[math-fun] Possibility puzzle
Apparently, possibility is the intersection of probability with Boolean algebra. A certain 4th grade teacher decided to enrich Saxon Math with a few days of re-education from a private copy of something called "Logic Liftoff", followed by a test supposedly copied therefrom, on which a certain confused 4th grader apparently was reduced to bluffing with ambigrams: gosper.org/logic.png <http://gosper.org/logic.png>. I don't understand how he got credit on the first five answers, since their correct answers are clearly "the sun will rise tomorrow." Or how he didn't lose 5 more points for "Febuary". I actually had to Google for reassurance that they weren't dumbing down the spelling. --rwg
* Bill Gosper <billgosper@gmail.com> [Feb 16. 2014 19:00]:
Apparently, possibility is the intersection of probability with Boolean algebra. A certain 4th grade teacher decided to enrich Saxon Math with a few days of re-education from a private copy of something called "Logic Liftoff", followed by a test supposedly copied therefrom, on which a certain confused 4th grader apparently was reduced to bluffing with ambigrams: gosper.org/logic.png
First answer reads: "we will bring our umbrellas" Valid answer.
<http://gosper.org/logic.png>. I don't understand how he got credit on the first five answers, since their correct answers are clearly "the sun will rise tomorrow."
Given the questions, there is no remotely reasonable way to put scores on the answers.
Or how he didn't lose 5 more points for "Febuary".
Or how the teacher wasn't shot, for the better of the kids. Note there is just the letter "r" skipped, perhaps one of the more forgivable spelling errrsr.
I actually had to Google for reassurance that they weren't dumbing down the spelling.
Hey, "aluminum" is a valid spelling!
--rwg [...]
Looking at this pathetic piece reminded me strongly of the feeling I had at school that I needed to "resist the nonsense" for the sake of staying sane. Non-withstanding, at least in my school they drilled proper math and natural sciences basics into us. The level of knowledge/preparation of many of today's students entering studies of engineering (that's what I see) often appears shocking to me. When I studied (physics; all forgotten by now) those who clearly didn't manage anything nontrivial (physics/math) just took a course in pedagogics (or something like that) and became ... ... guess what ... yes, school teachers. Case closed. Best, jj
I had to argue with with a graduate student over an ambigram. On two adjacent true/false questions, he wrote "yes" and "no" respectively, then very lightly drew arrows reversing them. The answers were wrong, and I refused to accept the reversal as a legitimate mark. He told me that in Germany, erasures and cross-outs are not allowed, and he had no choice but to use arrows. Nice to see that Americans are now learning to apply European techniques. As for the test in general, I strongly believe that these things are part of education in the broader sense. Thinking about ill-posed problems is an important skill, especially in math. Realizing that your teacher is deeply confused and coping gracefully with him is an important life skill. My grandfather was a sports writer, and he knew the difference between probable and possible. Hilarie
From: Bill Gosper <billgosper@gmail.com>
Apparently, possibility is the intersection of probability with Boolean algebra. A certain 4th grade teacher decided to enrich Saxon Math with a few days of re-education from a private copy of something called "Logic Liftoff", followed by a test supposedly copied therefrom, on which a certain confused 4th grader apparently was reduced to bluffing with ambigrams: gosper.org/logic.png <http://gosper.org/logic.png>. I don't understand how he got credit on the first five answers, since their correct answers are clearly "the sun will rise tomorrow." Or how he didn't lose 5 more points for "Febuary". I actually had to Google for reassurance that they weren't dumbing down the spelling. --rwg
Probable-Possible, my black hen, She only lays eggs in the relative when. She never lays eggs in the positive now, For she is unable to postulate how. —Dan On Feb 16, 2014, at 2:46 PM, Hilarie Orman <ho@alum.mit.edu> wrote:
My grandfather was a sports writer, and he knew the difference between probable and possible.
* Hilarie Orman <ho@alum.mit.edu> [Feb 17. 2014 08:15]:
I had to argue with with a graduate student over an ambigram. On two adjacent true/false questions, he wrote "yes" and "no" respectively, then very lightly drew arrows reversing them. The answers were wrong, and I refused to accept the reversal as a legitimate mark. He told me that in Germany, erasures and cross-outs are not allowed, and he had no choice but to use arrows. Nice to see that Americans are now learning to apply European techniques.
... of boldly lying to the instructor. A rather large proportion of students considers cheating in exams as OK. Is that a German (European?) disease?
As for the test in general, I strongly believe that these things are part of education in the broader sense. Thinking about ill-posed problems is an important skill,
... it is considered part of intelligence ...
especially in math.
erm, of all things, shouldn't math (more so school math) rather be a shining example of clarity and unambiguity? Actually, in written exams I detest ambiguity in questions, no matter what the topic is, at the very least in those "exact" sciences. It appears to me that students silently assuming questions are unclear and have to be reinterpreted is a positive obstacle when it comes to math. Would you agree?
Realizing that your teacher is deeply confused and coping gracefully with him is an important life skill.
Yes, sadly. Also, that two teachers tell you the exact opposite and you have to give him "their" version of answer. Also, to never correct them, even at the most glaring and idiotic errors; something I try to make my students unlearn, which seems incredibly hard.
My grandfather was a sports writer, and he knew the difference between probable and possible.
Hilarie
[...]
Best, jj
From: Joerg Arndt <arndt@jjj.de>
As for the test in general, I strongly believe that these things are part of education in the broader sense. Thinking about ill-posed problems is an important skill,
... it is considered part of intelligence ...
especially in math.
erm, of all things, shouldn't math (more so school math) rather be a shining example of clarity and unambiguity?
So many things should be shining examples! But no, I don't think that an education that represents math solely in that manner is beneficial. Students must learn to question problem statements, to look for ambiguity, to seek the clarity where it seems to be missing. If they believe that mathematics emanates flawlessly from oracles, then they will be reluctant to sully it with their own flawed intellects.
Actually, in written exams I detest ambiguity in questions, no matter what the topic is, at the very least in those "exact" sciences.
Written exams have too much tension associated with them to be useful to anyone but the instructor. I read today about a teacher's complaint that a textbook recommended giving elementary school students the assignment to "draw nobody". Personally, I think it is a terrific concept.
It appears to me that students silently assuming questions are unclear and have to be reinterpreted is a positive obstacle when it comes to math. Would you agree?
But so many questions are unclear that if a student does not realize that early on, success is impossible. Many seemingly fundamental questions are unclear. Of course, a large dose of contradictions and errors in instruction would be simply frustrating, and I am not advocating bad instruction as a goal. But, I think that some amount of "think about what this might mean" is a good thing, I recommend embracing the occasional error in homework assignments with intellectual gusto rather than contempt. In 7th grade our math teacher was irritated with the class for complaining about a math problem that involved the cost of a "night letter." We didn't know what it was, couldn't even guess. He told us to find the actual cost of such a thing by the next day. Our Western Union office got 35 calls about it, and they were as confused as the students, "night letters" having been eliminated years before. We all learned a valuable lesson. Mine was an eye-opening revelation about the kind of people who wrote our textbooks. They were probably ... OLD!! Hilarie
I read today about a teacher's complaint that a textbook recommended giving elementary school students the assignment to "draw nobody". Personally, I think it is a terrific concept.
There is a chapter in Surely You're Joking Mr. Feynmann's called ``Is it Art?'' beginning on page 263 is a discussion of how supportive the artists all were in finding merit in his drawings. They were the kind of people who would have appreciated an assignment to ``draw nobody.'' Whit
participants (6)
-
Bill Gosper -
Dan Asimov -
Hilarie Orman -
Hilarie Orman -
Joerg Arndt -
Whitfield Diffie