I’ve been trying to gin up good moodle based problems for my tutees– which is why I’m discussing “teaching” instead of topics of greater interest to many of the visitors. In comments thread of a previous post, I mentioned that I’d seen yet another problem that seemed rather physically unrealistic. In particular, I mentioned what appeared to be an implausible food drop. My memory was close, but not quite right. I now have a screenshot of the problem!
Like the problem of the kid flinging flowers on to the balcony, this “unrealistic drop” also contains what I consider a sub-optimal image that (a) doesn’t help the student visualize the features required to solve the problem and (b) presents a degree of cognitive dissonance. Perhaps perfect images are not important, but then there the question itself The the values of the knows! Oh the values….!
Of course I’ll let you judge for yourselves. Here is as it is presented to a student (with the answer obliterated):
Note: If we go by the image, in this problem the propeller driven aircraft flying at 257 m/s is dropping “emergency food supplies”. (My recollection when I previously reported this was faulty. I recalled a slower aircraft. 🙂 )
Now for the oddities that can make one think “huh?” Maybe not “that’s impossible”, but still “huh”?
- 257 m/s corresponds to a speed of 575 mph. This speed is achievable by a bomber or a commercial jet The “Russian Bear” is propeller driven and can also fly this fast. That said: I’m not sure whether the Russians would use a Russian Bear to drop “emergency food supplies”. I imagine someone dropping “emergency food supplies” would want fly a bit slower if they could. (Or maybe that’s just me.)
- In the image, the package appears to have a parachute attached. Despite the presence of the parachute, I suspect the ‘correct solution’ requires students to neglect drag. Mind you, this is high school physics, so the students wouldn’t know how to deal with drag when it’s important.
Still: Why use a picture that suggests that ‘neglect drag’ would be incorrect? My answer: one should avoid choosing an illustration that communicate notion that an assumption students are expected to make would be incorrect. To avoid cognitive dissonance for students who might have experienced “aerodynamic drag” when sticking their hand out a car window or who might be familiar with the existence and purpose of parachutes: don’t ‘sex up’ questions that require them to neglect drag with pictures that include parachutes.
- But I have even greater cognitive dissonance when I solve the problem neglecting drag. If there were no drag and the package was dropped from 1.4 km, these supplies will hit the ground with a speed of ~306 m/s (i.2. sqrt(257^2+2*9.8*1400), Mach 0.9, 816 mph). While it’s not impossible for dropped objects to achieve such speeds, I can’t help but worry about the integrity of the packaging. Can a wooden crate hitting the ground with that speed survive impact? What are these “emergency food supplies packed in? Real questions.
On the one hand, I don’t necessarily expect students to think about this. But in reality we actually do want them to ‘reality check’ their answers. In this case, the supposedly “correct” answer forces one to conclude “The person who organized this drop is a blithering idiot.”
Of course some of the questions that make one think “huh” go away if (a) the parachute is removed from the image and the (b) “emergency food supplies” are a bomb. In those cases drag might be modest relative to gravity and we don’t want the bomb to survive an impact with the ground. Perhaps this question was merely ‘converted’ by substituting “emergency food supplies” for “bomb”. That’s not a very good excuse for not changing the numbers to something reasonable, but it might explain the magnitudes that make one go “huh”?
But as DeWitt previously observed
lucia,
They could have said a bomb instead of a package, but that would be non-PC. Bombs are dense enough that ignoring air resistance is a reasonable assumption. That speed is about right for a small plane. A Piper Cub couldn’t go even that fast, top speed 137 km/hr. The cruising speed of a Japanese WWII Betty bomber was 315km/hr at 3km altitude.
The solution to that problem is why the atom bombs dropped on Japan had parachutes attached.
Yep. Even bombs often have parachutes attached.
All in all, I can’t help thinking: Why the heck not adjust the numbers to suggest the “emergency food supplies” are being dropped by a guy flying an old fashioned crop duster? Why not have supplies dropped from something that can fly lowish and slowish? I suspect the answer is “Numbers were spit out by a random number generator programmed with little thought about realistic choices.”
Mind you: This sort of question remains a good exercise in the sense the student learns or is tested on the procedure for solving problems in projectile motion. But it’s sub-optima if we hope for the side effect of student’s a sense of what might really work in the real world.
That said, I don’t actually mind unrealistic problems. When I want students to learn the process, I prefer full on “unrealistic” and do this:
(Actually, I’m thinking of moving the base camp to 50 m/s and increasing the ‘hover velocity’. I have no idea what the minimum ‘hover velocity’ would be for an alien space craft, but I’d like to change the values to would ensure students who forgot horizontal velocity when computing the answer to (9) would get a different result from those who remembered to include it. )
As I mentioned before: There’s a good reason Wil E. Coyote and Road Runner appear in many projectile motion problems!
Yeah, that’s awful. The parachute would have baffled me.
I guess the student is supposed to figure number of seconds for something dropped from 1.4 km to hit the ground and multiply # seconds with horizontal speed. Obviously the package isn’t going to continue on at 257 m/s any way you slice it, unless the package is traveling through a vacuum, in which case that’s the wrong sort of plane and a parachute has no place… ugh. That final delivery velocity is a little hot as well. 🙂
lol! 🙂
.
On a serious note, I very much like the paragraph you supplied at the bottom of the [edit: your] problem. More work for you, but that’s the lifeline a student who’s wondering what assumptions are valid needs in my view.
Mark
I haven’t verified by having the student follow that method, enter the number and have it ‘confirmed right’. This problem is various incarnations appears in many high school texts and that’s the correct solution method. So yes, I assume that’s the intention of the assignment.
That said: In Serway and Faughn, the airplane flies at 40 m/s not 257 m/s. The plane is 100 m above the ground, not 1.4 km. Depending on package contents (bubble wrap vs. densely packed grain) and size, shape and other features, ‘neglect drag’ might work well or poorly with the Serway and Faughn values. Also, the drop might not result in little more than crate splinters and destroyed food stuffs.
Quite possibly. Though if there is no friction, it won’t heat up while falling. 🙂
I really am going to cut the distance and increase the speed of my space aliens. I want to avoid
{ sqrt(vy^2 + vx^2) / vy } ~ 1 and the current values fail that criterion. (I also need vy≠vx; )
These two criteria mean some answers obtained when making common conceptual errors are not within rounding error or answers computed correctly.
It’s perfectly easy to come up with “good” ranges of knowns … if you think about it and then use a script!
Food droppings over The Netherlands at the end of WWII using Lancaster bombers typically occurred at 300m altitude with a speed of 275 km/h.
http://www.deweekkrant.nl/files/pdfarchief/GV/20150429/GV_GV-15_150429_1.pdf
Hans
So 76. m/s which is less than 257 m/s and
300 m which is less than 1400 m.
“Dropped at Mach ~0.75”
Fast food!
Delivery of a free falling nuclear bomb from a bomber, without the bomber being destroyed in the explosion, is an interesting problem. One ‘solution’ was to toss the bomb. This was done by having the bomber execute an Immelmann turn and releasing the bomb at some point before the bomber was flying vertically. The bomb would then follow a parabolic arc to the target while the bomber was completing the turn and flying away. Even with a relatively high speed jet bomber, it was never clear that this would actually work.
I can envision all sorts of problems you could generate from that scenario.
DeWitt,
There’s a limit how ‘interesting’ you can make problems in high school. Many of the students are just taking algebra II and trig. So their facility with setting equations and solving them is just developing. Also, this is the class where they first set up sketches to visualize physical processes. Any 3 d sketch will lose quite a few of the students.
If there was a “plane flying” club, I’m sure you could get any kid who did physics and flew a plane to spend time developing their skills on that problem and it would be good. But if used as a general problem, you’d lose kids in a first contact high school class that way.
I had a hiccup with “hover speed”. If it’s hovering, I’d assume at first that it’s stationary, like a helicopter hovering. Obviously, the intention is clear, but maybe using the term “hover” here makes things less than totally clear?
Szilard,
I agree. But I haven’t thought of a verb that communicates it is mostly staying in one place, but moving around at a fairly low speed. “Cruise” sounds like it’s going some where.
I guess people saying “Circling the airport”, but that doesn’t imply some low speed. I’ll figure something out using “circling”.
Lucia,
‘Loitering’ is the term for drones that when they stay up over an area a long time. I don’t know that it would make it clearer to students, but it’d probably make sense to military guys.
Loitering is perfect!
These aren’t intended as tests. They are intended as worksheets to make them learn to identify the “key” points, ignore unimportant ones, and give answers that are requested. The precise verb is unimportant, so I think on the worksheet it’s fine if they learn a new term.
Different students have different challenges. But some challenges are shared by all the high school students I’ve encountered. (Mind you: the sample is biased by “students whose parents hire tutors.) But one of the challenges is reading the problem and fishing out “relevant” from “irrelevant”. Initially you don’t want too much irrelevant. But a little is good. I do have to chose a verb– so it’s best to pick the correct term. But what matters is it’s ‘moving’. Even with the bad verb (hovering) I think most would figure that out. Circling isn’t quite right. Loitering will be good.
They wanted the food to arrive fully cooked and separated into servings.
The unrealistic drop question is bad because it trains students to give the “right” wrong answer. The question did not say “ignore drag”, so the correct answer is that “we don’t know enough to calculate this” or “the question is not well formed”. I assume that these answers would be rejected.
.
When these students grow up and become climate modelers, they will leave out things they don’t know how to calculate from their models and claim they are right. Check against observations? They never told us to do that!
.
We are training students to be gullible when we should be training them to be skeptical.
.
In the movies, there is “suspension of belief” and Hollywood is getting so good at CGI and FX that we don’t even notice anymore when they “jump the shark”‘. But in science, we are supposed to keep it real.
Ledite
I’m sure the answer box does not permit that answer. 🙂
I don’t know about that. Students will probably survive this sort of question just fine. They’ll develop the skill of judging if it’s reasonable later on. But it’s still best if those things that seem to match the real world are realistic.
So for example: Even if I write a question using “aliens visiting earth”, I try to avoid picking numerical values where friction will affect the answer more than 10% if the student is expected “know” he “should” neglect friction when in real life and the student is expected to use “book rules” for round off and so, when given “knowns” stated to 3 significant figures enters an answer to three significant figures. Yes, aliens are obviously unrealistic. But if they did visit, we don’t suspend the laws of physics when they drop things!
I’m not a math or physics wiz, but did take math and physics in college back in…well, after the slide rule and before the internet. All I know is, we often had to diagram the problem before solving instead of having the diagram provided. I think this helped more to understand the problem than just getting the math right. Unfortunately, I think (though I could be wrong) that a lot of today’s teaching is geared to getting the right answer but not necessarily understanding the problem.
Phil R,
Figuring out your own diagram remains a skill the students need to develop.
I think today’s teaching is just as geared toward understanding as in the past. Certainly, instructors in the past drew sketches on the blackboard while showing the student the steps involve in solving the problem. Textbooks also included examples with sketches as soon as printing figure was inexpensive.
As in the past, some teachers are better, some are worse. Different people have different views about how much “skaffolding” is required while having students work through problems.
For my tutees, I like to have questions in my bank that cover a the same material at a range of difficulties:
1) Some like the worksheet above that have a sketch and a table as a ‘huge hint’. (These hints are “scaffolding”. The student is thinking about the problem and working it through while being given some support.)
2) Some that might have a less informative sketch (if necessary.)
3) Some that are only text.
Bear in mind: if the students already mastered the text only problems from class I don’t spend time with them on that. We spend time on the issues that are perplexing them. In those cases, we need to go back to (1) before then can get to (3). But (3) is the goal.
A don’t write their actual exams, nor do I technically assign homework. I am helping where they have problems and questions.
Nearly all my students are enrolled in a for credit class somewhere. These students will be tested with questions that do not provide useful sketches. So, my ‘aliens’ question would never be a test question, nor should it be.
That said: I do object to inserted images that contain distracting information or worse images that suggest the opposite of what is intended. In the one contained in the blog post, the image contains a parachute while the student is supposed to assume there is no drag. Removing the image would improve that problem. Heck, I think replacing the image with a parachute attached to the package with an image of opus the penguin would improve it!
The problem is that every free falling object has a terminal velocity. A human sky diver has a terminal velocity of about 120 mph.
Now if the terminal velocity is to be neglected the question should have been posited for the moon.
The terminal velocity for a kinetic bomb or a bullet is around 200 knots which is less than half the speed of the airplane.
Oh and the reason Propellor driven planes can’t go supersonic is because of the tip speed, if it goes supersonic it tears the blade apart.
Extremely stupid example question in my mind.
Genghis,
!20 MPH is the terminal velocity of a sky diver in spread position. When assuming a more streamlined shape with arms close to the body and head down, a skydiver can reach well over 200MPH. In fact, the world skydiving speed record, according to Wikipedia is 330.21MPH. You’re way off on bombs too. The terminal velocity of a 1600lb AP bomb is 270m/s or nearly 1,000KPH.
Bullets are a different matter, they’re a lot smaller than bombs so their terminal velocity is slower. Of course, they far exceed terminal velocity at the exit of the barrel of the gun. The muzzle velocity of an AR-15, for example, is 975m/s, supersonic.
Not sure what the sound barrier really is and what the effect of going faster than sound is on structures doing so.
The propellers breaking up are more due to their composition I think. A sturdier material might not break up.
Jet engines can go faster than sound, have some revolving parts and yet do not normally tear apart.
Genghis,
Terminal velocity for a bullet is also likely to only apply to bullets fired nearly straight up so they come to a stop and then start tumbling when they fall. Bullets fired at a low angle, unless from high altitude, will probably hit the ground before they slow to the terminal velocity of a tumbling bullet because they won’t be tumbling.
DeWitt,
With respect to the homework question in the blog post, I think the importance of terminal velocity is that at terminal velocity, drag force and gravitational forces just balance. So if the velocity difference in the problem exceeds terminal velocity, it’s a bit much to expect students to just “know” they ‘should’ “neglect drag”. In reality, teachers who intend students to assume “no friction” should go to the trouble to pick knows that make sure the velocity difference when the food is pushed out of the airplane is not close to the terminal velocity; it should also certainly not exceed the terminal velocity.
My theory of why this is not done is that with some frequency, some teachers have been teaching high school physics, and do not themselves know anything much about drag force. In particular, they likely did not do any engineering fluids that involves finding drag forces, finding forces to hold pipes in place and so on. Consequently, they don’t know how to estimate drag and so on.
If so, it would be better if the teacher recognized his/her limitation and not change the numbers from text book problems. . Failing that, they should at t least not change them more than 10%-20% which at least would usually fall in the range of ‘not embarrassing.
When this problem is in books, the elevation and speed of the plane are not ridiculous for a food drop. But here it is.
OT
Lucia, I wish you would comment on Dr. David Evans’ ongoing analyses of climate models’ flaws, in preparation of the presentation of his new and improved solar-climate model.
Fifth article in the series:
http://joannenova.com.au/2015/09/new-science-5-error-2-model-architecture-means-all-feedbacks-work-through-the-surface-temperature/
I’m content to refrain from commenting at least until the end of his series. That it appears it will involve a “solar model” means I’m unlikely to ever comment on it.
Patially off topic, but ironic. Some people may remember my displeasure when my 10-year-old daughter’s teacher told me that I couldn’t give her a chocolate chip cookie for a snack. Guess what her school is asking that I buy at its fund raiser– cookie dough.
That’s hilareous!
Kids around here do hawk over priced candy near Christmas. The boyscouts hawk well priced wreaths. We hope to be home when the boyscouts come around. He cross our fingers and hope not to be home for the candy.
Students should be so lucky to have a teacher like Lucia and class discussions like the above comments!
I like Lucia’s comment in her preview question about “back of the envelope estimates”. It bothers me about computerized questions that there is a leap into significant digit answers even before the concept is clear to the student. Of the two parts, the concept is the most important.
I was looking at Google for speeds of propeller tips and helicopter blades and found info about the TU-114, Thunderscreetch, and many other fascinating planes. Thanks for nudging me to do this!
I will leave just one link (nice photos, appropriate for future supersonic food drops):
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/soubar.html
Ledite
“Computerized” isn’t what causes this. “Computerized” questions have sufficient flexibility to allow all sorts of questions and they person entering the question can program to have the script accept answers with a reasonable number of significant digits. Plus, teachers who are obsess about “significant digits” in answers predate computerized questions. My statics professor Freshman year must have had some sort of Aspergers issue; he was totally obsessed with significant figures. That made him the exception in college. But you just needed to learn to attend to the significant figures applying the level of significance he “liked” at the end of the problem, so it wasn’t a huge burden for the student He also explained solution methods, so on the balance the class was fine. (Not inspiring, but ok.)
The potential big advantages of computerized questions is that– if properly programmed– the system can reduce the work load of grading freeing the teacher up to do other things. Also, students can self-test– provided the system gives proper feedback. If the questions are properly organized and written they can learn what materials they need to review based on the self test. Whether that happens in an actual class… dunno.
I think Khan academy tries to write algorithms that provided lessons based on student performance on particular questions on. How well that works… dunno. But it’s an interesting idea.
But like anything, computerized questions can have downsides. So of those have direct analogs in non-computerized questions; some are unique to computerized questions.
Computerized questions (and answers) have been totally underused in my experience, and that of my kids now reaching college.
Easiest to illustrate by example. Suppose we want to test historical facts. So three multiple-choice style questions, each with three choices for answers and two students to be tested.
Student 1’s test:
1) The first U.S. vice president was: (a) Jefferson (b) Jackson (c) Adams.
2) The treaty ending the War of 1812 was signed in: (a) Paris (b) New Orleans (c) Belgium
3) The Third U.S. president was (a) Adams (b) Madison (c) Jefferson.
Student 2’s test:
1) The treaty ending the War of 1812 was signed in: (a) Belgium (b)Paris (c) New Orleans
2) The Third U.S. president was (a) Madison (b) Jefferson (c) Adams
3) The first U.S. vice president was: (a) Jefferson (b) Adams.
(c) Jackson
Now there is less opportunity to convey information in the form “What did you put on Question Two, ‘A’ or ‘C’ ?” Each student could have a unique permutation of questions and answers with a matching unique answer key. And even so the information content is completely fair — same questions, same possible answers, completely “standardized” so all students have the standard opportunity to get it right, or not, without changing to “harder” questions or “trickier” answers.
Pouncer,
That’s one of the advantages. Also: the test can even be administered on paper if you add a barcode to the question form and the answer form. The answer form, with its barcode can be scanned.
There are some advantages to administering the test on paper, which include permitting some working-memory sparing strategies to students taking the test, eliminating the need for the school to have a zillions secure machines for administering the test and avoiding potential problems with system crashes. That one can gain all “anti-cheating” advantages with paper tests is useful.
Would like to ask commenters here about grading policies. This fall we moved to a new, much more academically accomplished school district and the move has gone well for my 9th grader son. Across the board, he currently has about a 93 average.
In science, he thought he understood the subject and didn’t study for a big test in the beginning and tanked it. His last test he scored 35 out of 35 to claw over a 90 score. The very last project (immediately after the test) he scored 20 out of 22. Now his average is 89.99!!! (and the teacher is giving him a B. She said 3 other people received the same score.) I give my son bonuses for “A”s and double the bonuses for all “A”s.
I will probably give my son a retroactive bonus (of 75% of what he would have otherwise received), if during the next quarter he scores something like a 93 or above in science.
Am wondering what commenters think about awarding a B for an 89.99 and what they would do if they had a bonus system in place like mine. My gut feeling is that the B is wrong but not all that wrong.
JD
JD,
Your son is lucky to have so generous a father. I worked a paper route from 5:00 AM to 6:15 AM every morning for spending money. Good grades were just expected.
.
WRT 89.99: depends on what the grading policy is. If ‘A’ means 90 or more, then 89.99999 is still a B. Sometimes life is tough; we all have to get over it. In the grand scheme of things, it is far more important what your son remembers from the class than what grade he got…. or how much of Dad’s money he pocketed for his efforts.
SteveF
I started caddying when I was 8 years old. When I was 16, I would get to the golf course at 6:45 in the morning, practice for a couple of hours and then work for 8 hours at the golf shop. After that I would play golf until dark. (I was a tournament junior golfer.) I would do this at least 6 days a week and thought nothing of it. (Believe me when you are a tournament golfer, playing golf is quite often not very enjoyable and a lot of work.)
The bonus system has worked very well for my son. When he was in the fourth grade, he was only in the top 23 % for the state of Ohio. The first year I implemented it he went from the top 23% to the top 5.1%. (and broke the bank) Since then he has maintained the same level and become interested in many things, including physical fitness — becoming ripped. I could mention several other things, but the point is that the bonus system has worked very well. A lot of times, the best way is the easiest and simplest way.
JD
Love it JD.
My uncle was a teaching pro at a golf resort. Here was our deal.
If I walked 36 he would give me a cart for the last 9 so I could finish before dark.
free gloves and shoes and lessons and clubs
Mosher, my father was a teaching pro at several golf courses, including a 36 hole golf course. One Monday (caddies day–no one on the course after 12 pm,) I walked 54 holes, eating apples that were on several holes on the course. Should mention that the activities described when I was 16 occurred in the summer.
JD
JD,
Yeah, I do this too. My kids definitely don’t ‘get’ why it matters. Oh, they can and will parrot back my explanation. But they don’t care the same way they care about short term rewards.
It’s all good. They’ll get it eventually.
Depends on your priorities and what you think your son needs to learn from the experience I guess. Judgement call.
JD,
In fifth grade, my dad was so thrilled I got straight A’s, he bought me a huge 1lb Hershey’s candy bar (which got split with the four kids– four includes me.) I continued to get straight As; he bought more candy bars.
Then my mother “put her foot down” that we shouldn’t be “rewarded” for grades. (And Dad “sneaked” some rewards behind her back– but smaller. Eventually, he was caught and had to stop.)
But really, the fact that I knew my Dad was so thrilled was motivating. So even though the “candy” no longer came when I got good report cards, I knew it made him so proud and happy.
Overall, I support the “bribes” in the sense that they express the joy and happiness of the parent. Kids want to make their kids happy even more than they want money.
That’s why SteveF’s “good grades were ‘expected’ ” works too. Kids know how much money their parents have– so often its “not the money”. Money is a symbol. But by the same token, if the parents have the money, and dole it out, that can communicate things.
If it’s “working” I’m guessing the kids are noticing that their getting good grades makes you happy. And they want to do that. So they like the money, and they like knowing they’ve made you happy. Be sure to express the joy!
Rewards aren’t bribes.
You pay a bribe in advance in the hope that the bribee will do something for you, often illegal. Although in many places it’s necessary to bribe someone to get the person to do what was supposed to be done in the first place. Performance bonuses in contracts aren’t bribes. Neither are rewards for getting good grades or job promotions or a long list of other things.
The saddest thing about the whole quality management thing was that the people conducting the part of the course on behavior modification would always insist that money wasn’t a motivator for performance. Of course they were being highly paid to teach the course. Irony increases again.
DeWitt
Of course money is a motivator for performance.
Otherthings are too. The conceit with “quality management” is that caring about “making the company/boss happy” will somehow trump wanting to “make more money” in a business relationship.
I mean, seriously: here’s the ‘boss/company’ wanting to get you to figure out how to “make them happy” without them being willing to give you what “makes you happy” as a reward for doing what they want? Which means they keep money they get to spend on their own selves and family? Obviously any employee with two working brain cells is going to figure out that the boss doesn’t give a shit about them and just want to maximize their own profits and so on. Obviously money is the main motivator in a business relationships.
Things are a bit different in families. Even children can tell when their parents would love to sacrifice for them if they could. Kids can tell when the choice is “Pay the rent” or “reward me for grades” vs. “buy a fur coat for Mom” vs. ” reward me for grades”. Kids do “get” that for some parents, the best reward is that the parents are so happy and relieved to know the kids are doing what will help the kids when they grow up– and that’s probably what Steve F sensed. But, by the same token, I went to highschool with kids whose parents were loaded. And … didn’t … really…. care. About academics. Money from those parents would just be …money. Which remains motivating. But that doesn’t mean that other things aren’t motivating in other circumstances.
But for many parents, the money is both a symbol of their pride and values and ‘ the money’. Don’t discount either.
FWIW: It’s interesting to view the families of kids I tutor. Needless to say: the fact the parents hired a tutor is an indication that all these parents care. So, i get a ‘biased’ sample. But I’d say some are loaded and some are really hunting for the funds to help their kids. And you know what? I think all the kids have a good grasp of just how much their parents care about them and about the importance of academics.
Lucia,
I thought this was mildly amusing. I guess trying to make physics problems interesting can be fraught with peril:
Link here.
🙂
Disclaimer; I neither condone nor find the concept amusing, of pushing refugees off rafts. That’s not what tickled me.
Mark,
Yep.
I’m assuming this was something to figure out the maximum carrying capacity of the boat. I think the kinder way to do the same problem is something like:
Mr X has a boat that weighs some amount. He wants to transport refugees, each of whom weighs some amount. What is the maximum number he can rescue? Throwing them off was the bad bit and not necessary for the physics.
I suspect it is a good example of what goes wrong when someone tries to make the scenario “more interesting”. After all, the “more interesting” in other problems was turning dense throwable objects into bouquets, making physical distances impossible and so on.
Lucia, as I have posted before I got off to a slow start in school. My parents as a result started rewarding money for A’s and B’s to me and my one brother and older sister (the younger sister was not in school and I think this process was shut down before she got in school). We at the time were cash poor farmers and thus those rewards were very meaningful and let us know that our parents thought grades in school were very important. The reward system was shut down after 2 or so years but we kept getting mostly A’s even without pay because I guess we realized that not only our parents thought it was important, but we were enjoying the challenge it presented and in some ways were competing with one and another. I have long suspected that it was me that needed the motivation and not my siblings, but they were happy to be along for the ride.
JD Ohio, as a parent I would probably have felt there was a lesson to be learned by the child from strict adherence to the original contract, while as a grandparent I would find a way to rationalize giving the grandchild the reward. Besides if I did not give the reward the grandmother would.
The way I use”bribes” goes under the rubric variable interval intermittent reinforcement schedule. It sounds like Kenneth’s good-grades reward works along those lines.
As a parent/grandparent, I’ve found “bribing” two-year olds to behave in the store works great. It breaks the association between being in the store and a certain (to the parent) undesirable behavior.
Over time, you can start “forgetting” to reward them and eventually they adopt the behavior without needing further rewards. That’s a form of random interval reinforcement schedule, and it’s been shown to be one of the best behavior shaping mechanisms. People find novelty interesting.
In my experience, the original “I’ll give you a reward if you …” quickly gets replaced with them negotiating with you for a treat based on their good behavior (“I did really well in the store. Will you get me a treat?”)