…must die.
I was reasonably well educated in the 60s and early 70s, but I was in one of the best educational systems in the country at the time, thanks to Charles Stewart Mott, and even then, I could see that a lot of my cohorts weren’t doing that well.
It’s gotten much worse.
In 1979, when the Department of Education was forced on us, the US’ education system was #1 in the world.
Today after 46 years of their ‘expertise’ the system is rated as #49
Well there was “New Math”. Which victimized me starting in 5th Grade right up until 7th Grade when our newly hired math/science teacher threw it all out! Disgusted by the fact that NONE of the students in his class could do math with fractions. Instead we’d been spending 2 years in Grade & Jr. High doing division using factors of 10 with remainders of the divisor and studying Set Theory and Venn Diagrams. I could tell you all about unions and intersections, even addition with non-base 10 numbers, and what a null-set was. But ask me to mix antifreeze of a specific percentage from alcohol and water? Forget it!
Nor could we do division of fractional numbers in decimal representation. Kinda handy when dealing with money. Of course if only we could get the US Mint to make coinage in the denominations of the divisors in our math problems, then we’d have been all set!
Yeah, I remember that, too. Fortunately, I’d learned how to do fractions before they started to torture us with that.
As was once said by a famous musical philosopher: “It’s the process that matters not the final answer.”
Yeah, I suffered through new math in first and second grades, I think. Fortunately it didn’t last long
In school, I was taught to calculate 60-19 by “borrowing” 1 from the 6 to leave 5 and subtracting 9 from 10.
Dad was a research engineer, and Mom directed us to “get help from your father” on math problems. But when I showed Mom this method of subtraction, she exploded, “Why are they teaching you this garbage in school! Here, let me show you how to do this.” I think her word for it was “schlamperei”, meaning “sloppiness”, but Austrian slang for “dumpster fire.”
Instead of borrowing, essentially subtracting a 1 from the 6, instead add a 1 to the next digit of 19 to make a 2, first subtracting 9 from 10 to give a 1 and then subtracting 2 from 6 to leave a 4, giving 60-19=41.
I don’t know if my explanation-in-words makes sense, but Mom illustrated with one example. But it made so much sense to me. Instead of subtracting 1 from “on top”, add 1 to the bottom, and it does the exact same thing. This became my first algorithm optimization in my career starting at age 7, which eventually resulted in Milenkovic, P. (2013) ASME J Dyn Sys Meas Control 135 p 051014.
How did Mom, who came from “backward” pre WW-II Serbia, know an advanced subtraction algorithm? Years later with the benefit of the Web, I learned that Mom’s method had a name: the Austrian Method https://en.wikipedia.org/wiki/Subtraction. Who knew, with much of what became Yugoslavia being Austria (remember that Franz Ferdinand dude and how an ugly diplomatic crisis between Austria and Serbia escalated into WW-I?), Mom would have learned the Austrian method in school?
The American method gets real clumsy, real fast when the borrowing needs to propagate to higher digits, whereas the Austrian method ripple-propagates gracefully–I believe the Wikipedia article mentions this. I asked a student in Madison public school to show me subtraction, and she showed me borrowing. I asked my colleague who teaches logic circuits for arithmetic in Computer Engineering courses, and Austrian subtraction was news to him too.
But are US private schools or US home schoolers, apart from South-Slavic refugee immigrants, still teaching “borrowing.”
That’s very amusing to me. I don’t remember whether someone had taught me that method, and I never knew it has a name and was ever taught in schools. I found it much quicker for mental calculations but it was verboten when teachers wanted me to “show my work.”
Just convert the bottom number to binary, invert it, add one, then add the two numbers together. ^_^
Pretty much what we teach in ECE 252 Introduction to Computer Engineering.
The “borrowing from the top” or “incrementing on the bottom” was actually in Tom Lehrer’s intro to New Math.
Just buy premixed anti-freeze. That way you can top off coolant lost to leaks in your old car without worrying about having the wrong glycol percentage.
That is unless you have a later model Toyota that needs that stupid red anti-freeze, or we should pity you for having a GM car with Dexcool, neither available in pre mix.
Yeah, we started getting all of that sets and Venn Diagrams stuff starting in fourth grade. Fortunately, except for a darling recent grad who quickly left teaching to get married barely into my 2nd-grade year, all of my teachers during my kindergarten and first three years of elementary school were no-nonsense women a year or two from retirement. They got us all through arithmetic as far as long division before the real nonsense arrived.
My 4th- through 6th-grade teachers were also veteran female specimens of only slightly younger vintage – with the exception of a splendid early-20s strawberry blonde in 5th grade. They all – including the strawberry blonde – mostly ignored the really stupid parts of New Math. That particular idiocy seems to have pretty much run its course by the time I hit junior high.
Maybe that was before my time (grade school in the 60s)–just a week or two of alternate bases, which I’d already learned from the World Book Encyclopedia–but otherwise pretty much traditional stuff. Even so, the state apparently had gotten tired of people graduating high school without knowing decimals and fractions and had added a math proficiency exam requirement about the time I graduated.
The corruption goes much deeper than the teachers. Last I checked it was over $17K per student per year in costs K-12. Obviously most of that doesn’t make it to the classrooms. Otherwise one wouldn’t hear of teachers buying student supplies with their own money. And running constant fund raisers for various activities.
As for education quality decades back, it is now 50 years since I p[assed a GED before finishing any high school night classes. That would not be possible if the test represented real education.
So defunding the public schools seems like a possible win.
My 6th grade teacher was complaining that too many parents regarded public education as free baby sitting, and that he’d be better paid if he were a baby sitter. That was around 1969.
Anyway, it’s going to be hard to convince people to give up free baby sitting.
I remember some of the New Math that was inflicted on us when I was in the 5th grade. Set theory, some Boolean logic, calculations in binary, octal*, and hexadecimal were staples of computer science, but personal computers didn’t exist. Computers were owned by government agencies, big corporations, and TV shows (spinning tape drives and flashing lights). The teacher couldn’t explain why she was teaching this stuff because she’d never seen a computer, either. It was about 15 years later before I ever touched a computer and started learning programming that this stuff made any sense.
* Octal is for losers who can’t count to F.
I used to joke that octal is mainly for people without thumbs.
However it was the favorite numbering system used in the CDC-6600. If it was good enough for Cray, I guess it was good enough for me too!
C’mon. You all know the reason for octal.
We are all geezers here of the generation that saw the transition from 6-bit ASCII to 8-bit ASCII. The transition to 16-bit ASCII came in the early 1980s, and that was superceded by things like UTF-8, which used 8-bit character codes plus escape codes to represent International character sets with variable-length strings.
If your character set is 6-bit, your word length will be a multiple of 6 as was everything from a PDP-8 (12 bit) to the CDC-6600 (60 bit). Octal (3-bit nibbles) is a natural shorthand for binary words.
I think the “push” for 8-bit characters with 4-bit nibbles coded in hex was an IBM 360 thing. Memory was still expensive, and going to 8-bit from 6-bit characters was a leap based on faith that memory would keep getting cheaper, or at least until a couple weeks ago.
6-bit? ASCII?
You whippersnappers had it easy! I had to do it with baudot!
Now get off my lawn!
So three fingers on one hand and two on the other?
You got to do it with Bardot?
I think the “push” for 8-bit characters with 4-bit nibbles coded in hex was an IBM 360 thing. Memory was still expensive, and going to 8-bit from 6-bit characters was a leap based on faith that memory would keep getting cheaper, or at least until a couple weeks ago.
I think it was more fundamental. The early SSI/MSI digital logic chips came in x4 packaging. Thus making a base-16 math a natural extension of what could be implemented in the fewest components.
I come by my hatred for octal naturally. Back in 1988, I was part of the initial crew for MCC-2 at what’s now Schriever SFB, CO (it was Falcon AFS back then, known as Falcatraz). I was a Planner Analyst for the DSCS-III comsat and the Command Database Specialist as an additional duty. At the time, we didn’t have permission to send commands to the satellites. The folks at Onizuka controlled the satellites and we just monitored. We couldn’t get permission to send commands until I could validate the D3 command database as being free from all errors.
D3 commands were either single commands, block commands, or special commands to perform RAM patch uploads. There were thousands of commands, each line being 20 bits long. They were stored as 7-digit octals instead of 5-digit hex values. I did some custom programming to imitate the satellite’s command decoder and compare that to what was in the database. It took a couple months to figure out my approach, write the program, then perform the analysis of the database. I found some errors. Eventually, they accepted my analysis.
The unit commander liked what I did, so I ended up having to do the same thing for the DSCS-II and NATO-III satellite families. All told, I validated well over 20,000 commands and developed a passionate hatred of everything octal.
Many would have liked to send sat C&C, most would be without a large dish with the high power Watkins-Johnson type cavity xmitters that would have drawn suspicion if ordered premade. That was line one of defense. Line two is the encrypted command set. Which you had to cipher and verify. Fun fun fun. Don’t try this at home kids. Even if you hand-rolled everything there are sats on station as I type this that do nothing but look down listening for rogue C&C emitters with pin-point accuracy. I know of a least one contractor that sells this service. Assuming of course the command set you worked on did more than play with transponders.
Ditto. The computer lab where I went to university had a CDC 3600 with 36-bit words and a CDC 6500 with 60-bit words. The original RISC processor. 6-bit characters. No addressable bytes. Everything was octal.
Didn’t encounter 8-bit characters until I wound up in a Xerox Sigma shop. EBCDIC character encodings. Same when I subsequently wound up in an IBM shop. Then there were DEC VAXes with 8-bit ASCII characters.
Being a code monkey taught me a healthy skepticism for “standards” if nothing else.
From your remarks, it sounds like you make your living doing at least some amount of computer programming. That it was 15 years after 5th grade that you first learn to code puts you in your mid 20s, which makes you an old geezer who sees a cardiologist on a regular basis like just about every other person here on Rand’s fine Web site. Today, people who become engineers learn to code in high school.
I am sorry you feel these math topics were inflicted on you and that your teacher couldn’t explain why this was taught, but some education bureaucrat in your school system somehow anticipated that computers would be everywhere and in everything.
You had superb preparation for learning to code that many of our age cohort did not have, which I know helped me “hit the ground running” when introduced to computers.
Are you trying to tell me that when the government gets involved, quality drops and cost skyrockets?!
Shocked, I tell you, shocked!
First contact with new math was in 1964 when I was 15 going on 16. Late the year before there was a competitive exam of all the high school kids in the State (Western Australia). I didn’t think I’d done well enough but to my surprise, got selected. Consisted of going to the local university (the only one in the State at the time) on Friday afternoon after school to get a lecture from a Prof. Daniel Finkbeiner from Chicago and after a meal, an hour of practical working problems. Learned probability, elementary statistics, set theory, Venn diagrams, Markov chains and other stuff I forget. At the end, the sponsor, British Petroleum gave us $20 each (over $300 today) and a nice tour of the local oil refinery. I guess that makes me the recipient of filthy fossil fuel money 🙂
I did find out I wasn’t really a mathematician although 20 years ago I had to find out the time constant of an aircraft response to vertical gusts. Set up the equation and recognised the solution to a first order differential equation so all worked out. Later found the same solution on the web where some guy called John C. Houbolt had derived it. I figured I was in good company.
Ah, but then there was Stuart R. Mott, politically opposite to his father, who I recall from a story that was probably in National Review around 1970. I think he was made fun of for inviting people to parties who were at least as radical as those at Leonard Bernstein’s at at the time.
Yes. Truly remarkable how many inheritors of great wealth are lefties.