In simple term, what was "new math?"
Later in high school I asked a math teacher, who was just a sub that day and blowing off time in PASCAL class, about "new math." Her reply was, "We have had 2 or so "new new maths" ago.
Doesn't answer the question. I've looked it up in wikapedia and seen that it involves "set theory" and do remember some first-grade "set" problems involving circling like sets.
I still don't quite grasp it all. I'm not an idiot but was wondering if some of you math folks could describe what "new math" was. Maybe some of you were older than 10 like I was when exposed to it all.
Keep in mind, that was a REALLY LONG TIME AGO for personal memories. I'm 55 now, I was 11 then. As a personal memory, not from looking around the internet, I remember Miss McCarthy ending lessons with, "What does this teach us?" Or, "What have we learned from this?" Those were probably moments where we all sat there wondering what the heck we were supposed to say, but I don't really remember. I do remember that we got taught sets after we'd already learned basic arithmetic; sets seemed really simple and dumb. They were introduced as a way to understand arithmetic. The relationship to higher mathematics wasn't really introduced, they were just another thing to learn. I do recall one school year ending right as we started getting into some higher concept, I don't remember what it was; 7th grade, Mrs Garcia. I always thought that she'd dragged the lessons out to end there because she didn't understand anything beyond that. 8th grade started with simple algebra, and diagramming equations. I don't know if diagramming equations was part of before new math, but I thought it was really cool that a circle could be shown as an equation.
Math was always math, New Math was a way of teaching it.
Quote:Some of you who have small children may have perhaps been put in the embarrassing position of being unable to do your child's arithmetic homework because of the current revolution in mathematics known as the new math. So as a public service here tonight I thought I would offer a brief lesson in the new math. Tonight we're going to cover subtraction. This is the first room I've worked in a while that didn't have a blackboard so we will have to make due with more primitive visual aids, as they say in the "ad biz". Consider the following subtraction problem, which I write up here: 342 - 173.
Now remember how we used to do that. three from two is nine; carry the one, and if you're under 35 or went to a private school you say seven from three is six, but if you're over 35 and went to
Public school you say eight from four is six; carry the one so we have 169, but in the new approach, as you know, the important thing is to understand what you're doing rather than to get the right way. Here's how they do it now.
You can't take three from two, Two is less than three, So you look at the four in the tens place.
Now that's really four tens, So you make it three tens, Regroup, and you change a ten to ten ones, And you add them to the two and get twelve, And you take away three, that's nine.
Is that clear?
Now instead of four in the tens place You've got three, 'cause you added one, That is to say, ten, to the two, But you can't take seven from three, So you look in the hundreds place.
From the three you then use one To make ten ones... (and you know why four plus minus one
Plus ten is fourteen minus one? 'cause addition is commutative, right.)
And so you have thirteen tens, And you take away seven, And that leaves five...
Well, six actually. But the idea is the important thing.
Now go back to the hundreds place, And you're left with two. And you take away one from two,
And that leaves...?
Everybody get one? Not bad for the first day!
Hooray for new math, New-hoo-hoo-math,
It won't do you a bit of good to review math.
It's so simple, So very simple, That only a child can do it!
Now that actually is not the answer that I had in mind, because the book that I got this problem out of wants you to do it in base eight. but don't panic. base eight is just like base ten really
You're missing two fingers. shall we have a go at it? hang on.
You can't take three from two, Two is less than three, So you look at the four in the eights place. Now that's really four eights, So you make it three eights, Regroup, and you change an eight to eight ones, And you add them to the two, And you get one-two base eight,
Which is ten base ten, And you take away three, that's seven.
Now instead of four in the eights place You've got three, 'cause you added one, That is to say, eight, to the two, But you can't take seven from three, So you look at the sixty-fours. "sixty-four? how did sixty-four get into it?" I hear you cry. Well, sixty-four is eight squared, don't you see? (well, you ask a silly question, and you get a silly answer.)
From the three you then use one To make eight ones, And you add those ones to the three,
And you get one-three base eight, Or, in other words, In base ten you have eleven,
And you take away seven, And seven from eleven is four. Now go back to the sixty-fours,
And you're left with two, And you take away one from two, And that leaves...?
Now, let's not always see the same hands. One, that's right! Whoever got one can stay after the show and clean the erasers.
Hooray for new math, New-hoo-hoo-math, It won't do you a bit of good to review math. It's so simple, So very simple, That only a child can do it!
Come back tomorrow night. we're gonna do fractions.
Now I've often thought I'd like to write a mathematics text book because I have a title that I know will sell a million copies. I'll call it tropic of calculus.
I never understood new math. I taught myself algebra and so that school year they thought I knew what I was doing. One complex question stumped most members of the class, I had, as usual, not done the homework but when called upon I correctly guessed "n equals minus two-thirds" which astounded the whole class and most certainly astounded me!
The only problem with mathematics was, as always, the math teachers and the absolute boredom of school.
What I learned about math and school in general is that a good teacher trumps nearly everything else. One math teacher I had tore up the curriculum for that year and re-ordered it so it made logical sense. That was my best year at math
Quote: FleaStiffNew math was largely a term for set theory. Sets have been morphed into crisp sets and fuzzy sets. Fuzzy being a determinant of set membership based upon semantic concepts such as "large number" or "close" or the like. The "set" of people in a room might include people standing in the doorway or people who've just left the room or who are usually in that room but are not now. This embraces concepts of probability as to existence of a member of a set.
I never understood new math. I taught myself algebra and so that school year they thought I knew what I was doing. One complex question stumped most members of the class, I had, as usual, not done the homework but when called upon I correctly guessed "n equals minus two-thirds" which astounded the whole class and most certainly astounded me!
The only problem with mathematics was, as always, the math teachers and the absolute boredom of school.
OK, I've read about "set theory" a few times and I remember in first and second grade or so looking at "sets." We would "circle" the "empty sets" which were groups of nothing. Or circle how many cats, how many kittens, how many cats with kittens. Nonsense like that.
But what is (was?) so good about this idea? I can se its use for marketing purposes-say I want to know how many people in my Las Vregas casino "Arizona Duffman's" who are sports bettors AND poker players but not BJ players to market them to the more profitable BJ tables since they are gamblers. Now, is this a good example of "set theory?"
If it is, why on earth is (was) this so important that they built a "new math" around it?
Yes, I know "new math" didn't work and it is unlikely that any "new math" will ever beat the way we teach arithmitic now. But from the prespective back then, why in simple terms, was this thought a good idea, other than to sell new textbooks?
Basically, one approach to mathematics is to say it's just a particular application of logical principles, one of many formal systems. A formal system is a logical system that has precisely defined symbols, axioms, and rules. From the starting definitions, you can build out increasingly complex theorems that will eventually give you all the rules of mathematics. Set theory is integral to defining mathematics formally, hence its emphasis in the curriculum.
New Math was also trying to get across the notion that math as most people know it is just a very small portion of the study of math. So there is nothing special about our representation of a number, hence the inclusion of math in other bases besides 10 -- once again, trying to get children to think very abstractly about mathematical and logical concepts.
I can kind of see why the idea would hold appeal, because most adults (even the educated ones) have a very limited understanding of the nature of math and logical systems. If you can teach them early on higher concepts, then it might be easier to teach them the specific applications. However as we learned it didn't work particularly well.
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Of course some Eastern European countries like Russia, Ukraine and especially Hungary had been excelling in math education for one hundred years.
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A lot of concepts were introduced but some got more attention than others. "Set theory" has always been singled out. It's interesting to note that the Nazi's hated set theory and would murder the professors by tossing them off balconies. It was termed "Jewish mathematics" especially because of it's association with Cantor. The idea of mathematics being controversial goes way back in history to the Greeks who believed that irrational numbers went against God's will. When they discovered that the diagonal of a unit square was irrational (sqrt(2) in modern language), they tried to hush it up. There is a famous story of a man who threatened to reveal the truth on a boat, and was drowned by his friends. Ultimately the unwillingness of Greeks to accept irrational numbers killed their advancement in mathematics.
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Before "new math" people probably didn't routinely say "decimal" since they didn't know any other base systems. You didn't have binary and octal. The only exposure to non-decimal systems was monetary in the British system of pounds and pence or the old Spanish system of pieces of eight (two bits equals a quarter).
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General abstract algebra principles like commutative and transitive were introduced since they were of such importance to modern physics. These concepts were subject to some of the greatest ridicule.
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I find it interesting that most people with a high school education in mathematics are familiar with the terms arc, secant, and tangent and complementary angles from geometry, and at the same time they are familiar with sine, secant, tangent, and cosine, ... but they have no idea why the same words are used for trigonometry as for geometry.
Here are two of his more light-hearted songs, appropriate for this math topic:
I fear students getting new text books in the next few years will find they are filled with utter disinformation.
Quote: ChumpChangeI was among the last of the boomer generation and we were getting new books to replace older books that were at least a decade old or older. The new text books revamped what older books taught. In what way, I don't know. It just felt good to get new text books.
I fear students getting new text books in the next few years will find they are filled with utter disinformation.
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They've been filled with misinformation and disinformation for a couple of decades at least. Texas and a few other higher-thinking states are straightening that out.
There has been no need to change mathematics books for schoolchildren for over 100 years. Real math, taught properly, does not change. It's really a bit of a scam, where book publishers know these books can be used indefinitely by a school system (and they once were. I remember getting textbooks in elementary school which were signed and dated by kids who were there 50 years prior.) and they want to sell more, so they issue a new edition every few years. Planned obsolescence.
They're also dumbed down, but complicated. I've seen recent kids textbooks with rather difficult concepts in it, but that can't be used as a foundation for the canonical math used in the sciences. I want to see classical geometry and the trigonometry that descends from it, algebra, polynomials, simultaneous equations, matrix operations- not some thing where you estimate what percentage of the odd numbers are prime as long as it's Tuesday. Kids who learn only that kind of thing are not going to be prepared for traditional higher education, and I do not believe that is unintentional.
Quote: AutomaticMonkey
There has been no need to change mathematics books for schoolchildren for over 100 years. Real math, taught properly, does not change. It's really a bit of a scam, where book publishers know these books can be used indefinitely by a school system (and they once were. I remember getting textbooks in elementary school which were signed and dated by kids who were there 50 years prior.) and they want to sell more, so they issue a new edition every few years. Planned obsolescence.
link to original post
Back when I hung out with math teachers socially*, they were more focused on new developments in pedagogy making it into new grade school textbooks, not new math.
These same folks were indeed writing the actual new math in their research offices, but they weren't even vaguely considering inflicting it on anyone under 15 years of age.
Quote: AutomaticMonkeyQuote: ChumpChangeI was among the last of the boomer generation and we were getting new books to replace older books that were at least a decade old or older. The new text books revamped what older books taught. In what way, I don't know. It just felt good to get new text books.
I fear students getting new text books in the next few years will find they are filled with utter disinformation.
link to original post
They've been filled with misinformation and disinformation for a couple of decades at least. Texas and a few other higher-thinking states are straightening that out.
There has been no need to change mathematics books for schoolchildren for over 100 years. Real math, taught properly, does not change. It's really a bit of a scam, where book publishers know these books can be used indefinitely by a school system (and they once were. I remember getting textbooks in elementary school which were signed and dated by kids who were there 50 years prior.) and they want to sell more, so they issue a new edition every few years. Planned obsolescence.
They're also dumbed down, but complicated. I've seen recent kids textbooks with rather difficult concepts in it, but that can't be used as a foundation for the canonical math used in the sciences. I want to see classical geometry and the trigonometry that descends from it, algebra, polynomials, simultaneous equations, matrix operations- not some thing where you estimate what percentage of the odd numbers are prime as long as it's Tuesday. Kids who learn only that kind of thing are not going to be prepared for traditional higher education, and I do not believe that is unintentional.
link to original post
Texas has the 34th ranked public school systems in the country. If I were looking for a higher-thinking state with good schools, TX wouldn't be on my list or anywhere near it.
Other posters are correct. "New math" is "old math", taught in methods that makes it easier to understand for young minds and brings them along incrementally. From where I sit, as far as math goes,the kids are alright.
Quote: GenoDRPhQuote: AutomaticMonkeyQuote: ChumpChangeI was among the last of the boomer generation and we were getting new books to replace older books that were at least a decade old or older. The new text books revamped what older books taught. In what way, I don't know. It just felt good to get new text books.
I fear students getting new text books in the next few years will find they are filled with utter disinformation.
link to original post
They've been filled with misinformation and disinformation for a couple of decades at least. Texas and a few other higher-thinking states are straightening that out.
There has been no need to change mathematics books for schoolchildren for over 100 years. Real math, taught properly, does not change. It's really a bit of a scam, where book publishers know these books can be used indefinitely by a school system (and they once were. I remember getting textbooks in elementary school which were signed and dated by kids who were there 50 years prior.) and they want to sell more, so they issue a new edition every few years. Planned obsolescence.
They're also dumbed down, but complicated. I've seen recent kids textbooks with rather difficult concepts in it, but that can't be used as a foundation for the canonical math used in the sciences. I want to see classical geometry and the trigonometry that descends from it, algebra, polynomials, simultaneous equations, matrix operations- not some thing where you estimate what percentage of the odd numbers are prime as long as it's Tuesday. Kids who learn only that kind of thing are not going to be prepared for traditional higher education, and I do not believe that is unintentional.
link to original post
Texas has the 34th ranked public school systems in the country. If I were looking for a higher-thinking state with good schools, TX wouldn't be on my list or anywhere near it.
Other posters are correct. "New math" is "old math", taught in methods that makes it easier to understand for young minds and brings them along incrementally. From where I sit, as far as math goes,the kids are alright.
link to original post
Normed for demographics. Not just taking the richest and whitest states and saying "Hey look how brilliant we are, peasants!" Slay me with another secret. It's not a measure of how effective the teaching is as much as a measure of what they started out with in terms of the carcasses coming in the front door in September.
Here's a study where they norm for economic demographics (not the other one) and Texas does pretty darned good. Nobody wants me to do my own but normed for the other thing and I'd get in trouble so I won't.
https://www.urban.org/research/publication/states-demographically-adjusted-performance-2024-national-assessment
As far as the teaching of math, our young minds were no different than our grandparents' young minds and we could do whatever they could. I learned math the traditional way and the most important thing about it is that it matched the concepts, skills, most of the notation that was in my college level math and science textbooks. Those are for adults and aren't getting rewritten to accommodate students who learned "new math." Some of my books I borrowed from the office bookshelves of my elders and betters, who took the same class and used the same book 20 years ago. Same math. This fru-fru stuff might be fun for the students and easy for the teachers but it is not appropriate preparation for a legitimate academic canon.
Quote: AutomaticMonkeyQuote: GenoDRPhQuote: AutomaticMonkeyQuote: ChumpChangeI was among the last of the boomer generation and we were getting new books to replace older books that were at least a decade old or older. The new text books revamped what older books taught. In what way, I don't know. It just felt good to get new text books.
I fear students getting new text books in the next few years will find they are filled with utter disinformation.
link to original post
They've been filled with misinformation and disinformation for a couple of decades at least. Texas and a few other higher-thinking states are straightening that out.
There has been no need to change mathematics books for schoolchildren for over 100 years. Real math, taught properly, does not change. It's really a bit of a scam, where book publishers know these books can be used indefinitely by a school system (and they once were. I remember getting textbooks in elementary school which were signed and dated by kids who were there 50 years prior.) and they want to sell more, so they issue a new edition every few years. Planned obsolescence.
They're also dumbed down, but complicated. I've seen recent kids textbooks with rather difficult concepts in it, but that can't be used as a foundation for the canonical math used in the sciences. I want to see classical geometry and the trigonometry that descends from it, algebra, polynomials, simultaneous equations, matrix operations- not some thing where you estimate what percentage of the odd numbers are prime as long as it's Tuesday. Kids who learn only that kind of thing are not going to be prepared for traditional higher education, and I do not believe that is unintentional.
link to original post
Texas has the 34th ranked public school systems in the country. If I were looking for a higher-thinking state with good schools, TX wouldn't be on my list or anywhere near it.
Other posters are correct. "New math" is "old math", taught in methods that makes it easier to understand for young minds and brings them along incrementally. From where I sit, as far as math goes,the kids are alright.
link to original post
Normed for demographics. Not just taking the richest and whitest states and saying "Hey look how brilliant we are, peasants!" Slay me with another secret. It's not a measure of how effective the teaching is as much as a measure of what they started out with in terms of the carcasses coming in the front door in September.
Here's a study where they norm for economic demographics (not the other one) and Texas does pretty darned good. Nobody wants me to do my own but normed for the other thing and I'd get in trouble so I won't.
https://www.urban.org/research/publication/states-demographically-adjusted-performance-2024-national-assessment
As far as the teaching of math, our young minds were no different than our grandparents' young minds and we could do whatever they could. I learned math the traditional way and the most important thing about it is that it matched the concepts, skills, most of the notation that was in my college level math and science textbooks. Those are for adults and aren't getting rewritten to accommodate students who learned "new math." Some of my books I borrowed from the office bookshelves of my elders and betters, who took the same class and used the same book 20 years ago. Same math. This fru-fru stuff might be fun for the students and easy for the teachers but it is not appropriate preparation for a legitimate academic canon.
link to original post
If Texas needs gimmicked numbers to make itself look good, they aren't so good in the first place.
You need to hang around more recent graduates of STEM majors if you think the new math is just fru-fru stuff. The kids are alright.
Because of this societal shift in the West, I don't think it's very surprising that I am the only representative of Gen Z in this forum.
I went to Catholic school for 6th grade, and we learned the metric system. We spent about a week on it, and perhaps an afternoon changing Imperial distances to Metric and vice versa. Seventh grade was in an Army-run school and we wasted at least a month practicing conversions. My grade was divided into three groups by academic ability. I was in the first section, which was then divided into three groups. Of nine groups in my grade, I was in the second. The first group spent about a week on conversions and moved on, while we in the second group were charged with helping the weakest students. It worked really well, as teaching a subject is a great way to learn it yourself.
Quote: harrisThe goal of New Math was to create geniuses who could compete with the USSR in the Space Race. By the time, I went to school (late 2000s-early 2010s) we basically just kept repeating the same material (like rounding and basic division) until the slowest 10% of the class finally got it. The goal of inclusion has completely superceding the goal of nurturing talent.
Because of this societal shift in the West, I don't think it's very surprising that I am the only representative of Gen Z in this forum.
link to original post
If that means the slowest 10% doesn't throwtheir textbook across the room and say "I hate math!" and the "new math" means they don't drop out and maybe-just maybe-are able to get in to college or get a better job, then I'm all for it.
So they should hold back the other 90% to hope that the 10% can grasp the concept.Quote: GenoDRPhQuote: harrisThe goal of New Math was to create geniuses who could compete with the USSR in the Space Race. By the time, I went to school (late 2000s-early 2010s) we basically just kept repeating the same material (like rounding and basic division) until the slowest 10% of the class finally got it. The goal of inclusion has completely superceding the goal of nurturing talent.
Because of this societal shift in the West, I don't think it's very surprising that I am the only representative of Gen Z in this forum.
link to original post
If that means the slowest 10% doesn't throwtheir textbook across the room and say "I hate math!" and the "new math" means they don't drop out and maybe-just maybe-are able to get in to college or get a better job, then I'm all for it.
link to original post
I think they need to do something different. Like put the slower students in their own class
Quote: harrisThe goal of New Math was to create geniuses who could compete with the USSR in the Space Race. By the time, I went to school (late 2000s-early 2010s) we basically just kept repeating the same material (like rounding and basic division) until the slowest 10% of the class finally got it. The goal of inclusion has completely superceding the goal of nurturing talent.
Because of this societal shift in the West, I don't think it's very surprising that I am the only representative of Gen Z in this forum.
link to original post
Your up-close perspective is noted and appreciated!
Quote: G. Michael HopfHard times create strong men. Strong men create good times. Good times create weak men. And, weak men create hard times.
It comes down to that. Most of my teachers were of the WWII and Silent generations, with the Boomers just starting to creep in, and the difference was noticeable.
See the older teachers knew how the world treated those who lacked education. Flophouses, body lice, and being in a knife fight over a $5/day job would be part of your life. That was real to them, not just something in a book or TV show.
So that bottom 10% was forced to learn the material. You were kept after school, you were stood up against the wall and called a dummy and a retard, other kids were allowed to ridicule you, you were punished. Yes, sometimes there was corporal punishment (usually at home but sometimes at school as well) not just for misbehavior or wilful neglect of work, but just for coming up short on a test. The justification for that was that there's nothing a teacher or parent would do to you that's as bad as what your life will be like if you do not learn. It was believed that a book applied forcefully to the head would cause the information in the book to spill out into the head. Similar to military basic training, where you might think your drill instructor is a mean guy, but what he will do to you is nothing compared to what the enemy will do to you if you fail to excel in combat. So what you learn to do to satisfy his demands may well save your life.
You also learned to learn by rote. Yeah, nobody likes it, seems stifling, but it's actually very important. Rote learning is in itself a skill, and there are certain things that can only be learned that way. (As every card counter knows.) And everyone can do it, including people who might not otherwise be considered smart. Actors are all great at it, even the ones who were hired for their looks. Some dumb "aspiring rapper" whose SAT and FICO are on a race to the bottom might be excellent at remembering all those words and the cadence with which they are to be spat. Why can't he do that with vocabulary words and math tables and formulae? He can! There just has to be someone with the balls to force him to.
And as a result of that, the smart kids didn't have to get dumbed down because instead the dumb kids are getting smartened up. The smart kids didn't get anything special either. Sure, here's your A, don't look down on people who got something else and don't be too proud of it, because life won't always be that easy. College is the place you go to stand out from the crowd; go find one challenging enough where you will be occasionally humbled. But now colleges have gotten weak too. We may need some hard times.
Quote: HunterhillSo they should hold back the other 90% to hope that the 10% can grasp the concept.Quote: GenoDRPhQuote: harrisThe goal of New Math was to create geniuses who could compete with the USSR in the Space Race. By the time, I went to school (late 2000s-early 2010s) we basically just kept repeating the same material (like rounding and basic division) until the slowest 10% of the class finally got it. The goal of inclusion has completely superceding the goal of nurturing talent.
Because of this societal shift in the West, I don't think it's very surprising that I am the only representative of Gen Z in this forum.
link to original post
If that means the slowest 10% doesn't throwtheir textbook across the room and say "I hate math!" and the "new math" means they don't drop out and maybe-just maybe-are able to get in to college or get a better job, then I'm all for it.
link to original post
I think they need to do something different. Like put the slower students in their own class
link to original post
NYC was making classrooms out of lavatories and supply closets. Adding classes means more teachers and more classrooms. Which means more taxes. Good luck with that.
What ends up happening is the worst students get assigned to classes where they rarely have a regular teacher, and the endless flow of substitute teachers is more zookeeper than teacher. If the troublemakers don't blow up the substitute, everyone is happy. Eventually, the kids get bored and quit school, becoming someone else's problem.
NYC schools receive roughly $200 per student per day from the government, so there is some incentive to keep the dropout class as long as possible.
The quick version: we had cubes representing 1s, strands of 10 x 1 blocks that represented 10s, planks of 10 x 10 blocks that represented 100s, and large 10 x 10 x 10 cubes that represented 1000. When you needed to carry or borrow things, you simply exchanged 10 of something for 1 of the next-larger item, or vice versa.
Here is Sally from "Peanuts" having to suffer through it...in October, 1965:
Quote: HunterhillSo they should hold back the other 90% to hope that the 10% can grasp the concept.Quote: GenoDRPhQuote: harrisThe goal of New Math was to create geniuses who could compete with the USSR in the Space Race. By the time, I went to school (late 2000s-early 2010s) we basically just kept repeating the same material (like rounding and basic division) until the slowest 10% of the class finally got it. The goal of inclusion has completely superceding the goal of nurturing talent.
Because of this societal shift in the West, I don't think it's very surprising that I am the only representative of Gen Z in this forum.
link to original post
If that means the slowest 10% doesn't throwtheir textbook across the room and say "I hate math!" and the "new math" means they don't drop out and maybe-just maybe-are able to get in to college or get a better job, then I'm all for it.
link to original post
I think they need to do something different. Like put the slower students in their own class
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Who was being held back?
Quote: Hunterhill
I think they need to do something different. Like put the slower students in their own class
link to original post
Yeah, so the wrestling team is getting an A- in "Business Math" for managing to total a stack of checks on a ten key, while the students with "so much potential" are struggling to pull a C in calculus to satisfy their math requirement.
Every individualization adds complexity and cost.
Quote: DieterQuote: Hunterhill
I think they need to do something different. Like put the slower students in their own class
link to original post
Yeah, so the wrestling team is getting an A- in "Business Math" for managing to total a stack of checks on a ten key, while the students with "so much potential" are struggling to pull a C in calculus to satisfy their math requirement.
Every individualization adds complexity and cost.
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My Senior year of High school, I was selling comics mail order and doing an occasional show, so i convinced my parents to let me take Business Math. I thought I'd be learning about depreciation and tax deductions. Instead, we spent a week on making change of a dollar before moving on to equally mundane feats. Luckily, it was only a one-semester class. I think that was because half the class dropped out of school.
Quote: DieterQuote: Hunterhill
I think they need to do something different. Like put the slower students in their own class
link to original post
Yeah, so the wrestling team is getting an A- in "Business Math" for managing to total a stack of checks on a ten key, while the students with "so much potential" are struggling to pull a C in calculus to satisfy their math requirement.
Every individualization adds complexity and cost.
link to original post
My mother was a school teacher early in her career. She taught business writing, letter composition,typing and business math. No making change for a dollar for her students. It was bookkeeping to the trial balance, and the mathematics that went along with it, including how to check your work. Not an easy A for the lunkhead athletes, and her children with her accountant/CPA husband became good in math as well. Same for her grandchildren.
Quote: GenoDRPhQuote: DieterQuote: Hunterhill
I think they need to do something different. Like put the slower students in their own class
link to original post
Yeah, so the wrestling team is getting an A- in "Business Math" for managing to total a stack of checks on a ten key, while the students with "so much potential" are struggling to pull a C in calculus to satisfy their math requirement.
Every individualization adds complexity and cost.
link to original post
My mother was a school teacher early in her career. She taught business writing, letter composition,typing and business math. No making change for a dollar for her students. It was bookkeeping to the trial balance, and the mathematics that went along with it, including how to check your work. Not an easy A for the lunkhead athletes, and her children with her accountant/CPA husband became good in math as well. Same for her grandchildren.
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We learned how to reckon interest on bonds, how to apply a 3% cash discount, and how to use several types of business calculators. We might have spent a couple days on proper useage of cash registers.It was geared towards a vocation, not a profession.
Quote: GenoDRPhQuote: DieterQuote: Hunterhill
I think they need to do something different. Like put the slower students in their own class
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Yeah, so the wrestling team is getting an A- in "Business Math" for managing to total a stack of checks on a ten key, while the students with "so much potential" are struggling to pull a C in calculus to satisfy their math requirement.
Every individualization adds complexity and cost.
link to original post
My mother was a school teacher early in her career. She taught business writing, letter composition,typing and business math. No making change for a dollar for her students. It was bookkeeping to the trial balance, and the mathematics that went along with it, including how to check your work. Not an easy A for the lunkhead athletes, and her children with her accountant/CPA husband became good in math as well. Same for her grandchildren.
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Ah yes, trial balance! I did that when I was in college, but not at school. Usually around 4 or 5 AM. On a machine that could be cranked by hand.
I'd be surprised if I was the only one here who ever had that job.
Quote: AutomaticMonkeyQuote: GenoDRPhQuote: DieterQuote: Hunterhill
I think they need to do something different. Like put the slower students in their own class
link to original post
Yeah, so the wrestling team is getting an A- in "Business Math" for managing to total a stack of checks on a ten key, while the students with "so much potential" are struggling to pull a C in calculus to satisfy their math requirement.
Every individualization adds complexity and cost.
link to original post
My mother was a school teacher early in her career. She taught business writing, letter composition,typing and business math. No making change for a dollar for her students. It was bookkeeping to the trial balance, and the mathematics that went along with it, including how to check your work. Not an easy A for the lunkhead athletes, and her children with her accountant/CPA husband became good in math as well. Same for her grandchildren.
link to original post
Ah yes, trial balance! I did that when I was in college, but not at school. Usually around 4 or 5 AM. On a machine that could be cranked by hand.
I'd be surprised if I was the only one here who ever had that job.
link to original post
...
. The ones who sold the textbooks were just trying to get rich. They could not truly have believed that Set Math was the key to teach math better
When I was in college, Math 101 was Logic, Sets and Numbers- just what the new math stressed. America thought the metric system was too hard; logic never had a chance.
Quote: billryanCalculators and computers made much of the old math teaching methods obsolete. My older sister spent about half a year learning how to use a slide rule. I never used one, nor were we taught. Calculators meant I didn't need to know that 32 X 17 is 544. Math is logic.
I disagree. While there is the joke that the teacher who said you will not always have a calculator didn't know the smartphone would come, you still need to build the basics to do better later.
I've told the story before. Teaching poker at a casino fun night at a local tech schools. Trying to explain pot odds. Ask two girls to divide say 43 by 4. Between the two of them they could not even make a guess.
Sure, you can use a calculator many times. But not at a poker table. Often you need to know on the fly. When you know your times tables cold you can think:
32 X 17
32 X 10 = 320
30 X 7 = 210
2 X 17 = 14
544!
You can think that out without a calculator or a piece of paper. But you cannot do that unless you learned math via the classic methods like times tables.
Yes, everyone hated memorizing times tables. Most early parts of all subjects are boring.
Quote: GenoDRPhQuote: HunterhillSo they should hold back the other 90% to hope that the 10% can grasp the concept.Quote: GenoDRPhQuote: harrisThe goal of New Math was to create geniuses who could compete with the USSR in the Space Race. By the time, I went to school (late 2000s-early 2010s) we basically just kept repeating the same material (like rounding and basic division) until the slowest 10% of the class finally got it. The goal of inclusion has completely superceding the goal of nurturing talent.
Because of this societal shift in the West, I don't think it's very surprising that I am the only representative of Gen Z in this forum.
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If that means the slowest 10% doesn't throwtheir textbook across the room and say "I hate math!" and the "new math" means they don't drop out and maybe-just maybe-are able to get in to college or get a better job, then I'm all for it.
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I think they need to do something different. Like put the slower students in their own class
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Who was being held back?
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The better kids in the class are being held back. We have it messed up in the USA. We put more resources to helping the slower kids. We should be helping the best minds achieve. And quit bragging what % do what level of math.
Quote: GenoDRPhMy mother was a school teacher early in her career. She taught business writing, letter composition,typing and business math. No making change for a dollar for her students. It was bookkeeping to the trial balance, and the mathematics that went along with it, including how to check your work. Not an easy A for the lunkhead athletes, and her children with her accountant/CPA husband became good in math as well. Same for her grandchildren.
link to original post
When I went to high school, there was a one-semester "general business" requirement; the math was pretty much limited to things like "how much interest do you earn if you invest $100 at 8% for 8 years?"
These are high school kids - do you expect them to learn the formula for calculating N given P, I, and M?
Business math was not in the academic track, and I needed special permission to take it. Part of the problem was that I attended four high schools, one of them overseas, and some of my courses didn't match up. I'd done a semester of geometry and another of algebra, but public schools in NY had those classes for a full year. I knew too much geometry to have to repeat the course, but not enough to take the next-level course. I ended up taking a Civil Engineering class that prepared kids for jobs as surveyors and the business math that was offered alongside shorthand and typing.
Quote: AZDuffmanQuote: billryanCalculators and computers made much of the old math teaching methods obsolete. My older sister spent about half a year learning how to use a slide rule. I never used one, nor were we taught. Calculators meant I didn't need to know that 32 X 17 is 544. Math is logic.
I disagree. While there is the joke that the teacher who said you will not always have a calculator didn't know the smartphone would come, you still need to build the basics to do better later.
I've told the story before. Teaching poker at a casino fun night at a local tech schools. Trying to explain pot odds. Ask two girls to divide say 43 by 4. Between the two of them they could not even make a guess.
Sure, you can use a calculator many times. But not at a poker table. Often you need to know on the fly. When you know your times tables cold you can think:
32 X 17
32 X 10 = 320
30 X 7 = 210
2 X 17 = 14
544!
You can think that out without a calculator or a piece of paper. But you cannot do that unless you learned math via the classic methods like times tables.
Yes, everyone hated memorizing times tables. Most early parts of all subjects are boring.
link to original post
Learning by rote and repetition is a horrible way to learn. Math is logical and beautiful when you understand it. Rote learning stifles creativity and doesn't develop deep thinking. It is everything wrong with today's schools. Someone almost 200 years ago decided it was important that every child learn that 12x12 is 144, but it isn't necessary to know that 15X15 is 225. New math failed because parents didn't know it, weren't comfortable with it, and hated change.
32X17.
32X20=640, subtract 32X3=96. 640-96=544.
Quote: billryanQuote: AZDuffmanQuote: billryanCalculators and computers made much of the old math teaching methods obsolete. My older sister spent about half a year learning how to use a slide rule. I never used one, nor were we taught. Calculators meant I didn't need to know that 32 X 17 is 544. Math is logic.
I disagree. While there is the joke that the teacher who said you will not always have a calculator didn't know the smartphone would come, you still need to build the basics to do better later.
I've told the story before. Teaching poker at a casino fun night at a local tech schools. Trying to explain pot odds. Ask two girls to divide say 43 by 4. Between the two of them they could not even make a guess.
Sure, you can use a calculator many times. But not at a poker table. Often you need to know on the fly. When you know your times tables cold you can think:
32 X 17
32 X 10 = 320
30 X 7 = 210
2 X 17 = 14
544!
You can think that out without a calculator or a piece of paper. But you cannot do that unless you learned math via the classic methods like times tables.
Yes, everyone hated memorizing times tables. Most early parts of all subjects are boring.
link to original post
Learning by rote and repetition is a horrible way to learn. Math is logical and beautiful when you understand it. Rote learning stifles creativity and doesn't develop deep thinking. It is everything wrong with today's schools. Someone almost 200 years ago decided it was important that every child learn that 12x12 is 144, but it isn't necessary to know that 15X15 is 225. New math failed because parents didn't know it, weren't comfortable with it, and hated change.
32X17.
32X20=640, subtract 32X3=96. 640-96=544.
link to original post
That is totally incorrect. We all learn by rote. Assuming our native language is English what did we all learn before the times tables, exactly the same way?
Ah, vous dirai-je maman? Ce qui cause mon tourment? But we didn't sing it that way, we sung it "A B C D E F G..." How else do you learn an alphabet except by rote? And everybody could do it; even the kid who turned out to be "a bit slow" could sing the Alphabet Song as well as anyone else. Learning that prepared our minds- it was the first time we realized that something can be the same way every time, that order is important, and the feeling of learning, that feeling of having something in your mind today that wasn't there yesterday.
Musicians learn by rote, athletes learn their plays by repeating them in practice countless times, we learn our prayers and rites that way, so many examples where that is the best or really the only way to learn. Euclid's Postulates- there's no rhyme or reason to them, they can only be learned by memorizing them. I'm not saying it should be always and only. But it gives you something to apply your logic to- Boolean/Aristotlean logic requires a priori facts that could be arbitrary (like the order of letters in the alphabet) and the only way to know them is to know them.
Quote: AutomaticMonkey
I'm not saying it should be always and only. But it gives you something to apply your logic to- Boolean/Aristotlean logic requires a priori facts that could be arbitrary (like the order of letters in the alphabet) and the only way to know them is to know them.
link to original post
For some reason (possibly misguided), that was my impression. The "old way" was that countin' to a thousand, addin', s'tractin', an' long division was enough math. "New math" said that was the alphabet and elementary vocabulary, and now there were interesting things to do once we'd gotten a handle on the rudiments. Learning the essentials under the old pedagogy seemed to make it harder to transition to the advanced stuff, but using the new math pedagogy to teach the foundation made it easier for more people to slide into the more advanced topics.
The frustration is sure to come when 3 out of 4 people really don't need more math than countin' to a thousand and a little s'tractin'.
Quote: GenoDRPhQuote: DieterQuote: Hunterhill
I think they need to do something different. Like put the slower students in their own class
link to original post
Yeah, so the wrestling team is getting an A- in "Business Math" for managing to total a stack of checks on a ten key, while the students with "so much potential" are struggling to pull a C in calculus to satisfy their math requirement.
Every individualization adds complexity and cost.
link to original post
My mother was a school teacher early in her career. She taught business writing, letter composition,typing and business math. No making change for a dollar for her students. It was bookkeeping to the trial balance, and the mathematics that went along with it, including how to check your work. Not an easy A for the lunkhead athletes, and her children with her accountant/CPA husband became good in math as well. Same for her grandchildren.
link to original post
Once upon a time I was a grad student and supposedly working on a PhD in math at a Big Ten university. At one point I had a teaching assistantship and had to teach a semester of freshman algebra. Around the 2nd week I got a letter from the athletic department telling me that one of my students was on the football team and they wanted to be informed if at any point he needed extra tutoring. Translation: “make sure our boy gets an A or your ass is toasted”. As it turned out he already knew the material and got the A without having to spend much time in class.
As to the rest of the class, I was always mystified that someone could be accepted at a major university without knowing basic high school algebra.
Quote: AutomaticMonkeyQuote: billryanQuote: AZDuffmanQuote: billryanCalculators and computers made much of the old math teaching methods obsolete. My older sister spent about half a year learning how to use a slide rule. I never used one, nor were we taught. Calculators meant I didn't need to know that 32 X 17 is 544. Math is logic.
I disagree. While there is the joke that the teacher who said you will not always have a calculator didn't know the smartphone would come, you still need to build the basics to do better later.
I've told the story before. Teaching poker at a casino fun night at a local tech schools. Trying to explain pot odds. Ask two girls to divide say 43 by 4. Between the two of them they could not even make a guess.
Sure, you can use a calculator many times. But not at a poker table. Often you need to know on the fly. When you know your times tables cold you can think:
32 X 17
32 X 10 = 320
30 X 7 = 210
2 X 17 = 14
544!
You can think that out without a calculator or a piece of paper. But you cannot do that unless you learned math via the classic methods like times tables.
Yes, everyone hated memorizing times tables. Most early parts of all subjects are boring.
link to original post
Learning by rote and repetition is a horrible way to learn. Math is logical and beautiful when you understand it. Rote learning stifles creativity and doesn't develop deep thinking. It is everything wrong with today's schools. Someone almost 200 years ago decided it was important that every child learn that 12x12 is 144, but it isn't necessary to know that 15X15 is 225. New math failed because parents didn't know it, weren't comfortable with it, and hated change.
32X17.
32X20=640, subtract 32X3=96. 640-96=544.
link to original post
That is totally incorrect. We all learn by rote. Assuming our native language is English what did we all learn before the times tables, exactly the same way?
Ah, vous dirai-je maman? Ce qui cause mon tourment? But we didn't sing it that way, we sung it "A B C D E F G..." How else do you learn an alphabet except by rote? And everybody could do it; even the kid who turned out to be "a bit slow" could sing the Alphabet Song as well as anyone else. Learning that prepared our minds- it was the first time we realized that something can be the same way every time, that order is important, and the feeling of learning, that feeling of having something in your mind today that wasn't there yesterday.
Musicians learn by rote, athletes learn their plays by repeating them in practice countless times, we learn our prayers and rites that way, so many examples where that is the best or really the only way to learn. Euclid's Postulates- there's no rhyme or reason to them, they can only be learned by memorizing them. I'm not saying it should be always and only. But it gives you something to apply your logic to- Boolean/Aristotlean logic requires a priori facts that could be arbitrary (like the order of letters in the alphabet) and the only way to know them is to know them.
link to original post
Correct. Craps is one of the hardest games to deal, and lots of it is rote memorization. We talked here years ago that an aspiring craps dealer should look at the license plate in front of them then figure odds on the last 2 digits. That is rote even if the number keeps differing.
We get a lot of "memorization is pointless" when it comes to things like times tables. I get that memorization is boring for teachers and students alike. But it is part of life.
Quote: AZDuffman
...We get a lot of "memorization is pointless" when it comes to things like times tables. I get that memorization is boring for teachers and students alike. But it is part of life.
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That's been almost unspoken here, but sure, in recent years education majors have had among the lowest standardized test scores in academia.
It seems like they are getting the girls who have the work ethic and reliability of strippers, but with short legs and boring personalities. Fear not, young lady, you have a future in the public education system!
How much of this new stuff was created mostly to accommodate incompetent, yet unionized, teachers, and spare them and their employers from having to face the truth about them?
Quote: TumblingBonesQuote: GenoDRPhQuote: DieterQuote: Hunterhill
I think they need to do something different. Like put the slower students in their own class
link to original post
Yeah, so the wrestling team is getting an A- in "Business Math" for managing to total a stack of checks on a ten key, while the students with "so much potential" are struggling to pull a C in calculus to satisfy their math requirement.
Every individualization adds complexity and cost.
link to original post
My mother was a school teacher early in her career. She taught business writing, letter composition,typing and business math. No making change for a dollar for her students. It was bookkeeping to the trial balance, and the mathematics that went along with it, including how to check your work. Not an easy A for the lunkhead athletes, and her children with her accountant/CPA husband became good in math as well. Same for her grandchildren.
link to original post
Once upon a time I was a grad student and supposedly working on a PhD in math at a Big Ten university. At one point I had a teaching assistantship and had to teach a semester of freshman algebra. Around the 2nd week I got a letter from the athletic department telling me that one of my students was on the football team and they wanted to be informed if at any point he needed extra tutoring. Translation: “make sure our boy gets an A or your ass is toasted”. As it turned out he already knew the material and got the A without having to spend much time in class.
As to the rest of the class, I was always mystified that someone could be accepted at a major university without knowing basic high school algebra.
link to original post
Then your school sucked. Around here, athletes get no winks-and-nods. They either pass on their merits or they don't.
Quote: GenoDRPhQuote: TumblingBonesQuote: GenoDRPhQuote: DieterQuote: Hunterhill
I think they need to do something different. Like put the slower students in their own class
link to original post
Yeah, so the wrestling team is getting an A- in "Business Math" for managing to total a stack of checks on a ten key, while the students with "so much potential" are struggling to pull a C in calculus to satisfy their math requirement.
Every individualization adds complexity and cost.
link to original post
My mother was a school teacher early in her career. She taught business writing, letter composition,typing and business math. No making change for a dollar for her students. It was bookkeeping to the trial balance, and the mathematics that went along with it, including how to check your work. Not an easy A for the lunkhead athletes, and her children with her accountant/CPA husband became good in math as well. Same for her grandchildren.
link to original post
Once upon a time I was a grad student and supposedly working on a PhD in math at a Big Ten university. At one point I had a teaching assistantship and had to teach a semester of freshman algebra. Around the 2nd week I got a letter from the athletic department telling me that one of my students was on the football team and they wanted to be informed if at any point he needed extra tutoring. Translation: “make sure our boy gets an A or your ass is toasted”. As it turned out he already knew the material and got the A without having to spend much time in class.
As to the rest of the class, I was always mystified that someone could be accepted at a major university without knowing basic high school algebra.
link to original post
Then your school sucked. Around here, athletes get no winks-and-nods. They either pass on their merits or they don't.
link to original post
Maybe that glare off the silver spoon has blinded you to the obvious reality that there are people going to D1 schools that are perfectly good schools academically, but that rely on D1 sports income to pay the bills and many/most/all of those varsity players would not be accepted by that school any other way.
For money talks, we all know what walks, and economics will always win. There are Harvard boys who are there because of what family they are from and no more, and they will get the same treatment, just from some chin-pulling pinky-raiser rather than the football coach. Some people think that's better. But I'd rather see the jock get franked through, at least he does something that normal people enjoy and are inspired by. What is the dummy of a legacy admission or a quota admission ever going to do for me?
Quote: acesideI totally agree. Another game that requires memorization is blackjack, in which basic strategy is the key to success. Most card counters have trouble memorizing the basic strategy table, not to mention extra deviation plays when counting cards.
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I didn't learn BJ by memorizing it; I learned it by analysis. Knowing why you should make a decision is infinitely superior to simply parroting a chart.
Rote learning teaches you what to think. Teaching someone how to think is vastly superior. Sadly, most people are more comfortable not having to think very much.
Quote: billryanQuote: acesideI totally agree. Another game that requires memorization is blackjack, in which basic strategy is the key to success. Most card counters have trouble memorizing the basic strategy table, not to mention extra deviation plays when counting cards.
link to original post
I didn't learn BJ by memorizing it; I learned it by analysis. Knowing why you should make a decision is infinitely superior to simply parroting a chart.
Rote learning teaches you what to think. Teaching someone how to think is vastly superior. Sadly, most people are more comfortable not having to think very much.
link to original post
I already know why I should make a decision. But I still have to know what the index number is (quantitative, not qualitative) and I'm not going to calculate it in the time it takes for me to see the cards to when I have to make a decision, which is seconds. So I'm going to memorize it.
I've composed many AP systems and my standard practice is to have all the data an experienced player needs to play it printed on one side of a 8.5x11 page. To learn it, I put that paper next to me on the desk and play with a simulator or an online game. After it doesn't seem like I really need the paper, I turn it upside down, and only turn it over if I'm really unsure. Then I fold the paper in half and put it on the other side of the room, so I have to get up and look at it if I'm unsure and that's annoying, so I take memorization more seriously to avoid the annoyance. That's a form of rote learning, that's a skill that can be applied to many things.
Quote: billryanQuote: acesideI totally agree. Another game that requires memorization is blackjack, in which basic strategy is the key to success. Most card counters have trouble memorizing the basic strategy table, not to mention extra deviation plays when counting cards.
link to original post
I didn't learn BJ by memorizing it; I learned it by analysis. Knowing why you should make a decision is infinitely superior to simply parroting a chart.
Rote learning teaches you what to think. Teaching someone how to think is vastly superior. Sadly, most people are more comfortable not having to think very much.
link to original post
So you want us to believe that instead of memorizing a chart that you can buy for $1 in most casino gift shops you wrote a computer program and used your computer programing and math knowledge to simply get the same info as is on the card?
