Should we aim teaching at potential experts?
#1
Posted 2014-May-19, 11:29
As a quick summary, this is a hand where declarer can make a slam by catering to a 4-1 club split in one hand or the other, but not both simultaneously. Declarer can figure out which hand can have long clubs by running diamonds and spades, keeping in mind that West opened a weak 2 and East made a preemptive raise. In some layout possibilities, an endplay is required.
I've been arguing that this hand is inappropriate for the beginner forum. To be sure, there is no single complicated idea involved, and no issues of judgement. However, getting the hand right requires counting at least 2 suits and keeping in mind that each defender has exactly 13 cards. Most beginners can't keep track of and put together all this information even while following the writeup, never mind at the bridge table.
I am a math professor at a mediocre university. Over the course of a semester I get a fairly good sense of my students' ability to analyze situations, figure out the information they need, keep track of the information mentally, and make logical deductions from the information to arrive at conclusions. I don't think more than 15% of my students could, if they learn bridge and play regularly for 10 years, become able to solve the problem at the table.
Those of us who do this kind of thinking every day and are good at it (not necessarily just at the bridge table) forget how big the cognitive load involved is and vastly overestimate the ability of most people to keep track of several pieces of information at once.
A few years ago, my retired Dad (who lives nowhere near me) decided he might want to take up bridge with also retired Mom. I was visiting and was asked to get them started. I started with playing a hand, and halfway into the first hand, Mom said "You mean I have to keep track of what high cards have been played in my head?" That was the end of that idea.
I imagine the average beginner looking at this lesson and saying "I have to think this hard to be good at bridge? I'd better give up now and take up knitting instead."
A lot of intermediates have trouble doing this kind of thinking either, but they at least have enough bridge experience to know that they don't need to give up bridge if they can't do this.
Now to the title of this thread. When we think that a beginner could profit by studying hands like these, we are implicitly already aiming at the beginners who have the potential to become experts, rather than at the beginners who will turn out to be solid players at the life novice level. By aiming at potential experts, we encourage and speed up the development of potential experts, but we also scare off the future solid life novices.
This is an issue in mathematics as well. It is a well-known truism that any large discussion among mathematicians (not mathematics educators) of elementary and secondary mathematics eduction has a tendency to degenerate into a discussion of promoting exceptionally mathematically talented youth. In the college classroom one has to make a choice between emphasizing the rules of thumb that will be useful to the solid life novice versus promoting the kind of thinking and cognitive development that will help develop a potential expert.
For mathematics, I have taken the position that we should teach in a way to develop the potential expert, with additional encouragement for those who don't yet have the requisite cognitive ability to work very hard to develop them. I teach lessons analogous to this bridge hand, where students have to put together all the ideas they have learned to analyze a situation carefully, keep track of significant amounts of information, pick out the important pieces, and come to a conclusion. It does mean that some students get discouraged and more or less give up. I take this position because I think that life novice level skills in mathematics are not very useful. The rules of thumb one learns to be a better life novice are already all programmed into Mathematica/Maple/Matlab, and a solid life novice will never be anything other than a somewhat defective version of a computer with such software. Also, in our increasingly automated society, it will only be those who have high cognitive skills who will get well-paying jobs and make serious economic contributions, and students need to develop these skills. I might add that there has been some professional cost to me for practicing this position.
For bridge my views are different. People don't learn bridge as part of their education; they learn it as a pastime. It seems crucial for our society that people become smarter; it doesn't seem so crucial that they become expert bridge players. Also, bridge won't survive if it's just the experts who play it, whereas, while mathematics will be less healthy with fewer students, it won't die off completely.
Further thoughts? Anyone want to weigh in from the perspective of yet another subject?
#2
Posted 2014-May-19, 11:34
As for tv, screw it. You aren't missing anything. -- Ken Berg
I have come to realise it is futile to expect or hope a regular club game will be run in accordance with the laws. -- Jillybean
#3
Posted 2014-May-19, 11:54
#4
Posted 2014-May-19, 12:24
#5
Posted 2014-May-19, 12:38
akwoo, on 2014-May-19, 11:29, said:
Win ♥A and cash ♣KA.
- If both opponents follow, then your fourth ♣ is good and you're home.
- If LHO shows out, then you take the marked finesse against RHO's ♣ J x for your contract.
- If RHO shows out, then you cash winners to reach a three-card ending. You're In hand with ♥ J and ♣ Q 8. You need to count only ♣. If LHO keeps fewer than two ♣, then you cash ♣ from the top. If LHO keeps two ♣, then you lead ♥J to LHO's presumed ♥Q to force a ♣ lead from LHO's ♣ J x into your ♣ Q 8.
akwoo, on 2014-May-19, 11:29, said:
akwoo, on 2014-May-19, 11:29, said:
This is an issue in mathematics as well. It is a well-known truism that any large discussion among mathematicians (not mathematics educators) of elementary and secondary mathematics eduction has a tendency to degenerate into a discussion of promoting exceptionally mathematically talented youth. In the college classroom one has to make a choice between emphasizing the rules of thumb that will be useful to the solid life novice versus promoting the kind of thinking and cognitive development that will help develop a potential expert.
For mathematics, I have taken the position that we should teach in a way to develop the potential expert, with additional encouragement for those who don't yet have the requisite cognitive ability to work very hard to develop them. I teach lessons analogous to this bridge hand, where students have to put together all the ideas they have learned to analyze a situation carefully, keep track of significant amounts of information, pick out the important pieces, and come to a conclusion. It does mean that some students get discouraged and more or less give up. I take this position because I think that life novice level skills in mathematics are not very useful. The rules of thumb one learns to be a better life novice are already all programmed into Mathematica/Maple/Matlab, and a solid life novice will never be anything other than a somewhat defective version of a computer with such software. Also, in our increasingly automated society, it will only be those who have high cognitive skills who will get well-paying jobs and make serious economic contributions, and students need to develop these skills. I might add that there has been some professional cost to me for practicing this position.
For bridge my views are different. People don't learn bridge as part of their education; they learn it as a pastime. It seems crucial for our society that people become smarter; it doesn't seem so crucial that they become expert bridge players. Also, bridge won't survive if it's just the experts who play it, whereas, while mathematics will be less healthy with fewer students, it won't die off completely.
Further thoughts? Anyone want to weigh in from the perspective of yet another subject?
#6
Posted 2014-May-19, 12:38
She told me later that she decided that if anyone asked her what she was doing at the party she would explain that she was a waitress at the local bar and I had picked her up on the way over.
Anyway, about overwhelming people . Your math class is different from a bridge forum. As an undergraduate I took classes that I had to take and classes that I was interested in. Sometimes the categories overlapped, but not always. The point is that if a B/I player looks at something and can make no sense of it, probably he just goes on to something he prefers. Your students can't do that, or at least there will be consequences.
Still, I take your point. I have taken on some of Ben's problems but have not had time lately. As near as I can tell, he has me rated as low Intermediate at best. I pretty much roll with this, especially because I really like the problems.
A student was once complaining to me about his teacher in his non-credit math course, the one you take so you can take the lowest level basic course for credit. It turned out that he had been attending a senior level course in Number Theory and was unaware of his error. They were studying quadratic reciprocity and he could not, he told me, understand a word of what the prof was saying. I got this straightened out for him. When I mentioned this fact to the instructor he said, and I kid you not, "Which student was it?"
One more story: My first year in grad school I took this final that was supposed to be three hours long. After four plus hours we were all still working and the professor announced that he had to go home,so we should just draw a line under where we had gotten so far and then take it home and continue. We did that although I had a serious cold and did not do all that much more. A couple of years later a friend who was in the same class with me told me he was making good progress on the second part of question 3 and thought he might be able to get a small paper out of it. But I think he still got stuck because I never saw the paper.
#7
Posted 2014-May-19, 12:41
I think bridge forums are for people interested in learning about bridge. it they were not interested in learning, they would simply log on to BBO and play hundreds of hands for enjoyment rather than study the game.
My philosophy for teaching play is to start with 7NT contracts. The first ones are very easy, just untangle your entries (don't block yourself early ones, active unblocking next), then introduce a finesse, then discovery plays, then some statistics for best suit to go for, then eventually, yes squeezes. For beginners reading this, there are a bunch of the 7NT hands in the early days of the beginner/novice forum. They are entitled "good idea" followed by a number. I have many more of those. NOTE. When the beginner.intermediate thread of old was divided into beginner/novice and intermediate/advanced. the "good idea" problems and many others got moved over to the intermediate/advanced although some of these are way easy.
Then I move to either 6NT, where you can add losing a trick to set up winners, endplays, more entry management, more discovery, more statistical analysis. Hands like this one, and yes, more on squeezes.
After 6NT I move to seven and six of a suit to introduce trump plays, the big ones here are ruffing a suit to set it up, ruffing finesse, dummy reversals, trump coups, trump elopement. In these hands, the idea is not just to pull trumps and then play 7NT, the trumps have to serve a purpose. So trump squeeze makes it way into the lessons.
The idea of using grand slams and slams is that the focus can be narrowed down so the lesson on each hand is clearer. This also explains why I have so many 7NT (earlier series) and 6NT hands. They are very easy for getting across a single point about the play. 3NT hands often have a lot of conflicting issues, but after players learn some of the basic playing principles in a clearer position, coming up with a game plan where you are going to lose quite a few tricks becomes somewhat easier.
This post has been edited by inquiry: 2014-May-19, 15:32
Reason for edit: added note when realized the beginner good idea problems got moved to a different forum
#8
Posted 2014-May-19, 13:05
Perhaps there should be a forum for hands that are intended for teaching. Mostly I think people post hand for discussion, the difference being that it is not seen as a student/teacher relationship. .Your hands are identified as those where you intend to make an instructive point or two, so that mostly takes care of it, but a forum for teaching might work well.
How do we learn? Lots of ways, it seems to me. Sometimes by trying to work out a difficult hand that we would never be given time for at the table, with the idea that the skill developed will still be useful in somewhat simpler hands. Other times by just going over basics. Not difficult concepts, but necessary ones. Generally people can sort themselves.
We have talked a bit before about assessing level. Hands on the I/A forum that you thought were really easy seemed to be a challenge to me and to others that I think are at least my equals. I don't think we all need to change our self rating to low intermediate. This could be more of a problem, psychologically, for the beginner I suppose. I guess that's the point of the OP. They will develop the necessary tough skin in time.
#9
Posted 2014-May-19, 15:00
I agree the beginners who come to the forums are looking to improve. But, at least for most of the real life beginners I know, most beginners looking to improve are looking for simple rules of thumb that will make them better life novices, not for what to them are cognitively overwhelming tasks that set them on the road to expert.
Let me tell a story from a regional tournament a few years ago. I pick up a partner for the day from the partnership desk. A few rounds in, we are defending 4♥. Partner leads the A♦. Dummy shows up with ♦xxx, ♥9xx, and 7 irrelevant cards. I hold ♦KJxxx and nothing else of value. I encourage; partner continues with the Q♦. I overtake and lead the J♦. Partner turns out to be the one who is doubleton in diamonds, and I lead a fourth diamond, setting the contract when declarer decides (erroneously as it turns out) to duck in hand on AKQTxx of trump. (If someone figures out the regional in question and finds the hand record, I don't swear I have even this level of detail right. Maybe spades were trump and the side suit was different. Maybe one of those small trump was actually in dummy.)
Okay - nothing remarkable there. What is remarkable is that partner was pleasantly surprised to have a partner who could count well enough to realize that overtaking the Q♦ was free. We're talking here about counting a single suit at trick 2 when no other suit has been played.
What's the point of this story? I think the situation I just presented is more appropriate as a beginner lesson. Some people might think it's too simple, but partner's reaction suggests otherwise.
(If I don't have my stories mixed up, I believe we got about half of the 5 or so gold points he still needed for Life Master. I don't know (maybe I did know at one point, but I don't remember) if he and his regular partner and teammates did well enough in the knockout the next two days to get the rest.)
#10
Posted 2014-May-19, 15:24
I certainly wouldn't spend much more than an hour learning the rules of Canasta or whatever only to find, at the end, that it wasn't for me. I'm two episodes behind on Game of Thrones as it is.
My experience here is that most of the BBO population is interested in bridge-as-a-pastime, not anything more serious than that. Goes for me too, most of the time.
Quote
Yeah. We have to make it much much easier to get started. I don't think this is the conventional thinking on the subject, though.
#11
Posted 2014-May-19, 18:05
kenberg, on 2014-May-19, 12:38, said:
We had recently a secondary math education major whose understanding of mathematics beyond calculus is akin to an illiterate medieval peasant reciting the Latin mass. As evidence, one professor mentions an incident where he once forgot to start a proof by labeling Proof:. The student asked after class, in complete earnestness, without a hint that he could guess the answer from context (which was obvious), where the statement of the theorem ended and the proof started. Bless his heart - I guess at least he knew that theorems should be followed by proofs.
The student was allowed to graduate with Cs and Ds from upper level courses purely from sufficient rote memorization of lecture. On an exam, he could not even get started on any problem that required something beyond word-for-word regurgitation of something from lecture. If you asked him to produce the proof of statement X, and hinted that this was part of the proof of Theorem Y, he would have no idea which part; the best he could do was produce, word-for-word, the entire proof of Theorem Y. Memorizing that much information without understanding is quite an achievement and undoubtedly required a lot of work, but I don't think it's the kind of achievement we are looking for.
I happen to disagree with my colleagues, and I think that letting this student graduate as a secondary math education major is a disservice to both him and his future students. I think he should have been first given more help in trying to think through the material, then counseled out when it became clear this was impossible, and, failing that, failed out of the major at least a year before he graduated. He needs to find something else in his life he is better at, though I'm worried there isn't any such thing. (Unfortunately, given the shortage of secondary math teachers, we'll probably be seeing the results of his teaching for years.)
#12
Posted 2014-May-19, 18:40
akwoo, on 2014-May-19, 18:05, said:
Luckily, secondary mathematics education does not usually go beyond calculus.
#13
Posted 2014-May-19, 19:58
Vampyr, on 2014-May-19, 18:40, said:
However, teaching mathematics at the secondary level requires the mental flexibility to evaluate and critique nonstandard solutions and provide explanations that are not in the textbook, which is something that this student clearly does not have.
#14
Posted 2014-May-19, 21:37
nige1, on 2014-May-19, 12:38, said:
It's natural for you to identify the lynchpin suit, but for novices it can be an ordeal. After being taught how to mechanically count tricks, some of them can manage if the suits are AQxx opposite KJxx, but when suit lengths are different or an irrelevant honor is missing, they lose sight of where the problem lies.
Promoting small cards posed another challenge. Figuring out that AKQxxxx opposite xxx is seven tricks was hard for them because it requires thinking ahead, and some of them found it hard to visualize things at that level.
Just to give you an idea, one hand we played in class was something like
Axx AKx AKx xxxx
Kxx Qxx Qxx xxxx
where you had to make 3NT, with the defense leading one of the triply-stopped suits. My wife and I were the only pair to attack the xxxx suit, even though there's literally nothing else that could ever work. People just played high cards at random and went down.
So, I think you've overestimating beginners with no potential. If I had to teach Bridge I'd separate people with potential and teach them in-depth from day 1, and teach all the rest the Bridge maxims and correct rules to apply to different bean counts to allow them to enjoy Bridge as a social game.
#15
Posted 2014-May-19, 22:09
For those that are content with doing well in a low level game they can get by on dictums without understanding the underlying logic. Frankly their initial success probably exceeds someone that seeks to understand why dropping the queen with four out is better than finessing.
X can be bridge, chess, maths, law, Torah, bible, history, or especially music.
There's limits to this but it's a reasonable start.
Winner - BBO Challenge bracket #6 - February, 2017.
#16
Posted 2014-May-20, 04:40
I guess there could be novices out there who stumble across the forum and get put off by the discussion level (and some of it is comically advanced) - are these people out there? My guess is that they are not - the type of beginner who can't make head nor tail of inquiry's problem has not surmounted the activation barrier to go looking for answers in the first place.
#17
Posted 2014-May-20, 07:00
1. This is my most serious point: The posting of the hand begins: "Another straight forward hand that should not be a problem for most participants in the BBO forums, explaining why I posted it in this section. ". This opening sentence is a gratuitous insult to anyone who cannot work this out. I think most people who regularly read the Novice/Beginner Forum will not be able to work this out.
2. After giving the problem some thought, and deciding I had a line that would usually lead to a sure solution, I scrolled down for the comments. Fluffy, clearly a novice (I am joking here) weighed in with his thoughts. There were several players commenting who I have had online discussions with, none of the names I recognized were novices. One of them notes that if this is a beginner hand he is going to switch to tiddly-winks. Ben says a few posts down from the original "I am glad that there has finally been some interest in this hand.". Well, yes. No one posted until the non-Beginners took it up. Thjs may say something.
3. The poll attached to the problem asks players to describe the type of play that is required. They are to select from a list including "squeeze" and "endplay". These words are not in the vocabulary of most beginners.
4. If I were going to use this hand as a teaching tool for beginners I would make it a multi-part question:
a. If the Bridge fairy whispers in your ear and tells you exactly how many spades/hearts/diamonds/clubs West holds, but not which cards in those suits, can you make the hand?
b. How can you find out enough about the distribution so that you have a good chance of making the hand?
c. If you follow this line, what problems do you foresee?
I give an improved solution below, but here is what I started with. The improves solution allows for the possibility that W bid 2♥ on a 5 card suit.
Even broken down like this I see it as tough at the assumed level.
What I would hope for in a. is that the preson says "If clubs are 3-2 I can always make this and if they are not 3-2 I can make it if I know who has the long clubs. A beginner who can come up with that is on his way, in my opinion.
For b and c I would hope for (but not really expect from a Beginner): If I play off two rounds of diamonds I know how they split. If W has at least two diamonds then I can play two spades, If W follows, I know, assuming he started with six hearts, that he cannot have four clubs. If W does not follow to both spades then I know the exact shape. The pronblems will arise when W has either 0 or 1 diamonds. If he has no diamonds I will play him for four clubs rather than four spades unless I can find out more but upon reflection I probably can find out more when he holds 0 or 1: . Running all five diamonds (tossing a spade on the last diamond) will put him under pressure. He has played one heart and he will be reluctant to come down to the stiff Q (and I will assume he started with KQxxxx) but he probably will. If he does, I will play off the AK of clubs. If E has four clubs I can finesse, if W has four clubs I can cash my top spades anding in my hand and , assuming W keeps his two clubs, throw him in with a heart. If, instead, he saves Qx of hearts as I run the diamonds then he comes down to five black cards. So I cash two spades and if he follows to both he cannot have four clubs so I play the K and then the Ace of clubs and finesse if I need to. if he shows out in spades then I know the original shape and play clubs accordingly.
I think I have now covered all possibilities, assuming W started with KQxxxx. I did not read the various solutions but I do not believe any Beginner would do (all of) this. At the very least, I do not think a Beginner should be told that it is unlikely anyone reading the problem will have trouble with it.
I guess it is sort of a squeeze/discovery/endplay in that on the run of the diamonds W is pressured to either come down to a stiff heart, leading in some cases to an endplay, or to two hearts, in which case I can find out enough about clubs when I cash the top spades. Nice hand, very nice hand, not at all a Beginner hand and I think the replies are not, as far as I know, from Beginners.
I repeat: Ben is doing this and I am not, so maybe I should just shut up. Nah.
Added: I see by reading the responses one of the respondents does regard himslef as a Beginner. He was quite enthusiastic about the problem. That's great, so maybe it's fine.A Beginner might look at this and say "Fascinating, I can't wait to learn more". Which is pretty much what was said be the responder who classified himself as a Beginner.
I think something such as my part a. above is a good question for beginners. I think b. is useful and some can realize, with guidance, what to do when W holds 2+ diamonds. Coping with 0 or 1 diamonds in a manner where they are confident that they have all they need for a 100% line? Not many, I think.
Better Solution (Added). I think this is right and does not depend on W starting with six hearts:
I started thinking about the possibility that W might have KQxxx. I think it doesn't matter.
T1, Heart A
T2-6, play diamonds, tossing a spade from the board.
T7-8 club K and A. If E held 4+ clubs run the ten and claim 12 tricks If clubs are 3-2 claim 12 tricks. If West hold 4 then:
T9-10 play spades, ending in hand. You now hold Q8 in clubs with T9 (and a spade) on the board., and you hold the J of hearts.
W has f three cards left. If he has pitched a club, cash your clubs. If he still has two clubs then he has only one heart. If he has pitched the ♥ Q (he might) cash your Jack. If he has kept two clubs and the heart Q, throw him in.. Given that he started with the heart Q (highly likely but not certain given the auction) and given that E has shown out on the second club, you know exactly what he has come down to.
The sole requirement here is that W hold the ♥ Q. The bidding doesn't matter, the original distribution doesn't matter.
After I posted tis solution on the forum I looked back at other posts. billw55 had the same solution much earlier. Whatever Bill and I are, I don't think Beginner is correct.
#18
Posted 2014-May-20, 07:35
uday, on 2014-May-19, 15:24, said:
I certainly wouldn't spend much more than an hour learning the rules of Canasta or whatever only to find, at the end, that it wasn't for me. I'm two episodes behind on Game of Thrones as it is.
My experience here is that most of the BBO population is interested in bridge-as-a-pastime, not anything more serious than that. Goes for me too, most of the time.
Yeah. We have to make it much much easier to get started. I don't think this is the conventional thinking on the subject, though.
The Minibridge we use for teaching is without a real bidding phase. You can teach the rules in less than an hour.
"Gamers" will discover finesses and other simple playing techniques by themselves.
When they are interested tell them
- there are more techniques to produce tricks and
- there is more fun with real bidding.
#19
Posted 2014-May-20, 08:30
hotShot, on 2014-May-20, 07:35, said:
Where do you use Minibridge to teach, hotShot? Do you use it as the recommended entre into the game? How do you transition them into players who know about the bidding? How is the teaching done? In person, over N sessions?
#20
Posted 2014-May-20, 09:08
uday, on 2014-May-20, 08:30, said:
I had no time for bridge for several years now, but Minibridge with a simplified bidding is part of the official German bridge material for pupils.
See this article titled "Bridge in 10 Minutes"
http://www.bridge-ve...picture/doc/100
You explain the order of cards, who gets the trick, introduce trump and how to count HCP.
The simplified bidding works this way:
If the player in the first seat has 12+ HCP he says: "I have an opening" (else he passes and the right to open passes on).
His partner writes his hcp and shape an a piece of paper and gives it to the opener. If his side has 20+ HCP Opener sets the final contract,
if his side has less than 20 HCP the player in the 2nd seat get the right to declare the contract after receiving the HCP and shape information from his partner.
There is a table HCP => bidding level and if you don't have an 8 card trump suit you play NT.
Usually you can get people to play their first contract withing a hour (or 1.5 h), with the idea that everyone has played one hands at the end of the first lesson.
The next lessons I used to let them play hands, replaying them with open cards when they finished playing, hinting them how to make better use of their cards.