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Merged No more algebra?

What your books and teachers have failed to explain to you is that you're not supposed to know. Since a definition of a term can only be fully understood by someone who understands the terms used in the definition, it's impossible to define everything. So something must be left undefined. Obviously, we would like to leave as few things as possible undefined, so it's pretty cool that mathematicians have found that it's sufficient for (I think) all known applications of math to leave exactly two things undefined: what a set is, and what it means for a set to be a member of a set.

You probably already understand statements like "2 is a member of the set whose members are 1,2, and 3" and "pi is a member of the set of real numbers". If you do, you already understand the two undefined concepts almost as well as a mathematician. The next step for someone learning about sets would be to learn in what ways you are allowed to construct new sets from the ones you already have.

Hmmm!!! Thanks, I think. Interesting because, if I remember rightly, they are now using the term "set" in the "new" math - early elementary and upward. I remember explaining it to a group of fourth-graders as like a set of dishes. They know what a set of dishes is. New Math? They also use "input" and "output" for "plus" and "minus". But, first came "add to" and "take away" which make much more sense to a six-year-old. Easy steps first?
 
As a chemical engineer from 1950-1990, my dad had to work out a lot of equations by hand and cheap TI calculators. When younger engineers would come up with results, my dad and his older colleagues would glance at the value and say, "That can't be right!". The young engineers would say, "But that's what the computer gave me."

Sort of like me at the corner store last weekend. Bread, tomatoes, two half-liter cans of beer -- €65 and change, please.
 
Where did it start? In kindergarten. It has become verboten to fail any child in school. It might damage his psyche. So, the first grader is too immature to grasp what is being taught. Instead of holding him back, you move him on into second grade. He gets "babied" along there with hopes he'll catch up. Not so. By third grade, he is lost. By fourth grade, he has learned to say 'you can't make me do homework'.

Not in my school district, parents can refuse retention a certain number of times, but gosh I can think of four students who were specifically retained in kindergarten. (In the last two years)

:)
 
In the middle '50s, there was a 14 year old lump in the 4th grade in Bowling Green VA.
That was as far as he wanted to progress in school.. waited to be the legal age to stop going to school at all.
16?
Somewhat of the bully in the 4th grade. :)
 
Not in my school district, parents can refuse retention a certain number of times, but gosh I can think of four students who were specifically retained in kindergarten. (In the last two years)

:)

They can also be retained here but only with the parents' consent and many will not give that consent.
 
He may be trying to say that but I still see it as part of the general dumbing down of education.

Weird, how there are so many people complaining about the supposed dumbing down, and also so many people complaining about how much demanding school has gotten. I have heard so much about how kindergarteners don't have any time for coloring/recess/etc. anymore, because we're pushing kids so hard, so fast.
 
Weird, how there are so many people complaining about the supposed dumbing down, and also so many people complaining about how much demanding school has gotten. I have heard so much about how kindergarteners don't have any time for coloring/recess/etc. anymore, because we're pushing kids so hard, so fast.

In other words, the entire system has gone berserk? Remember, we have many different systems and many different attitudes. It isn't as easy to guide or control education in a country the size of ours as it is in England/Wales or other smaller places.
 
My dad's a civil engineer, and similar things have happened to him. One design spec came in with a triangular room whos corners added up to more than 180 degrees. Took my dad fifteen minutes to explain to the kid that this couldn't possibly happen, and that the structure could not be built.


Maybe it was a very large room?
 
Weird, how there are so many people complaining about the supposed dumbing down, and also so many people complaining about how much demanding school has gotten. I have heard so much about how kindergarteners don't have any time for coloring/recess/etc. anymore, because we're pushing kids so hard, so fast.

Hard work=/=effective work. You can bail water by hand in a sinking boat all day, and all you'll do is drown faster. Or, you can flip a switch and start a bilge pump, put forth minimal effort, and get home safely. Similarly, a lot of what students are expected to do these days simply isn't effective--it's busy work, or so inconsistent the students don't know what's going on. My wife (who starts teaching in a week) keeps saying how you can't expect kids to sit through an hour-long lecture--despite the fact that she's teaching 9th graders and by the time I was in the 9th grade I'd learned how to handle much longer lectures. The difference is made up in after-school workload.

Also, teachers aren't teaching subjects anymore--classes are basically year-long study sessions for aptitude tests. I'm not saying this for fear-mongering or the like; it's the simple truth. In California, at least, teachers' pay and job security is determined, in large part, by how well their students do on the aptitude tests. So teachers will take those tests and use them as a guide for planning their lessons. Given how much they have to cover, they can ONLY use those tests as guides. Thus, the entire school year is nothing more than studying for a single test. And may whatever gods you believe in have mercy on your soul if you suggest that some students simply aren't going to pass! I've made that argument, backed by statistics and pedegogy references (it's widely known that until the student takes ownership of the material there's nothing a teacher can do to make the kid learn), until I'm blue in the face, but teachers simply can't listen. They're told that if X% of their students don't get Y% right on their exams (varies a bit depending on the school) they're out.

So we're basically never teaching children to focus, and we're hamstringing our teachers by evaluating their performance via poorly-thought-out exams.
 
Hard work=/=effective work. You can bail water by hand in a sinking boat all day, and all you'll do is drown faster. Or, you can flip a switch and start a bilge pump, put forth minimal effort, and get home safely. Similarly, a lot of what students are expected to do these days simply isn't effective--it's busy work, or so inconsistent the students don't know what's going on. My wife (who starts teaching in a week) keeps saying how you can't expect kids to sit through an hour-long lecture--despite the fact that she's teaching 9th graders and by the time I was in the 9th grade I'd learned how to handle much longer lectures. The difference is made up in after-school workload.

Also, teachers aren't teaching subjects anymore--classes are basically year-long study sessions for aptitude tests. I'm not saying this for fear-mongering or the like; it's the simple truth. In California, at least, teachers' pay and job security is determined, in large part, by how well their students do on the aptitude tests. So teachers will take those tests and use them as a guide for planning their lessons. Given how much they have to cover, they can ONLY use those tests as guides. Thus, the entire school year is nothing more than studying for a single test. And may whatever gods you believe in have mercy on your soul if you suggest that some students simply aren't going to pass! I've made that argument, backed by statistics and pedegogy references (it's widely known that until the student takes ownership of the material there's nothing a teacher can do to make the kid learn), until I'm blue in the face, but teachers simply can't listen. They're told that if X% of their students don't get Y% right on their exams (varies a bit depending on the school) they're out.

So we're basically never teaching children to focus, and we're hamstringing our teachers by evaluating their performance via poorly-thought-out exams.

You have it right. When will those in charge wake up to it? I've decided never.
 
Just to add to the testing idea, it gets even worse.

The local elementary school where I live is regarded as a very good one...one of the reasons we moved where we did. They scored high on the aptitude tests. However, the state expects improvement every year. Year before last they passed something like 95% on the standardized tests, and almost unheard of number. Last year, though, they only got about 90% (note, I can't recall the exact numbers, but they were +/- 5% from those given here). Because they lost 5%, they are losing some funding.

Even at the 90% mark, they're still one of the highest ranked schools around. But because they lost percentages they were punished. So not only must teachers test the test (and only the test, and often don't even have time to cover all of that), they have incentive (at least here) not to teach it too well, or they'll be up the creek the next year.
 
Can't we do this with almost every subject? Is knowledge of ancient South American society necessary? Is knowledge of The Great Gatsby necessary?

SA society - for me yes - at least aspects of it. Not needed for general cultural literacy

The Great Gatsby - yes for anyone who does not want to seem culturally illiterate in the US - it's a classic and a meme for a US (and British) "type".
(Also: Scarlet Letter, Moby Dick, Walden, Uncle Tom's Cabin, Call of the Wild,Adv. of Tom Sawyer, Huckleberry Finn.......)
 
I disagree because I work in K-5 and have a son in high school. the fact that they may not include Shakespeare is not a rule out in favor of dumbing down the curricula. The schools may be trying something more accessible, I am a fan of language and reading, I find Shakespeare difficult and boring many times. Hamlet is about the easiest read outside of some of teh comedies.

Now how many colleges have changed that I don't know (I suspect an outlier), but I am familiar with the books my son reads in high school, they frequently cover modern but difficult material none the less. Beloved is on his list this year. Now the books that the district requires for everyone in a grade level are a little less challenging by and large There Are No Children Here, The Absolutely True Diary of a Part Time Indian, and The Kite Runner. And that last one is an optional read with an opt out alternative.

But in his freshman lit class at HS they read some challenging material like the Odyssey and Things Fall Apart.

:)


With Shakespeare, just subtly hint that he liked to put in naughty jokes - hidden in the text. Romeo and Juliet being a lovely example thereof.
 
Like Spell Check but far more serious. A teacher once asked me to look at a problem that she and the student "knew they had the right answer to" but the computer kept telling them they were wrong. It involved decimals. I looked at it. No decimal point. I suggested they put the decimal point . "Oh, that isn't necessary", said the teacher. I insisted. They did. The computer said 'correct'. Always that human element.

Yes, computers can be wrong and so can simple calculators. Electronics goes haywire like anything else. Students should not be allowed calculators of any kind until they understand the concept. Then they'll spot the error when they see it. But can you convince anyone of that?
Not a math whiz here - and in an emergency year at achool essentially taught as an extension of the actual teacher (who was in another room with AP students) a math loaded Phys 1 Honors class. The kids were not thrilled and considerd it bad for them until the brightest of the students handed his paper in the 4th or fifth day of class and I looked at his calculations re: the initial drawing of the vectors and told him his answer was wrong. His response: But you don't even know how to do this.!!! Mine: No, but I do know that your problem has a force moving east and a force moving north acting on your object but your answer has the object moving south and west. I'd be checking the signs you entered. Hilarity ensued.( A year plus a bit later the same student asked a question out in the hallway re: a physiology problem which I answered correctly. He was never surpised after that - sometimes it just takes a little time:):) and paying attention:):) .
 
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With Shakespeare, just subtly hint that he liked to put in naughty jokes - hidden in the text. Romeo and Juliet being a lovely example thereof.
.
Some of her lines are quite amusing when read out loud by a teenage boy... in class... :)
 
fuelair said:
th Shakespeare, just subtly hint that he liked to put in naughty jokes - hidden in the text. Romeo and Juliet being a lovely example thereof.
The way my family did it was, my father let us read his essay on how R&J was Shakespeare's greatest comedy. My older sister and I wrote essays like that just to watch our English teachers twitch. They were very well-written and well-supported essays, which was what caused the twitching--we were wrong, and the teachers KNEW we were wrong (because the book said so), but they couldn't find any flaws in our reasoning!

Tsukasa Buddha said:
Can't we do this with almost every subject? Is knowledge of ancient South American society necessary? Is knowledge of The Great Gatsby necessary?
On school my wife interviewed with bragged about their high university placement rates, and that they push ALL students to go to a university. This, to me, is absurd. Sure, my job requires a university education; no other environment will work to teach me what I need to know. But that's just me. I also had a good friend growing up that wanted to be a mechanic. That's all he wanted out of life--to work on cars. EVERYTHING he did was with that in mind, just as everything I did was towards my goal. Going to a university would have been a torturous waste of his time. He went to a two-year tech school and worked part-time in a small-town garage instead, and now builds race cars for a living. There are also innumerable people I grew up with who have degrees in business, or education, or whatever, and who are professional farmers. They went to school because they were expected to, wasted four years of their lives, then did something that they could have learned better under an apprenticeship, or even just working for their parents (farming tends to run in families where I grew up).

The whole point of education, after a certain point (I'll go so far as high school), is to get someone a job. Some jobs simply don't require as much education as others, and forcing kids to go through college--which is what the testing is really designed to do--is a waste of their time.
 
Hmmm!!! Thanks, I think. Interesting because, if I remember rightly, they are now using the term "set" in the "new" math - early elementary and upward. I remember explaining it to a group of fourth-graders as like a set of dishes. They know what a set of dishes is. New Math? They also use "input" and "output" for "plus" and "minus". But, first came "add to" and "take away" which make much more sense to a six-year-old. Easy steps first?

Uhm, interesting, "new" math - with sets and such (quite specifically) was introduced in many public schools around 1963-7. I remember Freshman math in college was also doing that because it was the first I had of such. Parts of it were fun. It interests me that it is now being re-introduced.Means - as often happens - someone is making money remembering how the did something a while ago. (But, it is a little late, it should have recycled in 2005).
 
SA society - for me yes - at least aspects of it. Not needed for general cultural literacy

The Great Gatsby - yes for anyone who does not want to seem culturally illiterate in the US - it's a classic and a meme for a US (and British) "type".
(Also: Scarlet Letter, Moby Dick, Walden, Uncle Tom's Cabin, Call of the Wild,Adv. of Tom Sawyer, Huckleberry Finn.......)

In some cases, maybe the word "necessary" isn't the right word. Much of what we learn can simply enrich our lives, making living more interesting and more fun. We specialize in a certain field, learn all we can about it, keep learning more with nose to grindstone but is that all? If all a CPA knows is how to balance books, manage investments, pay taxes, won't he eventually get so burned out with the "same old" that he'll fail at his job or give it up, or become, not just a total bore, but himself totally bored when in others' company or a totally different environment. We've all heard stories of the genius who is gifted in one field but cannot figure out how to do the simplest household task.

South America? Some of our ancient native Americans actually came from Central America and, before that, South America. For a teacher or geography or history, such knowledge is "necessary". For the rest of us, it adds to our knowledge and understanding of our world. Then comes Gavin Menzies who wants to change the entire scene and tell us the Minoans discovered America first. (Just an example of enrichment driven by curiostiy)

Curiosity comes naturally to the human being. Anyone who has raised a child knows all about "why is....". Somewhere along the line, that "why is" gets squelched as we force the child to conform.

I'm sorry. I'm going on too long but the word is "enriches" our lives, gives us more things to think about and enjoy. I shall be eternally grateful for the broad education that I received. I won't say I was "forced" to study so many fields (the basics, that is). These subjects were required but I am thankful that I had them.

It does have one disadvantage, though. The more you delve into so many subjects, the harder it is to choose your life profession.
 
The whole point of education, after a certain point (I'll go so far as high school), is to get someone a job. Some jobs simply don't require as much education as others, and forcing kids to go through college--which is what the testing is really designed to do--is a waste of their time.

I agree with you and I think that's really sad. I'm one of those who had no interest in college when I was in high school. I wanted to be (and managed to become) a dancer. That's all I ever wanted. Admittedly we start working much younger than people in other fields, but by the time I was 21 I had the career I wanted. But I also had developed a burning intellectual curiosity about pretty much everything I didn't know. As a teenager I didn't know I would be interested in ethnomusicology or Andalusian poetry or geology. All I wanted was dance. Why waste my time in school?

Eventually that curiosity led me to try college (lit major,) a different grad program, field research and travel, and finally teaching dance and being a late-in-life mommy.

I took off several years between what would have been the end of high school and the start of college. I think the break made me realize how badly I really DID want to study something on a deeper level than we got in high school -- even if it wasn't dance. Maybe taking that break, of at least a year or two, should be a recommendation for kids who think they don't want a higher education?

And dangit parents, LET your kid major in one of the liberal arts!! Don't encourage them to study communications or business (or for crissake EDUCATION) as a "fallback career." Maybe that's the trouble with some teachers -- they wanted to be musicians but Mom and Dad made them major in education? Just the kind of people I want teaching my kid. :/
 
The whole point of education, after a certain point (I'll go so far as high school), is to get someone a job. Some jobs simply don't require as much education as others, and forcing kids to go through college--which is what the testing is really designed to do--is a waste of their time.

Our high school had two programs: academic for those wanting (or showing aptitude) to go on to university and technical for those wanting to follow a trade (or showing no college aptitude). Once in a while, a mistake can be made doing this but it really is a good plan. Some who go into a trade will go on to college later in life. Most will be perfectly successful as mechanics, carpenters, etc. And don't we need those? Whatever would a doctor do if he had to repair his own car, re-wire his own house, keep the streets in his neighborhood clean and the sewers flushed out. Everybody needs everybody.
 

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