procore

[PassedOut]

From the Post today: Many parents hated Common Core math at first, before figuring it out

 

I asked readers to email me what they thought of the new methods derived from the standards.

 

Astonishingly, given the political controversy and my own ambivalence about Common Core, almost all of the reactions from people with children in schools have been positive, particularly when talking about math.

 

Nearly every one of them said they disliked the program at first but changed their minds when they realized that their kids, with good teaching, were learning more with greater enjoyment than they did at that age.

Jeb! should have one of his people link to this article.

[y66]

From the WaPo story cited by PassedOut:

 

Claus von Zastrow, a father at Ben W. Murch Elementary in the District who has worked in education policy, recalled the derision over new alternative approaches to math. There is, for instance, the “make a 10” method of doing 9+6=15. Students could just memorize that arithmetic fact, von Zastrow said. But making a 10 allows them to put the numbers together in a way that promotes number sense: 9+6=(9+1)+5=10+5=15.

 

“The make-a-10 method is in common use in high-performing countries,” he said, but Common Core critics “had a field day with it because it takes half an hour to explain and about 20 seconds to ridicule.”

My dad learned to do arithmetic that way 80 years ago. I never met anyone who could do arithmetic problems in their head faster than he could or who enjoyed doing them more.

[Zelandakh]

My dad learned to do arithmetic that way 80 years ago. I never met anyone who could do arithmetic problems in their head faster than he could or who enjoyed doing them more.

I always feel this technique is more useful for subtraction. The classic example is working out the age of someone born in the late 1900s. So 1977 for example, you make up to 2000 with 23 and then add the 15-16 years for 2016 giving an answer of 38 or 39. For addition I find simply adding the numbers together directly in groups with normaly carrying works better. It is sometimes useful for multiplication though (eg 9999 * 6). To be honest, I thought it was standard all over the world to learn the technique, just not necessarily to use it for problems such as the one given (9+6).

[kenberg]

I can't say that I remember learning ot add but I do remember learning to multiply. I had some trouble with 9 times 6=54 versus 8 times 7=56. But I could count by 6s or 7s, or by 8s or 9s, and I understood that 8 times 7 was the sum of 8 7s so I could check it.

 

Now I think that I have a point. Our task was to learn 9 times 6 and 8 times 7. A useful technique was to add in our heads until we could state the result from memory. Yes, we learned the connection between addition and multiplication along the way.

 

For the addition: I would like it better if students were required to learn that 9+6 = 15, and were helped, as a technique, to understand that 9+6=9+1+5=10+5=15. Presenting this technique as being the right way to add (if that is what is done) seems odd. Along the lines of what Zel says, I once would add 33+42+77 by first rearranging to get 33+77+42=110+42-152, but later i decided this was more trouble than it was worth.

 

If you ask me the age of my kids, right off I don't know. But the younger was born in 1967, the older in 1961, these numbers don't change every year, and I can work it out, usually just as Zel says. Eg 2000 minus 1961 is 39, add 15 not 16 since her birthday is in August, done.

 

Really what strikes me as odd is that parents have opinions on these matters. My mother saw to it that I was in bed at a reasonable hour, I was allowed to sing myself to sleep, I usually got up on my own, she gave me breakfast, i went to school. She no more would have told the teacher how to teach me arithmetic than she would have put up with the teacher telling her how to fix my breakfast. Actually by that time I was probably fixing my own, but you get the oint.

 

 

Anyway, I expect Common Core is fine. Most things stand or fall on how well they are executed.

[barmar]

Really what strikes me as odd is that parents have opinions on these matters. My mother saw to it that I was in bed at a reasonable hour, I was allowed to sing myself to sleep, I usually got up on my own, she gave me breakfast, i went to school. She no more would have told the teacher how to teach me arithmetic than she would have put up with the teacher telling her how to fix my breakfast. Actually by that time I was probably fixing my own, but you get the oint.

I suspect some of this come from the idea "We learned it the old way, and we came out fine -- why change what isn't broken?".

 

Also, parents are often expected to help their kids with homework. If they don't understand the way the subject is being taught, they won't be able to help very well. Wasn't that a common complaint about "New Math" back in the 70's?

 

And these days, there probably are people (probably including teachers) weighing in on how parents should fix breakfast (and other parental duties). If they find out that a student isn't getting a good breakfast, they might contact the parents and recommend that they do a better job, as it's a prerequisite for learning well.

[kenberg]

I suspect some of this come from the idea "We learned it the old way, and we came out fine -- why change what isn't broken?".

 

I can recall two times that my mother voiced an opinion on my schooling. She had about a year and a half of high school but she had opinions.

Once she was upset over some technical point of grammar having to do with predicate phrases. We had an intense argument, neither of us backing down.

 

The other time was during the Korean War. My teacher was explaining about the Red Menace. My mother saw this, pretty much correctly, as indoctrination. She asserted that all wars were about oil. I replied that I did not believe that there was any oil in Korea. She had a fine response: "They are fighting there, there is oil there".

 

Other than that, she stayed out of my school work. Except that after a heavy snowstorm she would sometimes call the school and report me as sick so that I could go out with a shovel and make some money.

 

 

 

Also, parents are often expected to help their kids with homework. If they don't understand the way the subject is being taught, they won't be able to help very well. Wasn't that a common complaint about "New Math" back in the 70's?

 

For most parents in most cases I think that this sort of help is a mistake. Partly this is just as you say. The teacher is teaching one way, the parent thinks a different way, the child becomes more rather than less confused. But also, if the homework is at all reasonable, the child can do it himself. Maybe not easily, but with practice it gets easier. And then the child gains the confidence that he can do it on his own. At one point I helped my younger daughter in algebra. But I had her show me what was being done in class and had her explain, as best she could, what the teacher was saying. Then I helped with that. When she got it straight, she went back to doing her own homework. I have had many mathematical colleagues who cannot seem to resist the call to explain to the teacher what s/he is doing wrong. Almost always, this is a mistake.

 

And these days, there probably are people (probably including teachers) weighing in on how parents should fix breakfast (and other parental duties). If they find out that a student isn't getting a good breakfast, they might contact the parents and recommend that they do a better job, as it's a prerequisite for learning well.

 

Unfortunately this is very true. There are many things about my childhood that were good. Being properly and regularly fed was one of many. I know that many kids today lack this basic building block of life. Fixing this, as to some extent is being done, is far more important than exactly how math is being taught.

[blackshoe]

If they find out that a student isn't getting a good breakfast, they might contact the parents and recommend that they do a better job, as it's a prerequisite for learning well.

More likely they'll call the cops and report the parents for child abuse. :huh:

[Zelandakh]

For most parents in most cases I think that this sort of help is a mistake. Partly this is just as you say. The teacher is teaching one way, the parent thinks a different way, the child becomes more rather than less confused. But also, if the homework is at all reasonable, the child can do it himself. Maybe not easily, but with practice it gets easier. And then the child gains the confidence that he can do it on his own. At one point I helped my younger daughter in algebra. But I had her show me what was being done in class and had her explain, as best she could, what the teacher was saying. Then I helped with that. When she got it straight, she went back to doing her own homework. I have had many mathematical colleagues who cannot seem to resist the call to explain to the teacher what s/he is doing wrong. Almost always, this is a mistake.

As someone that has done some work as a maths tutor I actually disagree with this quite strongly Ken. One of the major advantages of teaching one-on-one is being able to tailor your methods to the way the student thinks. There are many areas of maths where 3 or 4 different methods are equally possible. If the student is struggling with one method and you can tell from the way they think that another will be easier, it is quite right and proper to try that. Understanding the method and being able to arrive at the right answers gives confidence.

 

What is bad is simply deciding arbitrarily that the method you learned is better than the one being used in class. As a general rule, the method being taught is the one suitable for the majority of students. You need to have a good reason for choosing a different one but forcing a student to stick with the wrong method is for me bad (lazy) tutoring. Whether a parent can apply the same thought process will naturally depend on their background. For those that can though, as well as for private tutors, my experience is that it is much less often a mistake than "almost always"!

[kenberg]

As someone that has done some work as a maths tutor I actually disagree with this quite strongly Ken. One of the major advantages of teaching one-on-one is being able to tailor your methods to the way the student thinks. There are many areas of maths where 3 or 4 different methods are equally possible. If the student is struggling with one method and you can tell from the way they think that another will be easier, it is quite right and proper to try that. Understanding the method and being able to arrive at the right answers gives confidence.

 

What is bad is simply deciding arbitrarily that the method you learned is better than the one being used in class. As a general rule, the method being taught is the one suitable for the majority of students. You need to have a good reason for choosing a different one but forcing a student to stick with the wrong method is for me bad (lazy) tutoring. Whether a parent can apply the same thought process will naturally depend on their background. For those that can though, as well as for private tutors, my experience is that it is much less often a mistake than "almost always"!

 

Sure, for someone who can do this, by all means. It takes both a decent knowledge of he subject and a willingness to see things from the student's perspective. It can be enjoyable for everyone when it works.

 

Does "almost always" overstate the case? OK, I don't know. in my own case, I was allowed/expected to take care of my own homework and I very much appreciated that. My father taught me how to scale and clean fish, my teacher taught me how to add fractions, I liked it that way.

 

When I was a grad student I tutored for money. I guess I was decent at it because I had plenty of business. And I have sometimes done some unpaid tutoring since then in various circumstances. A while back Becky was helping a guy of very limited education with reading. They went through a very basic book about the planetary system. The next time he came back he was all excited. His elementary school age grandchildren had come to visit, he told them what he was learning, and one of the girls named off all of the planets in order from the Sun. He was very proud of his granddaughter and delighted to have had this conversation. There can be rewards.

 

A cartoon in the Feb AMS Notices goes in the other direction. A graduate assistant in a calculus course is talking with the prof about the course. [some may want to stop reading here]

 

GA: A student asked what exponential functions are good for.

Prof: Great, what did you tell them?

GA: I explained how they could be used to construct infinitely differentiate functions with compact support.

Prof: You did? How did that go?

GA: I'm not sure that they understood it. Should I tell them it won't be on the test?

 

Anyway, it's a judgment call but if homework is such that the parents regularly have to be involved I start to wonder just what is going on. Homework is supposed to be for students, and the parents who are least abe to provide assistance are likely to be the parents least able to afford tutoring.

[barmar]

Does "almost always" overstate the case? OK, I don't know. in my own case, I was allowed/expected to take care of my own homework and I very much appreciated that. My father taught me how to scale and clean fish, my teacher taught me how to add fractions, I liked it that way.

I get the impression that you're a very smart person, and you were probably a good student. Your parents could see that, and they encouraged you to figure things out on your own. But I think this makes it difficult for you to understand the perspective of parents of less adept children. Some children struggle with some subjects, and they need help to learn it.

 

Of course, it's possible that I'm reverse cause and effect. Maybe you were a good student because your parents didn't hold your hand, they forced you to work on your own. But if that really held true in general, many of the children of parents who don't have time to help their kids, because they're struggling with multiple jobs, would be exceptional students since they can't rely on their parents as crutches. This is clearly not the case. Although that's also likely to be because these students are in poor school districts, so they're not getting a good education at school, either.

 

It's a complex system of positive and negative feedback, so it's hard to determine precise cause and effect. But I'm pretty sure that I've heard that when normalizing for other effects, children whose parents take an active role in working with them generally do better.

[kenberg]

It helps to be from Minnesota, where all of the children are above average. I am of course joking. Sort of. At least in the early 1950s St. Paul the scores on standardized exams seemed to support this claim.

 

I would love to have a way to check on my recollections. To the best of my knowledge, no parent of any kid I knew ever helped with homework or hired a tutor. It just wasn't done. My parents were of modest education, 8th grade for my father, a year or two of high school for my mother. By mid-adolescence most but not all of my friends came from more educated families. It didn't matter. parents, educated or not, did not help kids with their homework. When I was 16 the father of one of my friends arranged for him to take a physics class at the U, paid for by the father. But that's different. My friend still did his own homework. With the prof's permission, I sat in as well. My father did not help with my homework :).

 

It is easy to romanticize one's childhood, so a reality check would be useful. But I honestly believe that my best learning experience from adolescence resulted from the car I bought. I learned about planning out a job, and the consequences of poor planing and/or poor attention to detail. I developed confidence in carrying out adult undertakings. Plus it was a lot of fun.

 

Adults helped me learn many things when I was young. Of course they did. But it seems to me that if parents are spending several hours a week helping with, or in some cases almost doing, their kids homework then something is wrong somewhere.

 

I have gone on about this at some length because I think it is important. It is good to know the quadratic formula (even if I cannot say exactly why this is good) but it is far more important to learn how to think for yourself. Too much assistance in coming to someone else's conclusions can interfere with this development.

[PassedOut]

I would love to have a way to check on my recollections. To the best of my knowledge, no parent of any kid I knew ever helped with homework or hired a tutor. It just wasn't done. My parents were of modest education, 8th grade for my father, a year or two of high school for my mother. By mid-adolescence most but not all of my friends came from more educated families. It didn't matter. parents, educated or not, did not help kids with their homework.

My experience was the same. My folks were both educated and any grade brought home lower than an A was absolutely unacceptable. Nevertheless we kids were completely on our own with homework.

 

The only time I recall where extra help came into play was with a younger sister who did not progress in her reading as quickly as my folks thought necessary. For a few weeks she went to our grandmother's house for extra reading lessons (our grandmother was a retired fourth-grade teacher) until she got on track. Then she was on her own again.

[hrothgar]

My experience was the same. My folks were both educated and any grade brought home lower than an A was absolutely unacceptable. Nevertheless we kids were completely on our own with homework.

 

When I was growing up, about the only thing that I could do wrong was slacking off in school.

Conversely, I think my folks were most proud of my academic achievements.

 

My folks didn't help me with most of my homework assignments. With this said and done:

 

1. They taught me to read at a very young age and instilled a genuine love of reading

2. Dinner table conversation often revolved around currents events. I was expected to have read both the New York Times and the Frankfurter Allgemeine Zeitung and be able to discuss them

3. The one area where my folks did tend to mettle was with assignments that focused on writing. My father especially would proof read my essays and suggest improvements.

[blackshoe]

I don't remember ever getting help with my homework, but then I don't remember ever needing it, either. But then most subjects, particularly math and science, came easily to me back then. College was something of a revelation in that respect. B-)

 

I do remember sitting in tenth grade math class one day, when Mr. Roberts, the teacher, noticed that I wasn't paying much attention — I was reading a book. The subject of the class was trig identities. Mr. Roberts wrote one, a fairly complicated one at that level, as I recall, and called on me to prove it. I walked up to the board, looked at it for a minute and said "well, if you take the derivative of both sides, you get this, and then you <multiply, add, subtract or some combination thereof, I don't remember the details> and you get this, and then you integrate both sides and it's proven". Something like that, anyway. Mr. Roberts' comment was "You can't do that! You don't know that yet!"

 

The book I was reading was Thomas' Calculus and Analytic Geometry, which two years later was the text for the AP calculus course. ;)

[gwnn]

To be fair to your teacher, it is true that you cannot take the derivative of both sides of a to-be-proved identity (you can only make "if and only if" steps, not "if" steps).

[kenberg]

To be fair to your teacher, it is true that you cannot take the derivative of both sides of a to-be-proved identity (you can only make "if and only if" steps, not "if" steps).

 

Well, if the derivative of the left side equals the derivative of the right side we are almost home, right? Just check for equality at one value of the variable.

 

I knew nothing of calculus at that age.

 

At its best, modern mathematics teaching is extremely impressive. Mathematical ability often develops early and when students are given the opportunity to develop the results can be wonderful.

[gwnn]

Sure, almost there. Just wanted to mention that the teacher did have a point, if the point was not to use derivatives left and right. Same story with multiplying both sides of inequalities. You can do it but you can get in trouble if aren't careful.

[kenberg]

Sure, almost there. Just wanted to mention that the teacher did have a point, if the point was not to use derivatives left and right. Same story with multiplying both sides of inequalities. You can do it but you can get in trouble if aren't careful.

 

And if the teach really wanted to be tough, this time on me, he could point out that showing the derivative of tan x cos x agrees with the derivative of sin x and then checking that tan x cos x and sin x agree at x=0 only establishes the identity tan x cos x =sin x on the interval (-pi/2,pi/2)..

I trust the general audience will forgive me if I do not explain this.

 

No doubt the teacher's real point was "Hey, buddy, I'm impressed as hell, now get with the program".

[barmar]

3. The one area where my folks did tend to mettle was with assignments that focused on writing. My father especially would proof read my essays and suggest improvements.

Seems like you still need him to proofread your forum posts for spelling errors. :)

[hrothgar]

Seems like you still need him to proofread your forum posts for spelling errors. :)

 

yeap

[blackshoe]

Sure, almost there. Just wanted to mention that the teacher did have a point, if the point was not to use derivatives left and right. Same story with multiplying both sides of inequalities. You can do it but you can get in trouble if aren't careful.

As I recall it, I was not allowed to use calculus (whether I got it right or not) because I "didn't know that" — i.e., had not been formally taught it — yet. :blink:

 

The main problem, I suspect, was that the rest of the class had no clue what the two of us were talking about. :P

[kenberg]

As I recall it, I was not allowed to use calculus (whether I got it right or not) because I "didn't know that" — i.e., had not been formally taught it — yet. :blink:

 

The main problem, I suspect, was that the rest of the class had no clue what the two of us were talking about. :P

 

A more basic point that you already mentioned:

 

" the teacher, noticed that I wasn't paying much attention — I was reading a book"

 

Teachers find that annoying.

 

I was once reading a comic book in class. The teacher asked what I was doing and I said "preparing my book report". It was a Classics Comic, perhaps appropriately Don Quixote. .

 

Teachers find that even more annoying.

 

I have no trouble at all looking back and realizing why teachers sometimes found me annoying. I was.

 

I can hear someone muttering "and some things never change".

[mycroft]

and then there are the teachers whose line was "If you keep a 70% average in my class, you can do anything you like provided you don't disrupt others, stay in your seat and keep your clothes on" (direct quote, and I can remember it <mumblety> years later) - if you weren't at 70+%, of course, face front, notes taken, ...

 

People continue to find the fact that I have difficulty concentrating on only one thing at a time - that if I'm having a conversation, I may be doodling off picross puzzles or the like - but I'm actually paying more attention then I could were I just sitting face first and listening (at least for more than 5 minutes). I agree with them - it's odd, and looks offensive. I try not to do it in situations where the offense would be taken.

[barmar]

and then there are the teachers whose line was "If you keep a 70% average in my class, you can do anything you like provided you don't disrupt others, stay in your seat and keep your clothes on" (direct quote, and I can remember it <mumblety> years later) - if you weren't at 70+%, of course, face front, notes taken, ...

70% seems to be a pretty low bar for that privilege. That sounds like anyone who isn't failing. 90% seems like a more appropriate cutoff.

 

I was a smart kid, but I don't think I ever got way ahead of the subject like blackshoe. I did have a friend or two who had already studied the calculus book while we were still doing algebra, but not me.

 

The one time I disrupted class was when I got into an argument with my Junior High Earth Science teacher over parallax. He claimed that a star that's 1 parsec away has a parallax of 1 second, 2 parsecs has a parallax of 2 seconds, and so on. But it's the opposite -- the farther away a star is, the smaller its parallax is. I went up to the blackboard, drew a simple diagram showing the two stars, and the angles, yet he still didn't get it right away. It dragged on after the bell rang. Eventually he realized I was right.

[kenberg]

70% seems to be a pretty low bar for that privilege. That sounds like anyone who isn't failing. 90% seems like a more appropriate cutoff.

 

I was a smart kid, but I don't think I ever got way ahead of the subject like blackshoe. I did have a friend or two who had already studied the calculus book while we were still doing algebra, but not me.

 

The one time I disrupted class was when I got into an argument with my Junior High Earth Science teacher over parallax. He claimed that a star that's 1 parsec away has a parallax of 1 second, 2 parsecs has a parallax of 2 seconds, and so on. But it's the opposite -- the farther away a star is, the smaller its parallax is. I went up to the blackboard, drew a simple diagram showing the two stars, and the angles, yet he still didn't get it right away. It dragged on after the bell rang. Eventually he realized I was right.

 

I don't mean to embarrass you with praise or anything but the above represents a key distinction with students. By Junior High you understood that the issue was logic rather than authority. Some ( I include myself and my friends at that age) got this. Others never did. What the teacher said was right, end of story.

 

One of my favorites along this line (I won't mention the author of the text although he would probably get a kick out of it, he is a good person): I was reaching an honors class for freshmen back before calculus was regularly taught in the high schools so I had these bright calc students and I was using an unusual text. After the usual techniques of integration were presented, a list of exercises was given by the author with the following comment: "It only took the author fifteen minutes to work these and it shouldn't take you much longer". I came in the next day and right away a student raised her hand. Yes? "I can see why it took him only fifteen minutes. He only worked every other one, and half of his answers are wrong". This was the right sort of text for the right sort of student. He had exercises, starred exercises, double starred exercises, and triple starred (some of them unsolved) exercises. One of the triple starred ones became a Ph.D. thesis. Despite the occasional typo (she overstated the number of wrong answers) on routine things his taste was excellent.

 

Math is supposed to be fun. It can be.