Comment by graycat | Hacker News Reader

Comment by graycat | Hacker News Reader

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> Who or What Broke My Kids?

From the OP, sounds like heavily that teacher did. Let's see why:

> understanding that all probabilities occur between zero and one

Better would be, "a probability is a number between 0 and 1 with both 0 and 1 possible".

Try not to use "occur" here because if event A is "it rains" and it does rain, then we say that "event A occurred". So, it is better wording to say that a probability "is" than to say that it "occurs".

> differentiating between likely and unlikely events

Using the word 'differentiating' here is not good because (1) it is crucial in calculus where it has a quite different meaning and (2) it is just too long for the simple concept of, say, 'identifying' likely and unlikely events.

The worst is,

> The basic premise of the activity is that students must sort cards including probability statements, terms such as unlikely and probable, pictorial representations, and fraction, decimal, and percent probabilities and place them on a number line based on their theoretical probability.

I have no idea what is intended here! Probability theory was the main foundation of my Ph.D. in engineering from my research in stochastic optimal control, and I can't make much sense out of the teacher's statement. Calculating probabilities of poker hands would have made much more sense. Or, just for a start:

We shuffle a standard deck of 52 cards and pick the top card. What is the probability

(a) the card is the queen of hearts?

(b) the card is a king?

(c) the card is diamond?

(d) the card is a spade?

(e) the card is a face card?

Suppose that first card was none of (a)-(e), and we pick the next card from that deck. Now what is the probability of each of (a)-(e)?

Or:

We flip a fair coin five times. What is the probability we get Heads exactly three times?

> where they can solve any computation problem with technology with no issue.

I wish that were so! I guess the teacher has not heard of the problem in the set NP-complete and how common such problems are in business planning and scheduling.

> the probability was 50% since it would either rain or not

Uh, can we place some real money on that!!!!!!

Your questions are on discrete probabilities with knowable objective answers (cards/coins/dice), but the teacher also needs to teach the sense that there are continuous probabilities with fuzzy subjective answers (weather/real life events).

This may be one source of the teacher's frustration: most likely the students are answering the question "what's the probability of rain tomorrow?" as though they are guessing the teacher's password "umm... is it 0.5?", as the teacher has effectively taught them to, when in fact they are being asked to have their own opinion.

For your first paragraph, I was trying to teach a little about probability. For the probability of rain, I mentioned that, and my mention implied the good lesson there: We can assume that there really is a probability of rain, that is, it definitely exists. Now, especially for deciding to place a bet, we could get an estimate of that probability. The 50% is a first cut estimate with some curious properties about 'total ignorance' but otherwise poor. So, how the heck to get an estimate? Likely the best practical way was by the student seeing a weather report on the news. Otherwise, for, say, the probability of rain of any day in, say, August "We might, what, class? Anyone? How might we get an estimate of that? ...?"

Or, "Billy, what company makes iPhones? Billy, you can't get the answer by teasing Sandra. Mary? Right, Apple! Okay, suppose we buy 100 shares of Apple stock today and sell it seven days from now. What is the probability we make over $1000? Assume that this probability exists and we want to estimate it. People especially good at such estimates can become among the richest in the world, fairly quickly. So, how might such an estimate be made? Information? Any ideas? Anyone remember the motorcycle, airport, and airplane in the movie 'Wall Street'? What was the role of 'information' there for an estimate of the probability that the stock of the steel company in Pennsylvania would go up a lot, soon? Anyone? Sandra?"

The point of the lesson/activity is to evaluate whether the students understand that 1/8, 0.35 and 50% are comparable things. It wouldn't be a great idea to assume that the preponderance of 7th graders have mastered this.

If you click through to the pdf, the language in the standards is more careful, so it's a little easier to make sense of.

> It's been a while for me, but I thought that that was fifth or sixth grade!

For the seventh grade I remember: "A race track is 2 miles around. A car travels the first half at 30 MPH. How fast does the car need to travel the second mile so that the average speed around the whole track is 60 MPH?"

Infinte speed! Mathematically but not physically possible.

You got it! Yup, it was a trick question! It took the class about 40 minutes before the first student got it! But the class didn't have any trouble comparing 1/8th and 50%.

Are you disagreeing with my assessment or just riffing on how much better your class was doing?

I wouldn't want to speak real confidently about things that happened 20 years ago, especially my 10 year old assessments of the mental states of other 10 year olds.

You wrote:

> The point of the lesson/activity is to evaluate whether the students understand that 1/8, 0.35 and 50% are comparable things.

It appeared that the teacher, in the 7th grade, was trying to teach probability, and your point about "1/8, 0.35 and 50%" is not not significantly about probability. Further your point about "1/8, 0.35 and 50%" is too elementary for the 7th grade. Uh, at one time I was in the 6th grade, and the 7th, and even, could one believe, the 8th and do remember some of it!

My 7th grade teacher was quite comfortable giving that little puzzle problem and letting the class spend the whole period on it. It was a good little lesson.

It appears from this thread and some other sources, e.g., from North Carolina, that probability is too difficult for most of the K-12 faculty. So, I gave some easy lessons on how to teach elementary probability.

I've been a student, am well qualified in probability, and have done a lot of teaching. I know fairly well what the heck I'm talking about.

Sorry, but that 7th grade teacher was not doing well.

Also the remarks above in this thread -- I tried to be nice and not mention them -- on "continuous probabilities" and "fuzzy" need to be flushed: Some probability distributions are continuous, but the 'probabilities' themselves are not. That is, we know in very fine detail just what 'continuous' means and what a 'probability' is, and 'continuous' does not apply to a 'probability'.

Further, 'fuzzy' is from a quite different subject. Saying 'fuzzy' seems to imply that maybe some probabilities do not really exist; no, this is a fundamental error, and quite serious. Instead, with meager assumptions we can assume that probabilities always exist; the issue, then, can be finding numerical values for the probabilities, and for that we usually have to make an 'estimate' and that is mostly in the field of statistics and usually makes use of at least the weak law of large numbers. That we have to make an estimate does not justify 'fuzzy'.

From the OP, I can believe that the 7th grade students are up to understanding probability but that the OP is not and is not up to teaching it. Sorry 'bout that.

It appears that the K-12 teachers have been in an echo chamber far too far from the solid material in US universities and now are frequently circling their wagons to defend themselves from attacks on their, let me pick the right word, incompetence. Instead, the teachers should learn some probability. I suggest texts by M. Loeve (long at Berkeley), J. Neveu (from Paris and a Loeve student), K. Chung (long at Stanford), L. Breiman (a Loeve student and long at Berkeley), or E. Cinlar (long at Princeton)? To read these texts, start with, say, W. Rudin, 'Principles of Mathematical Analysis' (at least once used in Harvard's Math 55), the first half of W. Rudin, 'Real and Complex Analysis', and H. Royden, 'Real Analysis'. Royden was long at Stanford. To read those books, be a college math major in a good program.

Then we can talk more about probability and how to teach it. In the meanwhile, if I had a student in that 7th grade class, I'd insist to the principal that the class receive some competent instruction in probability from a different teacher.

Probability is a nice subject, and it is possible to do a good job with an elementary introduction, but the OP showed that the content of the teaching was a mess. E.g., there was "percent probabilities" and "theoretical probability", and the informed mind boggles. With such teaching, probability will be several times more difficult than necessary; with such teaching, the students are done real harm and later will have to "unlearn what you have learned". So, the teaching is not just babysitting but harmful babysitting.

And we pay real estate taxes for such garbage?

Am I making myself more clear?

You were clear enough before. You still hand wave aside the question about whether the majority of the students are ready for the material (this is separate from the question of whether they should be).

(I agree that the comparison is not probability, but understanding the comparison is what makes probability useful in everyday life...)

> hand wave

You are are hand waving that 7th grade students are not yet ready for 5th and 6th grade work.

Why the heck not?

If we take your hand waving seriously, then there are problems much more difficult and serious than elementary probability.

I have no patience with your assumption: If I had a child in such a class, they'd be home with home schooling or some such alternative before the teacher first touched chalk to the board. No patience at all. Can't build a strong house on a rotten foundation.

The school I went to expected the students to keep up with the right material. I have no patience with lowering the standards to meet poor students.

> understanding the comparison is what makes probability useful in everyday life

Where can one get the really strong funny stuff someone needs to be smoking to assume that such a triviality is "useful"? That "comparison" is just triviality from trying to bend education down to students not ready for 7th grade work. You are welcome to pursue such things if you want, but any of my children would be out'a there and home schooled, charter schooled, privately schooled, etc. in a nanosecond. The teacher, the principal, and the school board would all hear from me loud, clear messages.

There are some good reasons for a local school board: Parents can scream bloody murder at incompetence and trivialities. E.g., my father in law was on his local school board, and my wife was Valedictorian, PBK, Woodrow Wilson, 'Summa Cum Laude', two years of NSF fellowship in one award, and Ph.D. There wasn't a lot of patience with grotesque incompetence.

My father got transferred to a new city and for a house first he looked at the schools. He picked what was by a wide margin the best school in the city and then picked a house in the district of that school. It was a decently good school although could have been much better.

We need much less patience with incompetence. "No child left behind" can't be permitted to mean leaving all the children behind.

You seem to be reading positions into my statements, positions that I don't mean to put into them.

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