Lots of fun stuff in the "more pizza" discussion. There was (possibly) some uproar over the concept that one 18" pizza is bigger than two 12" pizzas. I say "possibly" because we don't know what percentage of readers did not comprehend this. We only know that the Daily Mail found some stupid comments among the twitter replies. We don't know whether those represent 1% or 90% of readers. I also note that some of those "stupid" comments looked suspiciously tongue-in-cheek, and others raised the somewhat fair questions of "it depends on what you want." If you can't get your pizzeria to divide your pie into the number of choices you would like, then two 12s might indeed be a better choice, and if what you really like is crust, then two 12s would be clearly superior.

The person putting this out was trying to make a math point, using pizza as an illustration, so those objections would seem irritating and beside the point to math people. Yet he did actually use pizza as his example, so he has invited the vampire across the threshold on that one. He also missed a trick in that is just barely works for 17" pizzas as well, because 17 squared is 289, one more than 12 squared times 2: 144 * 2 = 288). Maybe no one makes 17" pizzas, so the issue never comes up.

I read the story at Powerline, who blames this on liberals. That is a partly unfair generalisation - I know plenty of liberals who can do math, and am told that theoretical math depts at colleges are largely liberal. However, I think it not entirely unfair. Practical math people, including engineers, are much more likely to be conservative, and the liberals I know at work are mostly innumerate. Sometimes jaw-droppingly so, even among those with graduate degrees.

But the deplorers have their own problems here. At the conservative sites carrying this story, there is a lot of moaning about how everyone knew pi-r-squared when they were in school, and liberals have ruined our educational system and created a handbasket shortage because of excess supply of passengers.

The students in your highschool did not all know this. No, no they didn't. That is a false memory on your part. First, there were the children who went to special schools, in our case Laconia State School was the biggie. They were only a few percent, but those children are regular classes now and create the impression that things are much worse. I note in passing that while many of these children had genetic or prenatal problems, some were those who had bicycle accidents while not wearing helmets and you never saw them again. In my high school in NH 1967-71 - remember that NH is one of those states that has the best testing scores in the country year after year - there was about a 25% dropout rate. It was a crossover period from the early 60's and 30% to the late 70's and 20% in NH. Either way, they never dealt with pi-r-squared.

Nor did the kids in vocational or business math, by and large. There were vocational, business, and college tracks at the time. (This was a better idea, which we have lost because of false aspirational goals.) The first category only got taught concepts like areas of circles to give them an idea of such things, and to perhaps identify those mechanical students who could be given further instruction. Similarly, the business students got such things in hopes that they would at least get the idea that numbers could prove things, and there were ways of using them that were helpful. Some of that group understood concepts like squares and areas just fine, but were happy to drop it and get on to accounting and budgets.

People commenting about educational topics in a historical context on the internet are simply not a representative group of society at large. They remember what they and their friends learned, forgetting that this was not everyone.

## 8 comments:

Good comment on the “diverting” of students with lower math ability from normal school rooms. But if you look farther back in time the level of instruction in the grade schools was more rigorous. My grandfather made it through 6th grade in the 1920’s but continued with self study until he died. His shelves were full of ICS and Devry home study courses in practical math and mechanics. His basic arithmetic and geometry taught in school was first rate. My experience with “New Math” in the 1960s must have been disasterous for students without innate ability. I didn’t see some of these concepts again until I was in graduate school. With my daughter in the late 1990s I was always tempted to send the school district a bill for my time in compensating for really bad math curriculums.

In my time there was a decided drop in instructional quality in the late 1960’s and early 1970s. Teachers unionization and the Vietnam war really did a number. You started to see more male teachers there to dodge the draft without any real interest in teaching. You could tell the difference between the older and younger men’s attitudes at once.

It's not just knowing the math. It's also whether you are willing to think through the logic to realize that the right answer is somewhat counterintuitive.

That's crazy, son. Cornbread r squared, Pi r round.

Roy, around here cornbread r round too!

AVII note in passing that while many of these children had genetic or prenatal problems, some were those who had bicycle accidents while not wearing helmets and you never saw them again.I am personally acquainted with several examples of normal intelligence children becoming mentally retarded, though high fever was the cause for them.

As opposed to the current trend of everybody taking algebra and 3-4 years of math, when I was a high school student, one could take a year of "General Math" to fulfill the graduation requirement. Most of the General Math people led productive lives.

DirtyJobsGuyMy experience with “New Math” in the 1960s must have been disasterous for students without innate ability.The New Math I took in high school was Illinois Math (UICSM). I loved all the proofs involved. In fact, I liked math more after being exposed to all the proofs involved in Illinois Math. The top students loved it, but those students hot at the top but who were still good students didn't like all the proofs. The President of my junior class wrote in my yearbook, "No more math misery." Well, it wasn't misery for me.

When you realize that Illinois Math was developed at the University of Illinois lab school- populated almost entirely by faculty brats- you realize why it wasn't appropriate for most students.

Roy, I first heard cornbread are square from my mother.

It's a general point. We only know what we know, because we weren't there for the rest of it. It can be quite difficult to imagine what others know from experiences we didn't have, or only partially shared. This is true even for the most widely shared experiences, like 'having a President.'

The median age of the US population in 2017 was 38. Taking that person born in 1979 as normal, this median American doesn't remember Reagan except as an image, or through stories heard later in life. (Reagan left office when median American was 9). They probably have very little sense of Bush I. Their real memory of American politics begins with Bill Clinton; they have known Clinton and Obama, plus Bush II. Bush II is the real outlier there, but he was a compassionate conservative who expanded Medicare.

Of course, this is the median; actually very few people were born in 1979 compared to the total. Many of us who figure into that median knew Reagan reasonably well; some remember Carter or Ford pretty well. A whole lot more can barely remember Clinton. The fat part of the population pyramid for 2017 was as old as 10 when Clinton left office. They don't remember the Gulf War, or Bosnia, or Somalia, or a time when gays weren't allowed in the military. Vietnam exists only in movies; they may not ever have closely known a Vietnam veteran.

One could go on elaborating this forever. Imagine a USA in which Reagan was never President. In a significant way, that's their reality. So too all these other things.

I agree, most people then did not, and most people now do not, know how to compare areas of anything at all, except extremely simple squares, and not always even then. It's not age dependent, either. Don't even get started on volume appreciation. Intuition is a bad guide of these things, and without the formulas and some basic (but rare) math tools, intuition is pretty much all people have.

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