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This seems so strange to me, this sharp distinction between algebra and non-algebra. I might have gone to school in the Soviet system so everything was backward

by rdtsc 8y ago

This seems so strange to me, this sharp distinction between algebra and non-algebra. I might have gone to school in the Soviet system so everything was backwards and such but we were introduced to https://en.wikipedia.org/wiki/Elementary_algebra https://en.wikipedia.org/wiki/Elementary_algebra very early and just did simple expression transformations, variable substitutions. That was a lot early than 8th grade. I even taught my 2nd grader a few of those. I have observed the curriculum so far in US, at least up until the 2nd grade and it's a hot mess. Even for double digit addition problems they jump right into "cool tricks" and "mathematical thinking" while there are just really a few steps to memorize and, guess what, kids are great at memorizing stuff. Later on it's time to show a few short-cuts and kids even discover those themselves. Now going back to algebra, I am firm believer that a simplified version of this has to be introduced much earlier. It's a bit like a spiral, do basic arithmetic, geometry, number line manipulation, simple word problems, next year do the same but more complicated, add some algebra in there and so on. But I guess that's just too boring and teachers, and probably higher level authorities, decide that they need to do "something" so they start making changes just to they can slap something on their resume. Developers do that too some extent, "here let me rewrite all this..." we can certainly understand that, but doesn't mean it's a good thing.

tomohawk 8y ago
Curriculum, most especially through 6th grade, is driven very much what whatever fad catches hold in the education establishment. It changes every 2 - 3 years. It's really just a symptom that there is very little accountability for the people making these decisions. Put out a curriculum with poor results? Who's going to notice? If anyone does, who will have the power to do something about it?
- linuxftw 8y ago
  This lack of feedback can be extrapolated to the entire government. It's a well defined problem: https://mises.org/library/economic-calculation-socialist-commonwealth https://mises.org/library/economic-calculation-socialist-com...
  - Shebanator 8y ago
    Do you think that is only a problem in government? Fads are a fundamental part of human nature. In tech, we have many examples: Agile, Ruby on Rails, React, RISC, OOP, microservices, and so on and so on. All have some real benefits, but also have or have had huge hype cycles. You can make the same argument for most other industries (if not all of them). And then there are things like diets, religions, etc.
    - WalterBright 8y ago
      > Do you think that is only a problem in government? Nope. But businesses fail when they succumb to fads, while government just raises taxes.
      - lern_too_spel 8y ago
        School boards and other elected officials get voted out. Not every time, but businesses that latch onto fads don't fail every time either, as anyone can see.
    - swebs 8y ago
      Read the post you're replying to. The problem is lack of accountability, not fads.
war1025 8y ago
I read somewhere, don't remember where, that when a business isn't going well, people start grasping at "process improvements" like it will bring about a huge transform in the way business is going. In reality it doesn't, but it's the sort of busy-work that makes people feel like they are being useful. I think it's very similar in education. There are vast swaths of the education system that are doing absolutely terrible. Much of the problems are outside of school administrator's control (broken families, gangs, poverty, etc), so they reach for "process improvements" and hope that makes a difference.
- dleslie 8y ago
  Sounds a lot like The Curse of the New HQ [0]. 0: https://www.businessinsider.com/poorly-timed-headquarters-2009-11 https://www.businessinsider.com/poorly-timed-headquarters-20...
  - WalterBright 8y ago
    Haha, my dad advised me to sell stock in companies that embark on a massive headquarters project. It's not just a curse - management spends their effort designing the HQ rather than working on the business.
- doctorpangloss 8y ago
  Maybe. Or... > [a study looked at] the relationship between eighth grade enrollment [in Algebra] and National Assessment of Educational Progress math exam scores at the state level. In short, they didn't find one... [In a different study], they found that early exposure was actually associated with a net decrease in average student math score exams within a given district. Maybe we're looking at the wrong metrics. Obviously introducing the average kid, whose average abilities change much more slowly than "process improvements," would have a decrease in today's math exam. Maybe there's something wrong with the exam! And not in the sense of what questions it asks, but more like, who the hell cares? I know what the answer is, I'm not stupid. But eventually, we'll have to square away the multitudes sitting inside of parent's brains: that they want their kids to actually learn something, while simultaneously having the highest scores / grades / metrics possible. The two cannot be true and honest at the same time. But the tension isn't learning versus evaluation. It's honest versus dishonest. Under the early algebra scheme, you get a more honest evaluation (students perform worse at harder, more realistic material) and more learning (they're not rehearsing stuff that's easy for them). The real dynamic is that no one is going to enroll their kids in a school with low test scores.
xvector 8y ago
And I think it's extremely harmful to delay these concepts for children like we do in the US. I wasn't particularly smart growing up, but my parents always kept me up to date with the math and science curriculum they had at their respective ages in their own country. At least up until the end of middle school, the difference was astounding and had a dramatic effect on my academic (and thus future) success.
- jimktrains2 8y ago
  > And I think it's extremely harmful to delay these concepts for children like we do in the US. I wonder how many people grow up hating math, like I did in elementary school, because they just don't like how rote arithmetic is and how trite simple word problems are because they steer away from algebra. It wasn't until I got to Algebra that I really, really started to love math.
  - PeterCorless 8y ago
    I was an algebra teacher and tutor for years. It isn't the subject matter. It's the contextualization into the student's life. How is this relevant? I once taught a girl who was a soccer nut how to use algebra to budget for an imaginary soccer team. Soon it wasn't just basic algebra. We created a whole spreadsheet to calculate the entire thing. Change a number and it cascaded down to the final budget. She was jazzed. It is vital not just to teach to the curriculum, but to teach to the student. And that's where a lot of modern education falls apart. It's not just algebra though. History. English (from literature to grammar). We're just failing to connect.
- xacintosh 8y ago
  I wasn't particularly smart growing up, either, and I failed to place into the middle-school algebra classes like most of my peers. Somehow clicked for me in high school, though, and I raced through the curriculum at an accelerated pace, finishing with Calculus my senior year. A few years after that I graduated from MIT with an aerospace engineering degree. My grandfather never advanced beyond trigonometry in high school, but went on to become a moderately famous theoretical physicist. So if we're looking at anecdotes, it's hard to form a clear conclusion. Today I teach high school mathematics and I see accelerated kids who fall to pieces their junior year, and also kids like me who arrive in the 9th grade knowing nothing, but somehow end up in an accelerated track by the time they graduate.
laretluval 8y ago
> kids are great at memorizing stuff Some are good at it, some are not. This curriculum is aimed at equalizing things for those who are not.
- 0815test 8y ago
  It's a relative comparison. Kids are far better at memorizing stuff and dealing with things that have been made "concrete" to them, compared to abstract thinking - because effective abstraction requires a sort of overall maturity of thinking that very few kids can be expected to develop at an early age! So it's better to just teach the memorization and concrete steps first, and focus on the more abstract stuff later on.
- AnimalMuppet 8y ago
  It would be good to find a way (an alternate path) that helps the kids who aren't great at memorizing. But don't do it in a way that makes things worse for the kids that are good at memorization. Don't "equalize" by making the best worse.
  - Viliam1234 8y ago
    The key to memorization is repetition. Also, paying attention. If I had to design a system that helps everyone with repetition, it would go like this: - each concept must be explained and understood first (never progress to repetition unless you are sure the child groks it); - afterwards, add the concept to your "spaced repetition" software (conveniently provided by the teaching institution); - give kids some time at school when they can do the spaced repetition exercises (so it doesn't become an extra homework). The first step avoids the kind of stupid memorization that people do when they don't have enough time, and that gives them problem (and even greater time pressure) in the future. This makes the entire thing more meaningful that current education. The second step avoids the situations like "I felt pretty sure I understood it yesterday, but now I have no idea where to begin". This makes the entire thing more efficient. > But don't do it in a way that makes things worse for the kids that are good at memorization. Uhm, if you complete the spaced repetition exercise and there is still some time left, you can go play or read something. Or perhaps take a bonus lesson that is not a part of the standard curriculum.
pavel_lishin 8y ago
Same. My grandmother taught me how to solve equations, and we'd do it for "fun" on the bus in Moscow; I was in, at most, fourth grade. And you know what, it was fun, and it wasn't hard. Granted, she was also a programmer, and my grandfather was a mathematician, and both my parents were engineers - so maybe my baseline for fun and education was set differently.
- Diederich 8y ago
  Wow! Can you share, if you know, what kind of programming your grandmother took part in?
  - pavel_lishin 8y ago
    I'm a bad grandson, so I have no idea! I'll have to ask.
    - Diederich 8y ago
      I doubt you're a bad grandson, but I'll share this story with you. I was raised by my grandparents, and I had enormous respect for my grandfather, who was the most badass human being I've ever known, though you would never know it to see him. He was very quiet, he spoke little, always watching and listening. But he grew up in the https://en.wikipedia.org/wiki/Great_Depression https://en.wikipedia.org/wiki/Great_Depression and fought in https://en.wikipedia.org/wiki/Guadalcanal_Campaign https://en.wikipedia.org/wiki/Guadalcanal_Campaign , with https://en.wikipedia.org/wiki/Merrill%27s_Marauders https://en.wikipedia.org/wiki/Merrill%27s_Marauders among others. He was in his 50s when I was born and lived with them permanently when I was 5 years old. He and my grandmother were my parents. They were always patient and kind, and always stoic about everything. One day while camping my grandpa was sitting next to a dart board, and one of the darts I threw went crazy wild; it hit and stuck deeply into his left calf. I just stood there with my mouth open while he puffed his pipe, staring at me. After a couple of moments, he calmly pulled it out, wiped the blood off of it, and carefully tossed it back to me, saying, "Careful where you throw those, boy." I always had a lot of respect for them, though I didn't show it. In fact, by my actions, I took them for granted. They both died of old age when I was in my 30s, even as I was just starting to truly appreciate them. Now, many years later, I would give almost anything to be able to spend another day with them. There's so much I'd ask, so much to learn. In summary: spend as much time as you can talking to your grandparents while you still have them, because once you're old enough to really appreciate their value, they might be gone.
jey 8y ago
Why are you advocating memorization? That just gets people to treat mathematics as a set of magical spells you have to receive from the holy scriptures and priests, and that problems just can't be solved without having received the appropriate spell from the masters. (It also encourages strange beliefs like that mathematics is a subjective human construction, like art and music.) Conveying that there's a deeper conceptual "mathematical thinking" seems much more important than memorizing the algorithm for "completing the square" or whatever.
- amanaplanacanal 8y ago
  My impression is that mathematical thinking isn't really the goal of mathematics education until post-calculus University level. Before that it is mostly learning rules for doing symbol manipulation. Although, this isn't entirely true, I remember doing proofs in Geometry class in Jr High School. So I was at least introduced to it, though we never really used it again.
- 0815test 8y ago
  I'm not seeing any advocacy of memorization? The only thing you might have to memorize, out of what parent listed, is the algorithms for doing written out arithmetic; and that too is in fact an exercise in mathematical thinking. After all, there's a reason we teach these algorithms, as opposed to just telling kids that they can punch numbers into a calculator.
  - beaner 8y ago
    Quote: "Even for double digit addition problems they jump right into 'cool tricks' and 'mathematical thinking' while there are just really a few steps to memorize and, guess what, kids are great at memorizing stuff."
    - 0815test 8y ago
      And rdtsc is entirely right about that. The Common Core math curriculum has been taken by many self-described "math teachers" and "educators" as an opportunity to just not teach the effective algorithms for doing arithmetic, and expect students to just "discover the results by themselves" via some mixture of trial-and-error, random guessing, and the rare "trick" or perhaps tiny flash of genuine "mathematical thinking". That was an unmitigated disaster, of course. It's probably part of the reason why Algebra is now being seen as way too difficult for Junior High students, and something that only HS students could approach effectively.
graycat 8y ago
Yes, but what did the Soviets know about math? Uh, Kolmogorov, Gel'fand, Dynkin, Shiryaev, Pontryagin, etc.???? My take is that by age 12 they should be doing calculus from one of the best college texts.
- Viliam1234 8y ago
  Kolmogorov had to go against a strong political pressure to convince the government to allow him to create a school for mathematically gifted kids. Also, a large part of Soviet mathematical output came from people who were politically forbidden from getting an official scientific job (and then the Academy of Science was filled with people like Lysenko), and sometimes had to get a manual job. So they did math in their free time, corresponding with each other. Which, paradoxically, probably provided more freedom than they would get in an academic institution: no pressure to "publish or perish", freedom to spend years solving some obscure problem with no impressive intermediate results, true cooperation between the outcasts instead of fighting for a limited number of academic job. A large part of Soviet mathematical progress was made in opposition to the regime. Or perhaps, to put it more mildly, the system was so hopeless that people didn't waste their time, and organized better mathematical education outside the system. Then they created things like the International Mathematical Olympiad (the first twenty years, it was an Eastern Bloc thing), various correspondence seminars, etc. But this all happened outside the official educational system.
  - graycat 8y ago
    My understanding of "strong political pressure" for the years of Kolmogorov in the USSR meant that ended up in a salt mine in Siberia and dead in a year or so. But apparently somehow Kolmogorov was smart enough to avoid that end. Yup, suspicions confirmed, all around the world, no matter what, bureaucracies have a lot in common: If have something good and want to kill it off, then set up a bureaucracy to help it!!!!! That's partly a black joke; likely the US NSF and NIH and lots of private efforts in math, physical science, medical science do terrifically good things. And, no joke that the LHC is a big bureaucracy and found the Higgs Boson, a darned good thing. Still there can be some truth to the joke. E.g., in the US I've seen some of what you said about publish or perish: While I never really wanted such an academic research career (I just wanted a JOB and to support a family and looked at my math Ph.D. as vocational education), eventually it dawned on me that actually in some fields the publication standards sufficient for publish or perish are low and that a good researcher should be able to toss out dozens of such papers, if only as side efforts, while otherwise doing the important stuff. Bluntly when I was considering academic math research, the main obstacle, and it was SEVERE, was that I didn't quite yet have access to a computer that could run Knuth's TeX math word processing software. Bluntly the word processing for typing in the math research was MUCH more challenging than doing the math research! There's another relevant rule: In social, political, bureaucratic, etc. systems, when want to do better, measure it, and, for that, create, design, implement, and setup measures. Then the system responds, does well on the measures, just the measures -- games, hacks, manipulates, tricks, fools, takes advantage of weaknesses in the measures -- with harm to what was being measured! Partly another black joke but, still, with some sad truth. With bad measures, the Soviets were not the only ones with the problem of "They pretend to pay us, and we pretend to work.". Then we get reminded that democracy and free enterprise are the worst systems ever invented except for all the other systems that have ever been tried. Another black joke; sometimes democracy and free enterprise do really well. E.g., in a democracy, we can elect liars, crooks, incompetents, etc. but eventually the disaster becomes obvious to enough voters, and then we get some better candidates and an ELECTION to throw the rascals out -- been known to happen, sometimes slowly, but, still, happens. I know next to nothing about the Soviet system, but from what little I know it looks like it was an astounding juxtaposition of just horrible suffering and lost opportunities, waste, e.g., on military efforts, lots of just horrible inefficiencies, yet at times some, maybe not enough, maybe with the movie remark "But do you know what it cost?", astoundingly good things -- Kolmogorov, Oistrakh in violin, Giles in piano, Garanca in voice (grew up in one of the Baltic states when they were part of the USSR), the Mariinsky Ballet, etc. I'm trying to get my startup live on the Internet; there are some ways it could help civilization. Otherwise I can't solve all the problems. But democracy and free enterprise when they work well -- in the US from 1929 to 1942 they didn't work so well -- can be amazingly good things.
maire 8y ago
Some school districts in the bay area are doing better than San Francisco. In the Los Gatos school district my daughter completed her first year of college level calculous and some second year calculous by the time she graduated from high school. This was better than my education as I only had access to pre calculus in my high school. As an aside - giving kids math puzzles is a much better preparation for math than memorization. The only thing I had to memorize was the multiplication table, everything else I could derive. I could always derive a formula faster than memorizing it even at a young age. I went to school in the era of "new math" where we were introduced to functions and variables in 2nd grade.
- rmah 8y ago
  I don't think anyone is suggesting that more advanced high school level math should be transformed into an exercise in memorization. They're talking about kids that are 7 or 8 years old memorizing their multiplication tables.
  - maire 8y ago
    We might be saying the same thing since the only thing you need to memorize is the multiplication tables. ;-) How long can that possibly take? My grandsons are between 3 and 8 - so they are in this age group. They are amazing at solving problems when it leads to something they want like winning a game against their brother. Puzzles are great for teaching math to this age group.
perfunctory 8y ago
> ...so they start making changes just to they can slap something on their resume. Developers do that too some extent... To some extent? Sometimes I feel like that's the only thing that developers do.
keithpeter 8y ago
Spiral curriculum is actually a widely used concept in teaching... https://www.teachwire.net/news/ever-increasing-circles-what-the-spiral-curriculum-can-do-for-your-students https://www.teachwire.net/news/ever-increasing-circles-what-...
WalterBright 8y ago
My impression is that the schools are endlessly looking for a way for kids to learn without effort and teachers to teach without doing any work. It's like giving a jogger a car. He arrives at his destination faster and easier, but didn't get any stronger.
Scaevolus 8y ago
Dragonbox produces an Algebra game for small children-- symbolic manipulation isn't that hard, you just have to be taught the rules: https://dragonbox.com/products/algebra-5 https://dragonbox.com/products/algebra-5

by rdtsc 8y ago

tomohawk 8y ago

Curriculum, most especially through 6th grade, is driven very much what whatever fad catches hold in the education establishment. It changes every 2 - 3 years. It's really just a symptom that there is very little accountability for the people making these decisions. Put out a curriculum with poor results? Who's going to notice? If anyone does, who will have the power to do something about it?

linuxftw 8y ago
This lack of feedback can be extrapolated to the entire government. It's a well defined problem: https://mises.org/library/economic-calculation-socialist-commonwealth https://mises.org/library/economic-calculation-socialist-com...
- Shebanator 8y ago
  Do you think that is only a problem in government? Fads are a fundamental part of human nature. In tech, we have many examples: Agile, Ruby on Rails, React, RISC, OOP, microservices, and so on and so on. All have some real benefits, but also have or have had huge hype cycles. You can make the same argument for most other industries (if not all of them). And then there are things like diets, religions, etc.
  - WalterBright 8y ago
    > Do you think that is only a problem in government? Nope. But businesses fail when they succumb to fads, while government just raises taxes.
    - lern_too_spel 8y ago
      School boards and other elected officials get voted out. Not every time, but businesses that latch onto fads don't fail every time either, as anyone can see.
  - swebs 8y ago
    Read the post you're replying to. The problem is lack of accountability, not fads.

war1025 8y ago

I read somewhere, don't remember where, that when a business isn't going well, people start grasping at "process improvements" like it will bring about a huge transform in the way business is going. In reality it doesn't, but it's the sort of busy-work that makes people feel like they are being useful. I think it's very similar in education. There are vast swaths of the education system that are doing absolutely terrible. Much of the problems are outside of school administrator's control (broken families, gangs, poverty, etc), so they reach for "process improvements" and hope that makes a difference.

dleslie 8y ago
Sounds a lot like The Curse of the New HQ [0]. 0: https://www.businessinsider.com/poorly-timed-headquarters-2009-11 https://www.businessinsider.com/poorly-timed-headquarters-20...
- WalterBright 8y ago
  Haha, my dad advised me to sell stock in companies that embark on a massive headquarters project. It's not just a curse - management spends their effort designing the HQ rather than working on the business.
doctorpangloss 8y ago
Maybe. Or... > [a study looked at] the relationship between eighth grade enrollment [in Algebra] and National Assessment of Educational Progress math exam scores at the state level. In short, they didn't find one... [In a different study], they found that early exposure was actually associated with a net decrease in average student math score exams within a given district. Maybe we're looking at the wrong metrics. Obviously introducing the average kid, whose average abilities change much more slowly than "process improvements," would have a decrease in today's math exam. Maybe there's something wrong with the exam! And not in the sense of what questions it asks, but more like, who the hell cares? I know what the answer is, I'm not stupid. But eventually, we'll have to square away the multitudes sitting inside of parent's brains: that they want their kids to actually learn something, while simultaneously having the highest scores / grades / metrics possible. The two cannot be true and honest at the same time. But the tension isn't learning versus evaluation. It's honest versus dishonest. Under the early algebra scheme, you get a more honest evaluation (students perform worse at harder, more realistic material) and more learning (they're not rehearsing stuff that's easy for them). The real dynamic is that no one is going to enroll their kids in a school with low test scores.

xvector 8y ago

And I think it's extremely harmful to delay these concepts for children like we do in the US. I wasn't particularly smart growing up, but my parents always kept me up to date with the math and science curriculum they had at their respective ages in their own country. At least up until the end of middle school, the difference was astounding and had a dramatic effect on my academic (and thus future) success.

jimktrains2 8y ago
> And I think it's extremely harmful to delay these concepts for children like we do in the US. I wonder how many people grow up hating math, like I did in elementary school, because they just don't like how rote arithmetic is and how trite simple word problems are because they steer away from algebra. It wasn't until I got to Algebra that I really, really started to love math.
- PeterCorless 8y ago
  I was an algebra teacher and tutor for years. It isn't the subject matter. It's the contextualization into the student's life. How is this relevant? I once taught a girl who was a soccer nut how to use algebra to budget for an imaginary soccer team. Soon it wasn't just basic algebra. We created a whole spreadsheet to calculate the entire thing. Change a number and it cascaded down to the final budget. She was jazzed. It is vital not just to teach to the curriculum, but to teach to the student. And that's where a lot of modern education falls apart. It's not just algebra though. History. English (from literature to grammar). We're just failing to connect.
xacintosh 8y ago
I wasn't particularly smart growing up, either, and I failed to place into the middle-school algebra classes like most of my peers. Somehow clicked for me in high school, though, and I raced through the curriculum at an accelerated pace, finishing with Calculus my senior year. A few years after that I graduated from MIT with an aerospace engineering degree. My grandfather never advanced beyond trigonometry in high school, but went on to become a moderately famous theoretical physicist. So if we're looking at anecdotes, it's hard to form a clear conclusion. Today I teach high school mathematics and I see accelerated kids who fall to pieces their junior year, and also kids like me who arrive in the 9th grade knowing nothing, but somehow end up in an accelerated track by the time they graduate.

laretluval 8y ago

> kids are great at memorizing stuff Some are good at it, some are not. This curriculum is aimed at equalizing things for those who are not.

0815test 8y ago
It's a relative comparison. Kids are far better at memorizing stuff and dealing with things that have been made "concrete" to them, compared to abstract thinking - because effective abstraction requires a sort of overall maturity of thinking that very few kids can be expected to develop at an early age! So it's better to just teach the memorization and concrete steps first, and focus on the more abstract stuff later on.
AnimalMuppet 8y ago
It would be good to find a way (an alternate path) that helps the kids who aren't great at memorizing. But don't do it in a way that makes things worse for the kids that are good at memorization. Don't "equalize" by making the best worse.
- Viliam1234 8y ago
  The key to memorization is repetition. Also, paying attention. If I had to design a system that helps everyone with repetition, it would go like this: - each concept must be explained and understood first (never progress to repetition unless you are sure the child groks it); - afterwards, add the concept to your "spaced repetition" software (conveniently provided by the teaching institution); - give kids some time at school when they can do the spaced repetition exercises (so it doesn't become an extra homework). The first step avoids the kind of stupid memorization that people do when they don't have enough time, and that gives them problem (and even greater time pressure) in the future. This makes the entire thing more meaningful that current education. The second step avoids the situations like "I felt pretty sure I understood it yesterday, but now I have no idea where to begin". This makes the entire thing more efficient. > But don't do it in a way that makes things worse for the kids that are good at memorization. Uhm, if you complete the spaced repetition exercise and there is still some time left, you can go play or read something. Or perhaps take a bonus lesson that is not a part of the standard curriculum.

pavel_lishin 8y ago

Same. My grandmother taught me how to solve equations, and we'd do it for "fun" on the bus in Moscow; I was in, at most, fourth grade. And you know what, it was fun, and it wasn't hard. Granted, she was also a programmer, and my grandfather was a mathematician, and both my parents were engineers - so maybe my baseline for fun and education was set differently.

Diederich 8y ago
Wow! Can you share, if you know, what kind of programming your grandmother took part in?
- pavel_lishin 8y ago
  I'm a bad grandson, so I have no idea! I'll have to ask.
  - Diederich 8y ago
    I doubt you're a bad grandson, but I'll share this story with you. I was raised by my grandparents, and I had enormous respect for my grandfather, who was the most badass human being I've ever known, though you would never know it to see him. He was very quiet, he spoke little, always watching and listening. But he grew up in the https://en.wikipedia.org/wiki/Great_Depression https://en.wikipedia.org/wiki/Great_Depression and fought in https://en.wikipedia.org/wiki/Guadalcanal_Campaign https://en.wikipedia.org/wiki/Guadalcanal_Campaign , with https://en.wikipedia.org/wiki/Merrill%27s_Marauders https://en.wikipedia.org/wiki/Merrill%27s_Marauders among others. He was in his 50s when I was born and lived with them permanently when I was 5 years old. He and my grandmother were my parents. They were always patient and kind, and always stoic about everything. One day while camping my grandpa was sitting next to a dart board, and one of the darts I threw went crazy wild; it hit and stuck deeply into his left calf. I just stood there with my mouth open while he puffed his pipe, staring at me. After a couple of moments, he calmly pulled it out, wiped the blood off of it, and carefully tossed it back to me, saying, "Careful where you throw those, boy." I always had a lot of respect for them, though I didn't show it. In fact, by my actions, I took them for granted. They both died of old age when I was in my 30s, even as I was just starting to truly appreciate them. Now, many years later, I would give almost anything to be able to spend another day with them. There's so much I'd ask, so much to learn. In summary: spend as much time as you can talking to your grandparents while you still have them, because once you're old enough to really appreciate their value, they might be gone.

jey 8y ago

Why are you advocating memorization? That just gets people to treat mathematics as a set of magical spells you have to receive from the holy scriptures and priests, and that problems just can't be solved without having received the appropriate spell from the masters. (It also encourages strange beliefs like that mathematics is a subjective human construction, like art and music.) Conveying that there's a deeper conceptual "mathematical thinking" seems much more important than memorizing the algorithm for "completing the square" or whatever.

amanaplanacanal 8y ago
My impression is that mathematical thinking isn't really the goal of mathematics education until post-calculus University level. Before that it is mostly learning rules for doing symbol manipulation. Although, this isn't entirely true, I remember doing proofs in Geometry class in Jr High School. So I was at least introduced to it, though we never really used it again.
0815test 8y ago
I'm not seeing any advocacy of memorization? The only thing you might have to memorize, out of what parent listed, is the algorithms for doing written out arithmetic; and that too is in fact an exercise in mathematical thinking. After all, there's a reason we teach these algorithms, as opposed to just telling kids that they can punch numbers into a calculator.
- beaner 8y ago
  Quote: "Even for double digit addition problems they jump right into 'cool tricks' and 'mathematical thinking' while there are just really a few steps to memorize and, guess what, kids are great at memorizing stuff."
  - 0815test 8y ago
    And rdtsc is entirely right about that. The Common Core math curriculum has been taken by many self-described "math teachers" and "educators" as an opportunity to just not teach the effective algorithms for doing arithmetic, and expect students to just "discover the results by themselves" via some mixture of trial-and-error, random guessing, and the rare "trick" or perhaps tiny flash of genuine "mathematical thinking". That was an unmitigated disaster, of course. It's probably part of the reason why Algebra is now being seen as way too difficult for Junior High students, and something that only HS students could approach effectively.

graycat 8y ago

Yes, but what did the Soviets know about math? Uh, Kolmogorov, Gel'fand, Dynkin, Shiryaev, Pontryagin, etc.???? My take is that by age 12 they should be doing calculus from one of the best college texts.

Viliam1234 8y ago
Kolmogorov had to go against a strong political pressure to convince the government to allow him to create a school for mathematically gifted kids. Also, a large part of Soviet mathematical output came from people who were politically forbidden from getting an official scientific job (and then the Academy of Science was filled with people like Lysenko), and sometimes had to get a manual job. So they did math in their free time, corresponding with each other. Which, paradoxically, probably provided more freedom than they would get in an academic institution: no pressure to "publish or perish", freedom to spend years solving some obscure problem with no impressive intermediate results, true cooperation between the outcasts instead of fighting for a limited number of academic job. A large part of Soviet mathematical progress was made in opposition to the regime. Or perhaps, to put it more mildly, the system was so hopeless that people didn't waste their time, and organized better mathematical education outside the system. Then they created things like the International Mathematical Olympiad (the first twenty years, it was an Eastern Bloc thing), various correspondence seminars, etc. But this all happened outside the official educational system.
- graycat 8y ago
  My understanding of "strong political pressure" for the years of Kolmogorov in the USSR meant that ended up in a salt mine in Siberia and dead in a year or so. But apparently somehow Kolmogorov was smart enough to avoid that end. Yup, suspicions confirmed, all around the world, no matter what, bureaucracies have a lot in common: If have something good and want to kill it off, then set up a bureaucracy to help it!!!!! That's partly a black joke; likely the US NSF and NIH and lots of private efforts in math, physical science, medical science do terrifically good things. And, no joke that the LHC is a big bureaucracy and found the Higgs Boson, a darned good thing. Still there can be some truth to the joke. E.g., in the US I've seen some of what you said about publish or perish: While I never really wanted such an academic research career (I just wanted a JOB and to support a family and looked at my math Ph.D. as vocational education), eventually it dawned on me that actually in some fields the publication standards sufficient for publish or perish are low and that a good researcher should be able to toss out dozens of such papers, if only as side efforts, while otherwise doing the important stuff. Bluntly when I was considering academic math research, the main obstacle, and it was SEVERE, was that I didn't quite yet have access to a computer that could run Knuth's TeX math word processing software. Bluntly the word processing for typing in the math research was MUCH more challenging than doing the math research! There's another relevant rule: In social, political, bureaucratic, etc. systems, when want to do better, measure it, and, for that, create, design, implement, and setup measures. Then the system responds, does well on the measures, just the measures -- games, hacks, manipulates, tricks, fools, takes advantage of weaknesses in the measures -- with harm to what was being measured! Partly another black joke but, still, with some sad truth. With bad measures, the Soviets were not the only ones with the problem of "They pretend to pay us, and we pretend to work.". Then we get reminded that democracy and free enterprise are the worst systems ever invented except for all the other systems that have ever been tried. Another black joke; sometimes democracy and free enterprise do really well. E.g., in a democracy, we can elect liars, crooks, incompetents, etc. but eventually the disaster becomes obvious to enough voters, and then we get some better candidates and an ELECTION to throw the rascals out -- been known to happen, sometimes slowly, but, still, happens. I know next to nothing about the Soviet system, but from what little I know it looks like it was an astounding juxtaposition of just horrible suffering and lost opportunities, waste, e.g., on military efforts, lots of just horrible inefficiencies, yet at times some, maybe not enough, maybe with the movie remark "But do you know what it cost?", astoundingly good things -- Kolmogorov, Oistrakh in violin, Giles in piano, Garanca in voice (grew up in one of the Baltic states when they were part of the USSR), the Mariinsky Ballet, etc. I'm trying to get my startup live on the Internet; there are some ways it could help civilization. Otherwise I can't solve all the problems. But democracy and free enterprise when they work well -- in the US from 1929 to 1942 they didn't work so well -- can be amazingly good things.

maire 8y ago

Some school districts in the bay area are doing better than San Francisco. In the Los Gatos school district my daughter completed her first year of college level calculous and some second year calculous by the time she graduated from high school. This was better than my education as I only had access to pre calculus in my high school. As an aside - giving kids math puzzles is a much better preparation for math than memorization. The only thing I had to memorize was the multiplication table, everything else I could derive. I could always derive a formula faster than memorizing it even at a young age. I went to school in the era of "new math" where we were introduced to functions and variables in 2nd grade.

rmah 8y ago
I don't think anyone is suggesting that more advanced high school level math should be transformed into an exercise in memorization. They're talking about kids that are 7 or 8 years old memorizing their multiplication tables.
- maire 8y ago
  We might be saying the same thing since the only thing you need to memorize is the multiplication tables. ;-) How long can that possibly take? My grandsons are between 3 and 8 - so they are in this age group. They are amazing at solving problems when it leads to something they want like winning a game against their brother. Puzzles are great for teaching math to this age group.

perfunctory 8y ago

> ...so they start making changes just to they can slap something on their resume. Developers do that too some extent... To some extent? Sometimes I feel like that's the only thing that developers do.

keithpeter 8y ago

Spiral curriculum is actually a widely used concept in teaching... https://www.teachwire.net/news/ever-increasing-circles-what-the-spiral-curriculum-can-do-for-your-students https://www.teachwire.net/news/ever-increasing-circles-what-...

WalterBright 8y ago

My impression is that the schools are endlessly looking for a way for kids to learn without effort and teachers to teach without doing any work. It's like giving a jogger a car. He arrives at his destination faster and easier, but didn't get any stronger.

Scaevolus 8y ago

Dragonbox produces an Algebra game for small children-- symbolic manipulation isn't that hard, you just have to be taught the rules: https://dragonbox.com/products/algebra-5 https://dragonbox.com/products/algebra-5