[y66]

From Tyler Cowen's conversation with Michael Kremer:

Quote

COWEN: Let’s say the current Michael Kremer sets up another high school in Kenya. What is it that you would do that the current high schools in Kenya are not doing? What would you change? You’re in charge.

KREMER: Right. We’ve learned a lot in education research in recent years. One thing that we saw in Kenya, but was also seen in India and many other places, is that it’s very easy for kids to fall behind the curriculum. Curricula, in particular in developing countries, tend to be set at a fairly high level, similar to what you would see in developed countries.

However, kids are facing all sorts of disadvantages, and there are all sorts of problems in the way the system works. There’s often high teacher absence. Kids are sick. Kids don’t have the preparation at home, often. So kids can fall behind the curriculum.

Whereas we’ve had the slogan in the US, “No Child Left Behind,” in developing countries, education system is focused on kids at the top of the distribution. What’s been found is, if you can set up — and there are a whole variety of different ways to do this — either remedial education systems or some technology-aided systems that are adaptive, that go to where the kid is . . . I’ve seen huge gains from this in India, and we’re starting to see adoption of this in Africa as well, and that can have a very big impact at quite low cost.

Quote

Michael Kremer is best known for his academic work researching global poverty, for which he was awarded the Nobel Prize in 2019 along with Esther Duflo and Abhijit Banerjee. Less known is that he is also the founder of five non-profits and in the process of creating a sixth. And Kremer doesn’t see anything unusual about embodying the dual archetypes of economist and founder. “I think there’s a lot of relationship between the experimental method and the things that are needed to help found organizations,” he explains.

[y66]

David Lipomi and Tyler Cowen discuss aspects of remote learning in covid times that will stay with us after on-site learning returns: https://youtu.be/cFcvzbJKWgw?t=1931 (starting at 32:11)

[pilowsky]

Elsewhere, there was a discussion about maths training and Bayes theorem.
I referenced a site that ranked countries according to success in a standardised maths test.
Here is a graph that compares rank in maths (Y-axis) against the number of Bridge players per 1,000,000 of population.
Turns out there is quite a decent relationship!
http://bit.ly/MathEdBridge

For added fun, here is a Geo Heat map of where Bridge is most popular/1,000,000 of population.
The data was taken from the WBF.
https://bit.ly/BridgePopularity

Obviously, the data from the WBF could underestimate some countries that do not pay subs for their full WBF membership - I note that Russia has exactly 1000 members - which suggests that the numbers are not completely reliable.

[barmar]

I refuse to take seriously a graph that pluralizes "math".

[hrothgar]

FWIW, I heard back from my nephew about Bayes theorem.

He did encounter it during his high school curriculum, but not until his multivariate calculus class (I have no idea why it showed up here).

For the sake of reference, he went to one of the top public high schools in New Jersey and will be attending Princeton next year. So, my guess is that most high school students in the US never receive any formal instruction on this topic.

[barmar]

hrothgar, on 2021-May-08, 10:28, said:

He did encounter it during his high school curriculum, but not until his multivariate calculus class (I have no idea why it showed up here).

When I was in high school (late 70's), my guess is that less than half the students took any calculus at all. And this was in an upper middle class school district.

[kenberg]

barmar, on 2021-May-08, 10:35, said:

When I was in high school (late 70's), my guess is that less than half the students took any calculus at all. And this was in an upper middle class school district.

I can't resist using this to illustrate just how much things have changed.

Brad Efron and I grew up in St. Paul, both finishing high school in 1956. We were not close but we both belonged to a teen-age discussion group (The Philosophers) and he was at my house a couple of times. He went to Central HIgh, the best public high school in St. Paul, I went to Monroe, which was, well, not the best. By my senior year, most of my friends went to Central. Greg (another Central friend, we still see each other) and I were talking about Brad and he told me that the math teacher (a trig course) brought in a calculus book, handed it to Brad, and said, here, read this, you are finding trig too easy.
I knew of no other high school senior anywhere who was involved with calculus. Greg and I had taken a non-calculus based physics course at the University of Minnesota the summer before (his parents paid for his enrollment, I asked the prof to sit in for free, permission granted). Greg, I, and others attended a free lecture series at the U of M, given by Paul Rosenbloom on Saturdays. But none of us knew any high school kid, except Brad, that was studying calculus.

What a difference, then and now.

It's great that kids are taking calculus now, or I suppose it is. I enjoyed working on cars, my car and cars that my friends owned, if I had to pick I think I would stick with the cars. But it would be nice to do both.

One problem that really bugs me. In the 50's, Monroe and Central were not all that much different. Central was better, a fair amount better, but today the gap between the good public high schools and those that are not so good is a chasm.

My apologies to Brad for telling this story w/o asking if it is ok to do so. Seems harmless enougjh.

[hrothgar]

So, here's MY Brad Efron story

Back when I was working at The MathWorks, I wrote up an amusing little app that I called "FitIt".

It used cross validation to select the optimal span for a smoothing spline and then used a bootstrap to generate confidence bounds. (Cleve Moler - one of the company's founders) was doing a walk about and really liked the application. he stopped to talk to me and asked me how I figured this all out. I explained that I had been reading a book called "An Introduction to the Bootstrap" by Brad Efron and it contained a very similar use case. The only thing that I had done was re-implement this all using MATLAB, added in GUI, and included an object to store the results of the fitting operation so folks could use it for interpolation.

Cleve gave a chuckle and said that Brad had been his roommate back in the day and that he knew the book and the example quie well. (He just wanted to see if I was dumb enough to try to claim credit for someone else's work)

[pilowsky]

When I finished high school research looked like a good choice.
And it was.
Every decade that followed publications where Australia was included as an Affiliation Country the start to the end of decade percentage of papers either stayed the same or increased.
In the last decade, it collapsed to 1970's levels.

[Cyberyeti]

barmar, on 2021-May-08, 09:37, said:

I refuse to take seriously a graph that pluralizes "math".

Maths is the standard word in the UK, math is an Americanism

[kenberg]

Cyberyeti, on 2021-August-20, 02:16, said:

Maths is the standard word in the UK, math is an Americanism

A relaxing early morning exercise.

I guess we could say maths is short for mathematics in the same way that langs could be short for languages. But while a person might study languages he might also study a language. The word "mathematics" is more like "civics". A person might study civics but I have never heard of a person studying a civic. Nor have I ever heard of a person studying a mathematic. Of course a person could study algebra and geometry at the same time, just as another person might study French and Spanish at the same time, so a plural form could have its uses. But that is not how "mathematics" is used. We don't say that a person taking a course in federal and state government is taking a civics course while the person studying only the federal government is taking a civic course. Same with algebra, geometry, mathematic and mathematics.

Or maybe I am wrong. Maybe in the UK a student could take a mathematic course and has to take two courses if he is to be studying mathematics.

This issue has not been disturbing my sleep.
A guy I once knew of English descent had to keep it straight which members of his extended family pronounced their name one way and which pronounced it in a very different way. That could be a crisis.

[y66]

I learned this word yesterday from Kim Stevenson (food writer): whatevs.

[Cyberyeti]

kenberg, on 2021-August-20, 06:45, said:

A relaxing early morning exercise.

I guess we could say maths is short for mathematics in the same way that langs could be short for languages. But while a person might study languages he might also study a language. The word "mathematics" is more like "civics". A person might study civics but I have never heard of a person studying a civic. Nor have I ever heard of a person studying a mathematic. Of course a person could study algebra and geometry at the same time, just as another person might study French and Spanish at the same time, so a plural form could have its uses. But that is not how "mathematics" is used. We don't say that a person taking a course in federal and state government is taking a civics course while the person studying only the federal government is taking a civic course. Same with algebra, geometry, mathematic and mathematics.

Or maybe I am wrong. Maybe in the UK a student could take a mathematic course and has to take two courses if he is to be studying mathematics.

This issue has not been disturbing my sleep.
A guy I once knew of English descent had to keep it straight which members of his extended family pronounced their name one way and which pronounced it in a very different way. That could be a crisis.

Mathematic is never used as something you study here or as "a mathematic" it is occasionally used as an alternative to mathematical.

[kenberg]

Cyberyeti, on 2021-August-20, 11:15, said:

Mathematic is never used as something you study here or as "a mathematic" it is occasionally used as an alternative to mathematical.

I majored in mathematics in the US. In Minnesota to be more precise. If I had pursued the same course of study at a college in England and I was asked "What are you studying?" my answer would be?

Let's assume I wanted a more formal answer than "I am studying maths". Or is that the preferred answer?

This is interesting. I had always assumed that I would just say "mathematics". I spent a month long ago at a maths conference (that's the correct usage?) in England once (the University of Warwick, a great place) and I cannot recall the issue ever coming up. Of course we all knew why we were there.

My memory focuses on strange things. While I was there I saw the movie version of Cabaret at the Lady Godiva theater. Yeah, I also did other things.

[Cyberyeti]

kenberg, on 2021-August-20, 11:56, said:

I majored in mathematics in the US. In Minnesota to be more precise. If I had pursued the same course of study at a college in England and I was asked "What are you studying?" my answer would be?

Let's assume I wanted a more formal answer than "I am studying maths". Or is that the preferred answer?

This is interesting. I had always assumed that I would just say "mathematics". I spent a month long ago at a maths conference (that's the correct usage?) in England once (the University of Warwick, a great place) and I cannot recall the issue ever coming up. Of course we all knew why we were there.

My memory focuses on strange things. While I was there I saw the movie version of Cabaret at the Lady Godiva theater. Yeah, I also did other things.

I have a maths degree also, and that's how I would say it in almost all circumstances.

[pilowsky]

From last years Advanced mathematics paper for final year students in NSW:

Quote

Question 21 (6 marks)
Hot tea is poured into a cup. The temperature of tea can be modelled by
T = 25 + 70 (1.5)^{−0.4 t},
where T is the temperature of the tea, in degrees Celsius,
t minutes after it is poured.
(a) What is the temperature of the tea 4 minutes after it has been poured?
...............................................................................................................................
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1
(b) At what rate is the tea cooling 4 minutes after it has been poured?
...............................................................................................................................
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2
© How long after the tea is poured will it take for its temperature to reach 55°C?
...............................................................................................................................
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...............................................................................................................................
...............................................................................................................................
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For Americans living outside Boston, this applies to coffee as well.

[kenberg]

pilowsky, on 2021-October-18, 19:25, said:

From last years Advanced mathematics paper for final year students in NSW:


For Americans living outside Boston, this applies to coffee as well.

I am not seeing what you have in mind. Is this copied verbatim? The first question is listed as (a), the next as 1 (b), the last as 2 . But I'll move on.

I am guessing some on this thread can work this, some can't. A good pre-calc class should prepare a student for the first and the third question, the middle question involves calculus. Calculus usually begins with polynomials but gets to exponentials (as here) fairly quickly. A teacher's view: They should be able to do this ("they" means the students in a calculus class meant for those who will be using calculus seriously) but the reality is that in any class I taught there would be somewhere between a few and several that cannot.

As far as I know modeling the temperature as an exponential decay is reasonable. It's a cup filled with fluid so that can have an effect on theory I suppose, but basically, Newton says temperature decays exponentially and who am I to disagree with Sir Isaac?

I guess they should stipulate the expected form of the answer. How many digits in the numerical answer? Or, if an exact answer is desired, can it be in the form of a logarithm to the base 1.5? Assuming no, then we want natural logs? e always gets into the act.

I guess I must be missing something. I am prepared to be embarrassed when you say what I missed.

[pilowsky]

No, you aren't missing anything. I should have been less oblique.
The numbers are the marks (totals 6).
I was discussing STEM literacy with a colleague yesterday and looked up the proportion of final year high school students in NSW undertaking various levels.
The maths that you and I probably took is called Maths Extension 1 and 2 - taken by only 16% of students.
Physics and chemistry by 24%.
The question was copied from a lower level maths called maths advanced (38%) - the majority of students take a lower form called 'standard'.
Only 42.49% took any form of science at all.
This is only a percentage of those students that get to the final level of high school.


There was almost nothing in the exam that would suggest a big emphasis on being able to work out whether or not one group was significantly different from another.
I suspect this explains the unwavering belief that so many people have in things that make no sense at all.


Agree about Isaac - it's hard enough trying to be a shoulder upon which he might have stood.

[thepossum]

Something that concerned me once in a recent STEM course (as a very mature age student) was being described as the Maths genius (or words to that effect) having not progressed beyond honours almost 40 years ago. I actually don't think they have a clue what being a maths genius would entail. I could vaguely remember notation and how to do rather elegant proofs (if I say so myself), but that's all. Also, I struggle immensely with the Maths plugin to Word. It took me hours to format a few lines of maths and make them look elegant. I did my Maths degree with the contents of a pencil case

[kenberg]

thepossum, on 2021-October-29, 01:45, said:

Something that concerned me once in a recent STEM course (as a very mature age student) was being described as the Maths genius (or words to that effect) having not progressed beyond honours almost 40 years ago. I actually don't think they have a clue what being a maths genius would entail. I could vaguely remember notation and how to do rather elegant proofs (if I say so myself), but that's all. Also, I struggle immensely with the Maths plugin to Word. It took me hours to format a few lines of maths and make them look elegant. I did my Maths degree with the contents of a pencil case

I can't say about Australia but here the default package for math typing is LaTeX. It's a command language if that's the right way to phrase it, meaning that after writing it you then click on typeset to get what you want, but it comes up as a pdf and just about everyone can open a pdf. It would surprise me if things are different in Australia, I think of LaTeX as the universal choice.

It's hard to know what prompted the "math genius" reference. Perhaps a way of saying "Are you sure you registered for the right course?". imagine a person registering for a course called "Learn better bridge". The instructor is discussing how to plan the play so that all necessary finesses can be taken in the right order, and a student suggests that an overtrick can be made by running a progressive double squeeze. He might not be a bridge genius but he is probably in the wrong course. But who knows. I have taken a couple of off-the-shelf courses, one in HTML, one in life-saving techniques, I would not suggest trusting me in using what I learned from either of them.

Of course another explanation could be that you are a math genius. Why rule it out?