical engineering class (materials, geometry, kinematics, loads, surfaces). Over the semester we had to design a gearbox. In the middle of the semester I noticed 2d technical drawing, front and up views. The girl was apperently ready to be defending her design. But I stopped her. She had a fatal flaw, which is only apparent when you have 3d understanding what those drawings mean. She did not have that, even though drawing looked good in other aspects (clean lines, correct sizes, top and front allign). The teachers were so strict about those clean lines that the student optimised to make it look good, not to match common sense. The shaft, which goes through the whole thing, was intersecting a gear of another shaft. Matter was passing through matter.
The crazy thing is, I am 80% sure teachers in my first uni would/did not notice that (her handmade kinematics draft must have been approved, since she was on the second stage), because of how they used to rigor for small imperfections (“You chose the wrong smootheness for this surface, go remake”) and to not watch the drawing for longer.
Both students and teachers can have faults in everything, even in common sense.
My teacher in Strength of materials also did not posess 3d imagination. When drawing a crystal structures, she only succeeded in flat images, failing immediately to draw tetrahedron and more complex projections. The students did not understand that she is drawing nonsense, and were just memorising, not questioning, really handicapping their understanding.
One of my teachers once made a silly mistake, so i thought. She forgot to place a minus in the exponent. So instead of 10^-11 there was 10^11. Knowing, that my classmates will blindly memorise it like this, I came to point that out. When I pointed that out, I was met with “I teach this formula like that for eleven years! Do you think I have been making a mistake for eleven years, or maybe you made a mistake?”. Her argument was basically authority and tradition! She was not willing to discuss with proper arguments, not willing to see how her formula implies molecules of galactic scale. Even if I was the one that had the confusion, the teacher still has to let the student describe his thought process, to see where is the mistake.
I once found a mistake in the lab book of a PhD professor. I came to tell that he has all indices swapped on couple pages. Like, the speed of electron 1 was multiplied by the mass of electron 2. Couple pages later another mistake, which magically cancelled it out and the resulting formula was correct. If this is indeed a book’s mistake, I knew most students will not understand, will just assume that they are too stupid to grasp and just go on, and thus the whole chapter is dangerous.
The teacher shouted at me. “You should have better went to the art school, like your mother...” (he overheard my private conversation with other student over break before) ”… look at the next page and everything will be clear, because the final formula is correct. I can’t handle that, every year some stupid students come with this question, learn to read first”. The “every year” basically showed me that there is indeed a mistake in his book and not in my understanding.
(The teachers were indeed outrageously stupid in my first uni, so I went to get an education abroad. Why am I thinking about the past and about teaching? I am in Masters program, and my faculty proposed that I teach Math2 in the next semester, and that is quite a responsibility, since I value proper teaching so high)
Continuation of my previous quick take about teachers.
Long ago I read a thing claiming that some types of anecdotes can be hard to remember because of their absurdity. Things that do not make sense are funny specifically because they do not match correctly into your knowledge. I think that is also why it is difficult to recollect confusions in education: at least one side of the conversation was having a wrong model, which cannot be remembered by just a natural association. It takes more space in memory to remember other person’s incorrect image of the world.
I am trying to recollect as many confusions as i can. I had an mechanical engineering class (materials, geometry, kinematics, loads, surfaces). Over the semester we had to design a gearbox. In the middle of the semester I noticed 2d technical drawing, front and up views. The girl was apperently ready to be defending her design. But I stopped her. She had a fatal flaw, which is only apparent when you have 3d understanding what those drawings mean. She did not have that, even though drawing looked good in other aspects (clean lines, correct sizes, top and front allign). The teachers were so strict about those clean lines that the student optimised to make it look good, not to match common sense. The shaft, which goes through the whole thing, was intersecting a gear of another shaft. Matter was passing through matter.
The crazy thing is, I am 80% sure teachers in my first uni would/did not notice that (her handmade kinematics draft must have been approved, since she was on the second stage), because of how they used to rigor for small imperfections (“You chose the wrong smootheness for this surface, go remake”) and to not watch the drawing for longer.
Both students and teachers can have faults in everything, even in common sense.
My teacher in Strength of materials also did not posess 3d imagination. When drawing a crystal structures, she only succeeded in flat images, failing immediately to draw tetrahedron and more complex projections. The students did not understand that she is drawing nonsense, and were just memorising, not questioning, really handicapping their understanding.
One of my teachers once made a silly mistake, so i thought. She forgot to place a minus in the exponent. So instead of 10^-11 there was 10^11. Knowing, that my classmates will blindly memorise it like this, I came to point that out. When I pointed that out, I was met with “I teach this formula like that for eleven years! Do you think I have been making a mistake for eleven years, or maybe you made a mistake?”. Her argument was basically authority and tradition! She was not willing to discuss with proper arguments, not willing to see how her formula implies molecules of galactic scale. Even if I was the one that had the confusion, the teacher still has to let the student describe his thought process, to see where is the mistake.
I once found a mistake in the lab book of a PhD professor. I came to tell that he has all indices swapped on couple pages. Like, the speed of electron 1 was multiplied by the mass of electron 2. Couple pages later another mistake, which magically cancelled it out and the resulting formula was correct. If this is indeed a book’s mistake, I knew most students will not understand, will just assume that they are too stupid to grasp and just go on, and thus the whole chapter is dangerous.
The teacher shouted at me. “You should have better went to the art school, like your mother...” (he overheard my private conversation with other student over break before) ”… look at the next page and everything will be clear, because the final formula is correct. I can’t handle that, every year some stupid students come with this question, learn to read first”. The “every year” basically showed me that there is indeed a mistake in his book and not in my understanding.
(The teachers were indeed outrageously stupid in my first uni, so I went to get an education abroad. Why am I thinking about the past and about teaching? I am in Masters program, and my faculty proposed that I teach Math2 in the next semester, and that is quite a responsibility, since I value proper teaching so high)