Math Education, elementary

[kenberg]

Since I am still trying to decide about the School Boad election, I went to the School Board website. They have various things for education, including videos. Here is a link to the first one I watched, it's on how parents might help with Geometry..

 

http://www.parenttoolkit.com/index.cfm?objectid=BB2BEB20-8A3B-11E6-B2BD0050569A5318&targetObj=20975EF0-8A40-11E6-B2BD0050569A5318

 

Oh my.

 

I found other suggestions on this site, such as watching movies with math in them. The Da Vinci Code, for example. Good grief. A Beautiful Mind was also suggested. A better movie than the idiotic The Da Vinci Code but I don't really see it as helping a youngster get a feel for math. I liked Proof. (The 2005 American film, not the earlier, and different, Australian one that I haven't seen.)

Here is from the Wik about the movie Proof:

Since 1993 (when Andrew Wiles first claimed to have proven Fermat's Last Theorem), there have been several feature films about mathematicians, notably Good Will Hunting (1997), A Beautiful Mind (2001), Proof (2005), Travelling Salesman (2012) and most recently, The Imitation Game (2014).

 

In 2006, mathematician Daniel Ullman wrote: "Of [the first] three films, Proof is the one that most realistically illustrates the world of mathematics and mathematicians." Timothy Gowers of the University of Cambridge, a Fields Medalist, and Paul Sally of the University of Chicago, acted as mathematical consultants,^[4] but Ullman praised the director too: "Madden should be credited with capturing the feeling of the mathematical world."^[5] He also called Proof: "richer and deeper, simultaneously both funnier and more serious, than either A Beautiful Mind or Good Will Hunting."^[5]

 

 

 

I liked Good Will Hunting, but I liked it for lines such as "I have to see about a girl", not for the portrayal of mathematics.

 

 

 

And by the way. The School Board, like the county in general, is pretty conservative. More contards than libtards by far.

 

It seems to me that kids need how to think and to plan. Some math, at least some arithmetic, arises naturally. When we were 12 Denny Bloom and I road our bikes to an amusement park on Lake Minnetonka, west of Minneapolis, from where we lived in St. Paul. Math was hardly the high point of our planning, but we did have to figure out how far it was and how long it would take. Kids should learn to handle money early on. Obviously this is important, and some math can arise. Suppose a kid is given some (probably not total) control over which clothing to purchase, subject to budget limitations.

 

As we get further on, science can be involved. Archimedes might or might not have said Eureka (probably not, see https://www.scientificamerican.com/article/fact-or-fiction-archimede/ ) but the general idea of buoyancy and the associated calculation might be of interest.

 

Scientific American was a big deal for me, but so was Hot Rod. In fact the latter brought up issues such s torque, horsepower and acceleration, among many other things.

 

Math is where you find it, but it seems we should start with providing kids with an interesting environment. They, many of them, are apt to take it from there.

[Zelandakh]

Oh my.

My favourite geometry question ever, written for a football-mad ManU fan. Eric Cantona is walking up to take a penalty in the last minute of the Champions League final. What angle should he kick the ball to score in the top corner?

 

On the subject of maths in popular culture, one of the better ones is perhaps the episode of Sherlock Holmes where they use trigonometry to solve a treasure hunt. None of these are likely to get a child interested in the subject though. I personally think the best way is to encourage a child to think about the world and want to find answers. The ability and interest comes directly from having such an inquiring mind and the skills are transferable to other areas.

[hrothgar]

FWIW, my nephew is just started 8th grade

 

Here's what we're using to get him up to speed wrt maths

 

https://www.mathworks.com/moler/exm/chapters.html

[kenberg]

FWIW, my nephew is just started 8th grade

 

Here's what we're using to get him up to speed wrt maths

 

https://www.mathwork...m/chapters.html

 

I'm guessing your nephew is not having trouble with how best to multiply 12 times 18 :)

 

Still, he may not be ready yet for the chapter on differential equations.

 

Next year maybe, no rush.

 

And I went to a talk not long age on Shallow Water Equations.

 

Good luck to him, and may he enjoy it!

 

And I will be reading chapter 11. Looks like a kick.

[hrothgar]

I'm guessing your nephew is not having trouble with how best to multiply 12 times 18 :)

 

Still, he may not be ready yet for the chapter on differential equations.

 

Next year maybe, no rush.

 

And I went to a talk not long age on Shallow Water Equations.

 

Good luck to him, and may he enjoy it!

 

And I will be reading chapter 11. Looks like a kick.

 

Agreed

 

the main goal is to get him used to working with numerical methods and get him familiar with linear algebra

[hrothgar]

I'm guessing your nephew is not having trouble with how best to multiply 12 times 18 :)

 

Still, he may not be ready yet for the chapter on differential equations.

 

Next year maybe, no rush.

 

And I went to a talk not long age on Shallow Water Equations.

 

Good luck to him, and may he enjoy it!

 

And I will be reading chapter 11. Looks like a kick.

 

Agreed

 

the main goal is to get him used to working with numerical methods and get him familiar with linear algebra

[PeterAlan]

It never occurred to me that none of them had verified it for truth, until ... I realized the possibility that all the people that related the story to me were misinformed.

...

This tells me that I need to do more fact checking, and intend to do that when I find a fact-checking site that not considered either liberal-leaning or conservative-leaning.

Three guidelines for your less credulous future self:

 

When you need a working hypothesis

 

• if something sounds too good to be true, it is
   
  
• if something could be a hoax, it is
   
  
• cock-up rather than conspiracy every time.
  

[Vampyr]

Three guidelines for your less credulous future self:

 

When you need a working hypothesis

 

• if something sounds too good to be true, it is
   
  
• if something could be a hoax, it is
   
  
• cock-up rather than conspiracy every time.
  

 

Another hallmark of an urban rumour is if a number of people have independently related it.

[kenberg]

Here is a rule I follow when trying to assess what is going on during the play of a hand. Most opponents are neither geniuses nor idiots. If you lay down the Ace and your opponent plays the King under it, chances are that he probably was not dealt the King-deuce. Ok, I can construct a hand where this would be the right play, and maybe even one where an on the ball opponent would see that it is the right play. But my default assumption is that he played the King from KQ or K stiff, not from K2.

 

So it is with many of these stories. Unless the Prof had some reason that he wished to be fired, or was on an acid trip, the story makes no sense. Yes, he could be strung out. But far more likely, someone made the story up.

 

Cynicism is bad, skepticism is good. This will carry a person through many difficult spots. And intuition is useful.

[mike777]

All this concern over the quality of education is nice but in practice I think we overlook, overlook on purpose, a very very important role that public schools play.

 

 

Schools are baby sitters for many parents. Teachers in practice find one of their most important roles is that of babysitter

 

 

I note in my state, cmy county that roughly `14-16% OFall teachers quit each year, every year.

[Kaitlyn S]

All this concern over the quality of education is nice but in practice I think we overlook, overlook on purpose, a very very important role that public schools play.

 

 

Schools are baby sitters for many parents. Teachers in practice find one of their most important roles is that of babysitter

 

 

I note in my state, cmy county that roughly `14-16% OFall teachers quit each year, every year.

It seems as though Elliana has showed us that she can teach the children while she babysits them. Perhaps the ones who leave can't do that. That would mean that in a school with 50 teachers, 35-40 would leave in 5 years, which pretty much is in line with my expectations about the talent of a typical teacher. That's pretty appalling and if we can fix that problem, we'll be much closer to solving problems with our education system.

[awm]

It seems as though Elliana has showed us that she can teach the children while she babysits them. Perhaps the ones who leave can't do that. That would mean that in a school with 50 teachers, 35-40 would leave in 5 years, which pretty much is in line with my expectations about the talent of a typical teacher. That's pretty appalling and if we can fix that problem, we'll be much closer to solving problems with our education system.

 

Not nearly so many leave the profession, although some do switch schools. The keys to retaining teachers seem to be competitive pay and mentorship/coaching. This article has some interesting stats.

[mike777]

It seems as though Elliana has showed us that she can teach the children while she babysits them. Perhaps the ones who leave can't do that. That would mean that in a school with 50 teachers, 35-40 would leave in 5 years, which pretty much is in line with my expectations about the talent of a typical teacher. That's pretty appalling and if we can fix that problem, we'll be much closer to solving problems with our education system.

 

 

thank you for taking the time to reply.

 

 

NOt sure what the problem is. In fact I dont know what the problem is. YOur post does not tell us what the problem is or provide any evidence what the problem is.

 

I only want to point out that we do not destroy schools and replace them with something or ten somethings it is true that my local grammer school rates highest....100% in math and reading yet my small tiny block sends students to private or home school.

 

In my local area we are a county district not just my local city. When you try and destroy a local school, forces, many forces rise up to stop you. Racism is number one.

 

 

It is true very true that when you try and destroy a school it is a minority school. In my county 30% of the students in public school are non minority.

[nige1]

I know, you probably believe that Obama is a socialist. You may even question whether he is a citizen....I'd guess that you claim that you don't really think he isn't but that one can never be sure. And of course that has nothing to do with the colour of his skin or his name...after all, you aren't a racist...we know that because you say it with such assurance.

 

Both of these delusions, and especially the one about Clinton being a socialist, stem from a third and most insidious delusion or, more accurately, a commonly-shared ignorance amongst most Americans, especially right wing Americans.

I recognize this style of argument :( Welcome back, Mike :)

[kenberg]

All this concern over the quality of education is nice but in practice I think we overlook, overlook on purpose, a very very important role that public schools play.

 

 

Schools are baby sitters for many parents. Teachers in practice find one of their most important roles is that of babysitter

 

 

I note in my state, my county that roughly `14-16% OFall teachers quit each year, every year.

 

As I said in the note just above this one, cynicism is bad, skepticism is good. A (just retired) second grade teacher lives next door. She sometimes spoke of frustration, but she never spoke of her job as baby sitting.

 

Society has changed (No S***. I hear you say). By necessity or preference both parents, when there are "both parents", have jobs. But that does not automatically turn the teachers into babysitters. There will always be issues of scheduling, and of course they are more intense when both parents work, even if one of them has somewhat flexible hours. If the schools, for some reason, have an unexpected closure, this can cause problems. This is not the same thing as when parents have to cancel an evening out because the babysitter got sick.

 

I do think there is a problem along the lines of what you are saying. It's ok that kids who come from poverty get fed at schools. I favor that. Strongly. But I do get the feeling, I don't know enough to say all that much, that teachers are sometimes expected to make up for the lack of other guidance that was traditionally parental. Even putting legal problems and school policies aside, there is only so much that a teacher can do.

[barmar]

Since I am still trying to decide about the School Boad election, I went to the School Board website. They have various things for education, including videos. Here is a link to the first one I watched, it's on how parents might help with Geometry..

 

http://www.parenttoolkit.com/index.cfm?objectid=BB2BEB20-8A3B-11E6-B2BD0050569A5318&targetObj=20975EF0-8A40-11E6-B2BD0050569A5318

 

Oh my.

 

I found other suggestions on this site, such as watching movies with math in them. The Da Vinci Code, for example. Good grief. A Beautiful Mind was also suggested. A better movie than the idiotic The Da Vinci Code but I don't really see it as helping a youngster get a feel for math. I liked Proof. (The 2005 American film, not the earlier, and different, Australian one that I haven't seen.)

 

I haven't looked at the site, but I'm guessing that they don't expect kids to learn math from any of these movies. The idea is for them to see mathematicians as real people, or math being used in interesting ways, to help them from being turned off by it.

 

It's similar to the way that diversity in TV shows helps people (especially youngsters) be more accepting of people of different races, ethnicities, sexual preferences, etc. It's hard to give students lots of real-world experiences, but exposing them to similar experiences in the media they watch is the next best thing.

[blackshoe]

This tells me that I need to do more fact checking, and intend to do that when I find a fact-checking site that not considered either liberal-leaning or conservative-leaning.

"You pilot always through an unknown future. Facts are your only clue. Get the facts!" -- Robert A. Heinlein

 

As for finding a site that isn't considered to lean one way or t'other, good luck with that. :ph34r:

[y66]

From Schools That Work by David Leonhardt:

 

When you talk to the professors about their findings, you hear a degree of excitement that’s uncommon for academic researchers. “Relative to other things that social scientists and education policy people have tried to boost performance — class sizes, tracking, new buildings — these schools are producing spectacular gains,” said Joshua Angrist, an M.I.T. professor.

 

... Perhaps the most important thing about the Boston study, however, is that it fits a larger trend. Again and again, analyses of “high expectations, high support” schools — in Florida, Denver, New Orleans, New York, even Newark, despite other charter-school disappointments there — have come to similar conclusions.

 

So why isn’t there a national consensus to create more of these schools?

 

Because the politics of education are messy.

 

First, no school can cure poverty on its own. At Match, for example, only about 55 percent of students go on to graduate from a four-year college. That’s much higher than at most public schools, but I’ll confess I still find it a bit disappointing because it means some charter graduates still struggle. And when we journalists write about schools (or most anything else), we often emphasize the negative. We have paid more attention to controversies — like harsh suspension policies in some places — than to an overwhelming pattern of success.

 

Second, many people understandably worry that charters harm children who attend the rest of the public-school system. But there is good news here, too. Two recent analyses of multiple studies concluded that charters do not hurt outcomes at other schools — and may even help improve them, by creating competition.

 

Finally, no matter how successful charters may be, they undeniably make life uncomfortable for some people at traditional schools.

 

The best place to see this dynamic right now happens to be here in Massachusetts. On Tuesday, the state will vote on whether to allow charters to expand. Doing so would have enormous benefits: It would improve the lives of some of the 30,000 children who have lost lotteries and are now on waiting lists.

[kenberg]

From Schools That Work by David Leonhardt:

 

This is a very interesting article. If the claims about success hold up to scrutiny, I think it outranks all objections. A few thoughts:

 

Achievement gaps: As a general rule, I often think we as a society are paying way to much attention to demographic categories. I get really annoyed at being classified as old, white and male. I am, but so what. But I make exceptions. Obviously we have a racial problem in the U.S., and I doubt that major progress will happen unless we can do something about the serious differences in educational outcomes. If (again that's if) the claims hold up then I think the people doing this should all receive some sort of presidential citation. I can think of few things, maybe no things, that are more important to our collective future.

 

Expectations: I was once a kid. When I was quite young I was, as I often was, in a neighborhood bar with my parents. This guy came up and offered me a dollar bill, a fair amount of money in the early 1940s, if I could add the digits on the serial number and get the right answer. I did. My mother kept that dollar bill for the rest of her life. It was, she said, the first dollar I had ever earned. A message was transmitted. [And no, the message was not that my mother was going to grab for herself any money that I earned.]

 

I realize, and strongly believe, that we must have all of our schools be good. But we do not have that. To say that some of the schools are not very good understates the problem severely. Some are awful.

 

The schools discussed in this article provide evidence of what can be done. We should do more of it. I regard this as unequivocally obvious.

 

 

Added: Looking at the two graphs again I notice something interesting. Assuming that I am reading them correctly, it appears that there was not much of any benefit for the white students. The peak of the curve for the whites students, first in 6th grade and then in 8th, is about the same, a little short of 0.5 on the horizontal axis. Possibly the standard deviation became a little less. And the 8th grade curve seems a bit more symmetric than the 6th grade curve.

 

 

The label on the graph says

"0 on the x axis is equivalent to an average score for all Massachusetts students." Exactly what 0.5 means isn't clear.

Anyway, it seems that on this scale the median white 6th grader was at 0.5, minus a bit, and same for the median white 8th grader after two years in this program. The progress was much more impressive for black students. The latter is good of course, but it just seems unlikely to me that the program only benefits the students of one race. At the least, I would like to hear the explanation. Surely white students are not so good that further improvement is impossible!

 

Am I somehow reading these graphs incorrectly?

[barmar]

You might have to find the graph in the original paper

 

https://seii.mit.edu/wp-content/uploads/2013/08/Stand-and-Deliver-January-2016.pdf

 

to find out how to interpret the details.

Surely white students are not so good that further improvement is impossible!

It's not the students who are already so good, but the schools that white students come from before enrolling in a charter. They'd already received a good education, so there's not as much room for improvement.

[kenberg]

I continue to be interested in that study. I was mulling it over with my afternoon trip to Starbucks.

 

It occurred to me that the horizontal scale reflects some standard deviation. The numbers seem reasonable for that. But standard deviation of what? All Massachusetts students, I suppose. The center is at 0, as they say. The curves are not really symmetric, but maybe close enough so that the peak can be thought to occur at the median.

 

This would mean that the median score for the black kids was approximately the median for the state when they entered the program in sixth grade, but then went up by about half a standard deviation by 8th grade. That's impressive.

 

But it still leaves me wondering why there was little if any change in the white scores. They were put into the same high expectations format, coupled with longer school days and monitoring of teachers. It produced no result at all? I was born a skeptic about data, and I have not grown out of it. I just don't understand this.

[kenberg]

You might have to find the graph in the original paper

 

https://seii.mit.edu...anuary-2016.pdf

 

to find out how to interpret the details.

 

It's not the students who are already so good, but the schools that white students come from before enrolling in a charter. They'd already received a good education, so there's not as much room for improvement.

 

I was posting my second thoughts as you were writing this. I in fact did go to that paper.Thirty pages or so, fairly dense. It has graphs, some similar to the ones in the article but I could not find the exact graphs.

 

I can well imagine a lesser effect. If the change in the school environment is not as large, presumably the effect will be not as large. But there appears to be almost no effect. That's harder to understand.

 

 

And it's a bit ominous. I imagine the kids have to travel further to get to this charter school than if they just stayed put. And the hours in school are longer. If there is no effect, why would anyone do this?

 

 

Becky went to Lowell high school in San Francisco, public but you had to apply. She worked hard in middle school to get into it, and she took bus and BART daily to get there. It paid off. Me, I just walked, or sometimes hitchhiked, to the nearest one.

[hrothgar]

It appears as if the authors are excluding poorly performing charter schools from their analysis

 

We set out to study the effects of attendance at six charter high schools

in Boston. These schools generated the lottery-based estimates of charter

high school achievement effects reported in our earlier study ðAbdulkadirog˘lu

et al. 2011Þ, and they account for the bulk of charter high school

enrollment in Boston today.3 Two additional charter high schools serving

Boston students in the same period are now closed. One school that is still

open has poor records and appears unsuitable for a lottery-based analysis.

[awm]

It appears as if the authors are excluding poorly performing charter schools from their analysis

 

In general the results from charter schools are very mixed. Some seem to do very well, others very badly. I think any blanket statement as to whether charters are good or bad is over-generalizing. The study seems to be specifically about a certain type of charter school which sets very high expectations of students and has very regular observing/coaching of teachers in a classroom environment. It's believable that this type of school tends to perform well, while some of the charters which seem more about cutting costs (and possibly making a profit for the organizer) are worse than the public schools. Of course, deciding which are the "good kind" of charter schools can be somewhat arbitrary, but it seems reasonable to try to learn from the "best practices" while shutting down the charters that perform worse than the local public schools.

[kenberg]

It appears as if the authors are excluding poorly performing charter schools from their analysis

 

 

 

Yes, very much so. As I understand their claims(s), it is not at all that "Charter schools are great". Rather it is that "High expectations coupled with long hours and good teaching produces good results".

 

The NYT may have been a bit too quick to accept the results at face value. I might or might not read the referenced article but I hope that it all receives the careful analysis such claims deserve.

 

If we can really bring about results such as the study claims this would be great news. I hope it stands up.