15 ms·

Calculus for Seven Year Olds [pdf]

319 points by barry-cotter 5y ago

fatnoah 5y ago
I don't know how I feel about this. I've always been good at math, and was one of five kids (out of class of 120) that took Calculus as a senior in high school in the early 1990's. To even take Calculus as a senior, you had to have taken four years of math in the previous three years. I was even the HS Math Champion" for my state. However, when I took Calculus in High School, it was taught similarly to this. Lots and lots and lots of math foundations, infinite series, areas under curves, and I was able to trudge through it but I didn't really grasp what it all meant or why I was doing it. Finally, about 2/3 of the way through the year, I was working on a problem and had an "oh, shit, this is just about how things are changing". It was a Eureka moment, and entirely based on such a simple statement that was never brought up in lectures or our crusty 1960's texbook.
- rezaprima 5y ago
  Can you elaborate more about that sentence? With example, perhaps?
  - fatnoah 5y ago
    This actually covers it very well: http://www-math.mit.edu/~djk/calculus_beginners/chapter00/section02.html http://www-math.mit.edu/~djk/calculus_beginners/chapter00/se...
- petermcneeley 5y ago
  What a great story. I dont think you are alone in this. I also think this applies to more than just math.
- vinsci 5y ago
  > It was a Eureka moment, and entirely based on such a simple statement that was never brought up in lectures Young me picked up the basics of cryptography at seven or eight, a couple of years before classes in the first foreign language began at age nine or ten. In Finland, for the Swedish-speaking minority, the first foreign language to learn is Finnish — often mentioned as one of the world's most difficult languages to learn. Neither the textbook nor the teacher mentioned how languages work, and specifically not how they are in no way related to cryptography. Young genius me concluded that surely the teacher will soon tell us how this crypto works, so we could move on. While waiting for that to happen, I skipped more or less everything. It took a couple of months to realize the actual situation, by that time the damage had been done. Picked up Finnish seven years later, the natural way through a colleague at a summer job. That little omission had a detrimental effect on my average grades throughout the school years though, and therefore I certainly do not judge anyone's abilities based on their paper qualifications.
  - justinclift 5y ago
    Hmmm, something seems to be missing from the explanation there? Why would the teacher be expected to know anything about cryptography, let alone know that a particular student has any interest in it?
  - schoen 5y ago
    Were you thinking that maybe foreign languages were substitution ciphers, and that you were eventually going to be taught the substitutions you needed? I think I had a similar thought when I was about six or seven and came across the Cyrillic alphabet printed in the back of a dictionary. I thought "oh wow, I guess if you learn this, then you know Russian!" -- thinking of Russian as something like English transliterated into Cyrillic. There are phenomena in language that do work a little bit this way (https://en.wikipedia.org/wiki/Relexification https://en.wikipedia.org/wiki/Relexification, https://en.wikipedia.org/wiki/Avoidance_speech https://en.wikipedia.org/wiki/Avoidance_speech) but usually at the word level and not in contexts that will really help second language learners.
- nanis 5y ago
  > one of five kids (out of class of 120) that took Calculus I am always puzzled by this. Calculus was 8th - 9th material in Turkey in the 80s. In classrooms with 45 - 50 kids per one over-worked teacher. We did set theory and Boolean logic in third grade. I think that is far more useful for understanding mathematical thinking than Calculus is.
  - koheripbal 5y ago
    Same in Canada. ...and then I moved to the US, and the school was a full YEAR behind, and only covered the basics. ...and I feel like it's getting worse.
casion 5y ago
I've taught 7-year olds, rich kids specifically in technology magnet program. The pre-requisite information necessary for this would be way above their heads. Adding fractions, conceptualizing fractions to graphs, graphing functions... and that's just the first part! Most 7-year olds can barely conceptualize fractions. First/second grade math curriculums are centered around basic multiplication, shape recognition and counting. 7-year olds aside, I don't even think most of the high-schooler freshmen I've taught would be able to grasp this content.
- tartoran 5y ago
  Maybe they’re implying 7 year old geniuses who could read by the age of 3 and speak 4 languages by the age of 4. Anyhow, I agree that it’s not for the average 7 year old but it’s a cool book nonetheless
  - thaumasiotes 5y ago
    > Maybe they’re implying 7 year old geniuses who could read by the age of 3 and speak 4 languages by the age of 4. Speaking four languages by the age of 4 is just ordinary development, assuming you're in an area where all four are spoken. You should be speaking them before the age of 2.
    - tartoran 5y ago
      My son speaks 2 at 3 years old. I’m amazed that is possible though, yes, it is an ordinary development in a bilingual household.
      - jdmoreira 5y ago
        I agree that's just standard but parent said they speak 4 languages before 2. That's total and complete BS. I have a 2 year old and I speak with her in one language the mom in another and me and the mom speak in a third language between us. She knows words in the 3 languages and can construct phrases in 1 or 2 of those languages. She is is also much more developed verbally than any of the kids her age we meet regularly but she definitely doesn't speak 3 languages.
DoreenMichele 5y ago
Copyright 1991. This was probably making the rounds of homeschooling circles I hung out in. We tend to do a sucky job of teaching math to kids. A lot of elementary school teachers are women who were encouraged to go into early education because they weren't doing so well in math and this is very much gender bias. My ex husband wasn't good at math. No one told him he should spend his days teaching little kids because of it. He was a career soldier and he just got tutored in college (by me) for his math classes. He was just expected to work at it if it didn't come naturally and he did. So we just culturally pass around this idea that math is scary and little kids can't learn it rather than going "Well, adults just need to up their game and, by god, explain it better." My oldest was math phobic by the time I pulled him out of school to homeschool. My one and only goal for math was to get him over his phobia. He loves physics. I hate calculus. Calculus makes sense to him and he has read calculus books for fun. I was good at explaining the math to him and he learned lots of solid math concepts even though he likely has dyscalculia and isn't good at crunching the numbers. But I got the concepts through to him and that's more important. He's what gets called "calculator dependent" in some circles.
- dvfjsdhgfv 5y ago
  > We tend to do a sucky job of teaching math to kids. A lot of elementary school teachers are women who were encouraged to go into early education because they weren't doing so well in math and this is very much gender bias. While this may be true and in general is in line with my experience, it might be better for you to reframe it in a more indirect way because sooner or later you'll find someone offended.
  - DoreenMichele 5y ago
    I appear to be the highest ranked openly female member on HN. I can suck up a few downvotes from people who don't like me or don't like what I am saying and that, in fact, seems to be par for the course here. Thank you for otherwise validating my position, but I'm not going to soften it. If the truth about our world bothers people, they are free to make something else true instead of asking me to cater to their feelings at the expense of stating the truth. Edit: I will add I am unwilling to back down on this point because we are actively giving young women a math phobia and crushing their dreams with it instead of telling them to get a tutor and work for what they want and we are doing so in a manner that causes them to pass their math phobia onto future generations. This isn't just a case of "sexism sucks." We are poisoning our entire society with this garbage and it negatively impacts huge numbers of people.
AndrewKemendo 5y ago
I really wish there were something like an "executive" refresher classes on basic maths with a focus on practical applications and modeling. I took Calculus II/III, Linear/Diff EQ and some others in college, but I haven't written a new mathematical model in almost two decades and am rusty.
- mhh__ 5y ago
  Try modelling something and see where it goes? The thing with "modelling" is that in my experience it's often justified post-facto so you don't actually learn anything when it comes to modelling as an art. That being said what you are describing is basically a physics textbook, I would say engineering, but they have no soul.
  - AndrewKemendo 5y ago
    I have done data modeling for a living and I don't agree that you don't learn anything and that it's used to justify something - you just have to do it rigorously. To that point though, most modeling with any accuracy is done by computer now, and not by hand, which is what my point is. It's impossible to gain an intuition about something if the computer just tells you the answer.
- cgh 5y ago
  Not sure if it’s precisely what you’re looking for, but I’m currently reading and working through Coding the Matrix, which is linear algebra by way of Python. There are few assumptions and you start coding pretty early on.
  - AndrewKemendo 5y ago
    Thanks, I feel like I've run across the book a few times over the years but never was suggested it. I'll check it out
- r0fl 5y ago
  Try Khan Academy, I found it to be a great refresher for things like that.
lanna 5y ago
My 6yo daughter has exceptional talent and interest for Math. She's already discovering some fundamental theorems for herself (number theory, algebra, geometry). Does anyone here know any resources to help her development?
- dharmab 5y ago
  The YouTube channel 3blue1brown has some great, accessible introductions to higher level math.
  - schoen 5y ago
    That's a truly fantastic recommendation. Other thoughts: * The "Exploding Dots" project came up with a creative way to present place value that leads into a lot of other concepts like number bases, algebraic structures, polynomials, and other things. (It's actually like a generalization of the abacus, with fun computer animation.) I'm not sure which presentation of this is best -- I think the original inventor has gone through like three different versions and there are several versions available online now. * I'm a huge fan of the late math journalist Martin Gardner, who wrote a lot of really entertaining stuff about math as well as puzzles and games. His books are really brilliant and cover a very wide territory. On the other hand, they were mostly written for adult audiences (originally, mainly readers of Gardner's Scientific American column) and may contain cultural references that kids wouldn't get, not least because some of them go back to the 1960s. :-( Also in some cases there have been further discoveries in the decades since the columns were published, so learning about them only from Gardner's old work may not give a good sense of where things have gone since then (e.g., he famously originally introduced both the Game of Life and the RSA algorithm to mass audiences, which then learned a lot about both topics in the ensuing decades). But maybe have a peek because they do stress the "math is fun and you can do it for fun" and also "math is all kinds of stuff and not just arithmetic" notions. * Gardner does have two math books for kids (the aha! series) that are very fun and introduce a lot of fascinating stuff about logic and paradoxes, among other topics. * Two online games that involve proof and circuit synthesis (spoiler alert: these are actually often isomorphic to each other because of Curry-Howard and stuff), which I think I heard about on HN: http://incredible.pm/ http://incredible.pm/ https://www.nandgame.com/ https://www.nandgame.com/ I totally loved both of these and I think they could conceivably be accessible for a very motivated and very talented child. Another online logic game that I also learned about on HN and loved: https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/ https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_g... Unlike the other two, this one uses (only) text and symbols instead of blocks and arrows. It's meant for college undergraduates, but I envision highly mathematically-talented middle-schoolers possibly being able to finish it. The user interface can probably also be improved a lot to make it clearer what you're allowed to do in each context. Maybe keep this one in mind for the future? :-) Contemporary pre-college math education is famously very weak on discrete math topics (like number theory, logic, and combinatorics). I don't know if this is due to a desire to train aerospace engineers for the Space Race, or because discrete math has radically increased its profile only in the past few decades with the rise of computer science, or as a kind of backlash against the New Math which tried (mostly unsuccessfully) to teach kids formal logical foundations through set theory. I wish I knew some more good discrete stuff for younger audiences. I haven't ever done any of it myself, but I hear Khan Academy's explanations (especially in math) are great and very self-paced.
_Nat_ 5y ago
Looks pretty out-dated (1991). A lot of the math is very poorly formatted, and a lot of code's in an ancient form of BASIC. Doesn't look like a good fit for a primary textbook since it's too scattered and slow, though some of the content might work as mini-games, sorta like crossword puzzles.
- bawolff 5y ago
  Does math really change? I guess the basic is less popular now that TI-89's are being replaced with smartphones, but its probably not as ancient as you think.
  - _Nat_ 5y ago
    Yes, math changes, but it's moreso the presentation that's ancient. The formatting is so retro that it seriously damages legibility while simultaneously failing to give students a taste of actual mathematical discourse, and the coding in the text is obsolete. That students are still required to use TI-89's in class is a travesty itself -- TI-89's are horribly obsolete in modern practice and really only serve to hamper cheating on exams. At best, teaching students with TI-89's to better prepare them for exams might be justified as a trick to inflate their scores, but it still seems like a wasted opportunity to acquire a working familiarity with actual tools that students might actually use in the future. The BASIC code is worse yet as it can't even be argued for as an exam-score-inflation trick; it's simply obsolete. Students learning coding ought to learn modern languages. The focus should be on what's best for the students. And this isn't it. The retro stuff belongs in a museum.
canada_dry 5y ago
This resource really isn't that great IMHO. For anyone (esp. children) to grasp a new concept it helps to have relatable problems that can be solved in gradual steps. After dividing up a cookie in Ch. 2 it continues further and starts to discuss proof via harmonics!
aryehof 5y ago
Let children be children, not experiments in the aspirations of parents and adults.
- Atreiden 5y ago
  Sometimes children seek this kind of stimulation. I used to love trying to solve 'advanced' problems. Making new connections, i.e. "wow, so THATS why that is the way it is" were some of my favorite memories. I did Math Olympiad as a kid not because my parents pushed me - on the contrary - I pushed on them (and my teacher) to get into the program. Obviously it's not for everyone, but I personally I would have killed to have started learning the 'interesting' stuff earlier in my life.
- boringg 5y ago
  How is this considered aspirations of their parents? One of the most thrilling things in life is to learn new skills and understand how the world works. My child loves to learn new things and is very excited when he does something new. I am sorry that you feel that way and maybe you personally did not like to learn new things. Don't cast your negative judgement on the enjoyment of others learning guised as "Just let kids be kids". You assume that people doing this are pulling a Beethoven's father or something. Check your assumptions.
- boringg 5y ago
  I'm also assuming here, but it does sound like you don't have children of your own.
- koheripbal 5y ago
  Don't educate people. Let them remain ignorant.
beardyw 5y ago
When I was 9, my next eldest brother of 16 was captivated by calculus at school and wanted to share it with me. Without algebra he managed to get across to me how it worked though I am sure I had no idea what the point of it was. Sadly I have little capacity for memorising anything so eight years later in my final school exams I was still using first principles. It didn't go too well.
jfmc 5y ago
During pandemic lockdowns I had the opportunity to teach my 7yo son maths at home. It does not work for all kids, but he showed a very strong interest in symbolic manipulation. School overemphasizes arithmetic and arithmetic algorithms ad infinitum (extremely tedious and boring!). Our work plan is simple: a problem each day (together when the concepts are new), immediate reward after he finishes, and increase difficulty once he is ready. After one year, we have just started trigonometric equations at home, while they are still working on simple multiplications at school. In the same way that some kids are good at sports, drawing, music, foreign languages, or playing videogames, some of them are very good managing abstractions. Those would be very happy learning calculus or other advanced mathematics, just for fun!
tmaly 5y ago
I will keep this for reference. It is a good starting point that I can build on with my kids.

319 points by barry-cotter 5y ago

I don't know how I feel about this. I've always been good at math, and was one of five kids (out of class of 120) that took Calculus as a senior in high school in the early 1990's. To even take Calculus as a senior, you had to have taken four years of math in the previous three years. I was even the HS Math Champion" for my state. However, when I took Calculus in High School, it was taught similarly to this. Lots and lots and lots of math foundations, infinite series, areas under curves, and I was able to trudge through it but I didn't really grasp what it all meant or why I was doing it. Finally, about 2/3 of the way through the year, I was working on a problem and had an "oh, shit, this is just about how things are changing". It was a Eureka moment, and entirely based on such a simple statement that was never brought up in lectures or our crusty 1960's texbook.

rezaprima 5y ago
Can you elaborate more about that sentence? With example, perhaps?
- fatnoah 5y ago
  This actually covers it very well: http://www-math.mit.edu/~djk/calculus_beginners/chapter00/section02.html http://www-math.mit.edu/~djk/calculus_beginners/chapter00/se...
petermcneeley 5y ago
What a great story. I dont think you are alone in this. I also think this applies to more than just math.
vinsci 5y ago
> It was a Eureka moment, and entirely based on such a simple statement that was never brought up in lectures Young me picked up the basics of cryptography at seven or eight, a couple of years before classes in the first foreign language began at age nine or ten. In Finland, for the Swedish-speaking minority, the first foreign language to learn is Finnish — often mentioned as one of the world's most difficult languages to learn. Neither the textbook nor the teacher mentioned how languages work, and specifically not how they are in no way related to cryptography. Young genius me concluded that surely the teacher will soon tell us how this crypto works, so we could move on. While waiting for that to happen, I skipped more or less everything. It took a couple of months to realize the actual situation, by that time the damage had been done. Picked up Finnish seven years later, the natural way through a colleague at a summer job. That little omission had a detrimental effect on my average grades throughout the school years though, and therefore I certainly do not judge anyone's abilities based on their paper qualifications.
- justinclift 5y ago
  Hmmm, something seems to be missing from the explanation there? Why would the teacher be expected to know anything about cryptography, let alone know that a particular student has any interest in it?
- schoen 5y ago
  Were you thinking that maybe foreign languages were substitution ciphers, and that you were eventually going to be taught the substitutions you needed? I think I had a similar thought when I was about six or seven and came across the Cyrillic alphabet printed in the back of a dictionary. I thought "oh wow, I guess if you learn this, then you know Russian!" -- thinking of Russian as something like English transliterated into Cyrillic. There are phenomena in language that do work a little bit this way (https://en.wikipedia.org/wiki/Relexification https://en.wikipedia.org/wiki/Relexification, https://en.wikipedia.org/wiki/Avoidance_speech https://en.wikipedia.org/wiki/Avoidance_speech) but usually at the word level and not in contexts that will really help second language learners.
nanis 5y ago
> one of five kids (out of class of 120) that took Calculus I am always puzzled by this. Calculus was 8th - 9th material in Turkey in the 80s. In classrooms with 45 - 50 kids per one over-worked teacher. We did set theory and Boolean logic in third grade. I think that is far more useful for understanding mathematical thinking than Calculus is.
- koheripbal 5y ago
  Same in Canada. ...and then I moved to the US, and the school was a full YEAR behind, and only covered the basics. ...and I feel like it's getting worse.

casion 5y ago

I've taught 7-year olds, rich kids specifically in technology magnet program. The pre-requisite information necessary for this would be way above their heads. Adding fractions, conceptualizing fractions to graphs, graphing functions... and that's just the first part! Most 7-year olds can barely conceptualize fractions. First/second grade math curriculums are centered around basic multiplication, shape recognition and counting. 7-year olds aside, I don't even think most of the high-schooler freshmen I've taught would be able to grasp this content.

tartoran 5y ago
Maybe they’re implying 7 year old geniuses who could read by the age of 3 and speak 4 languages by the age of 4. Anyhow, I agree that it’s not for the average 7 year old but it’s a cool book nonetheless
- thaumasiotes 5y ago
  > Maybe they’re implying 7 year old geniuses who could read by the age of 3 and speak 4 languages by the age of 4. Speaking four languages by the age of 4 is just ordinary development, assuming you're in an area where all four are spoken. You should be speaking them before the age of 2.
  - tartoran 5y ago
    My son speaks 2 at 3 years old. I’m amazed that is possible though, yes, it is an ordinary development in a bilingual household.
    - jdmoreira 5y ago
      I agree that's just standard but parent said they speak 4 languages before 2. That's total and complete BS. I have a 2 year old and I speak with her in one language the mom in another and me and the mom speak in a third language between us. She knows words in the 3 languages and can construct phrases in 1 or 2 of those languages. She is is also much more developed verbally than any of the kids her age we meet regularly but she definitely doesn't speak 3 languages.

DoreenMichele 5y ago

Copyright 1991. This was probably making the rounds of homeschooling circles I hung out in. We tend to do a sucky job of teaching math to kids. A lot of elementary school teachers are women who were encouraged to go into early education because they weren't doing so well in math and this is very much gender bias. My ex husband wasn't good at math. No one told him he should spend his days teaching little kids because of it. He was a career soldier and he just got tutored in college (by me) for his math classes. He was just expected to work at it if it didn't come naturally and he did. So we just culturally pass around this idea that math is scary and little kids can't learn it rather than going "Well, adults just need to up their game and, by god, explain it better." My oldest was math phobic by the time I pulled him out of school to homeschool. My one and only goal for math was to get him over his phobia. He loves physics. I hate calculus. Calculus makes sense to him and he has read calculus books for fun. I was good at explaining the math to him and he learned lots of solid math concepts even though he likely has dyscalculia and isn't good at crunching the numbers. But I got the concepts through to him and that's more important. He's what gets called "calculator dependent" in some circles.

dvfjsdhgfv 5y ago
> We tend to do a sucky job of teaching math to kids. A lot of elementary school teachers are women who were encouraged to go into early education because they weren't doing so well in math and this is very much gender bias. While this may be true and in general is in line with my experience, it might be better for you to reframe it in a more indirect way because sooner or later you'll find someone offended.
- DoreenMichele 5y ago
  I appear to be the highest ranked openly female member on HN. I can suck up a few downvotes from people who don't like me or don't like what I am saying and that, in fact, seems to be par for the course here. Thank you for otherwise validating my position, but I'm not going to soften it. If the truth about our world bothers people, they are free to make something else true instead of asking me to cater to their feelings at the expense of stating the truth. Edit: I will add I am unwilling to back down on this point because we are actively giving young women a math phobia and crushing their dreams with it instead of telling them to get a tutor and work for what they want and we are doing so in a manner that causes them to pass their math phobia onto future generations. This isn't just a case of "sexism sucks." We are poisoning our entire society with this garbage and it negatively impacts huge numbers of people.

AndrewKemendo 5y ago

I really wish there were something like an "executive" refresher classes on basic maths with a focus on practical applications and modeling. I took Calculus II/III, Linear/Diff EQ and some others in college, but I haven't written a new mathematical model in almost two decades and am rusty.

mhh__ 5y ago
Try modelling something and see where it goes? The thing with "modelling" is that in my experience it's often justified post-facto so you don't actually learn anything when it comes to modelling as an art. That being said what you are describing is basically a physics textbook, I would say engineering, but they have no soul.
- AndrewKemendo 5y ago
  I have done data modeling for a living and I don't agree that you don't learn anything and that it's used to justify something - you just have to do it rigorously. To that point though, most modeling with any accuracy is done by computer now, and not by hand, which is what my point is. It's impossible to gain an intuition about something if the computer just tells you the answer.
cgh 5y ago
Not sure if it’s precisely what you’re looking for, but I’m currently reading and working through Coding the Matrix, which is linear algebra by way of Python. There are few assumptions and you start coding pretty early on.
- AndrewKemendo 5y ago
  Thanks, I feel like I've run across the book a few times over the years but never was suggested it. I'll check it out
r0fl 5y ago
Try Khan Academy, I found it to be a great refresher for things like that.

lanna 5y ago

My 6yo daughter has exceptional talent and interest for Math. She's already discovering some fundamental theorems for herself (number theory, algebra, geometry). Does anyone here know any resources to help her development?

dharmab 5y ago
The YouTube channel 3blue1brown has some great, accessible introductions to higher level math.
- schoen 5y ago
  That's a truly fantastic recommendation. Other thoughts: * The "Exploding Dots" project came up with a creative way to present place value that leads into a lot of other concepts like number bases, algebraic structures, polynomials, and other things. (It's actually like a generalization of the abacus, with fun computer animation.) I'm not sure which presentation of this is best -- I think the original inventor has gone through like three different versions and there are several versions available online now. * I'm a huge fan of the late math journalist Martin Gardner, who wrote a lot of really entertaining stuff about math as well as puzzles and games. His books are really brilliant and cover a very wide territory. On the other hand, they were mostly written for adult audiences (originally, mainly readers of Gardner's Scientific American column) and may contain cultural references that kids wouldn't get, not least because some of them go back to the 1960s. :-( Also in some cases there have been further discoveries in the decades since the columns were published, so learning about them only from Gardner's old work may not give a good sense of where things have gone since then (e.g., he famously originally introduced both the Game of Life and the RSA algorithm to mass audiences, which then learned a lot about both topics in the ensuing decades). But maybe have a peek because they do stress the "math is fun and you can do it for fun" and also "math is all kinds of stuff and not just arithmetic" notions. * Gardner does have two math books for kids (the aha! series) that are very fun and introduce a lot of fascinating stuff about logic and paradoxes, among other topics. * Two online games that involve proof and circuit synthesis (spoiler alert: these are actually often isomorphic to each other because of Curry-Howard and stuff), which I think I heard about on HN: http://incredible.pm/ http://incredible.pm/ https://www.nandgame.com/ https://www.nandgame.com/ I totally loved both of these and I think they could conceivably be accessible for a very motivated and very talented child. Another online logic game that I also learned about on HN and loved: https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/ https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_g... Unlike the other two, this one uses (only) text and symbols instead of blocks and arrows. It's meant for college undergraduates, but I envision highly mathematically-talented middle-schoolers possibly being able to finish it. The user interface can probably also be improved a lot to make it clearer what you're allowed to do in each context. Maybe keep this one in mind for the future? :-) Contemporary pre-college math education is famously very weak on discrete math topics (like number theory, logic, and combinatorics). I don't know if this is due to a desire to train aerospace engineers for the Space Race, or because discrete math has radically increased its profile only in the past few decades with the rise of computer science, or as a kind of backlash against the New Math which tried (mostly unsuccessfully) to teach kids formal logical foundations through set theory. I wish I knew some more good discrete stuff for younger audiences. I haven't ever done any of it myself, but I hear Khan Academy's explanations (especially in math) are great and very self-paced.

_Nat_ 5y ago

Looks pretty out-dated (1991). A lot of the math is very poorly formatted, and a lot of code's in an ancient form of BASIC. Doesn't look like a good fit for a primary textbook since it's too scattered and slow, though some of the content might work as mini-games, sorta like crossword puzzles.

bawolff 5y ago
Does math really change? I guess the basic is less popular now that TI-89's are being replaced with smartphones, but its probably not as ancient as you think.
- _Nat_ 5y ago
  Yes, math changes, but it's moreso the presentation that's ancient. The formatting is so retro that it seriously damages legibility while simultaneously failing to give students a taste of actual mathematical discourse, and the coding in the text is obsolete. That students are still required to use TI-89's in class is a travesty itself -- TI-89's are horribly obsolete in modern practice and really only serve to hamper cheating on exams. At best, teaching students with TI-89's to better prepare them for exams might be justified as a trick to inflate their scores, but it still seems like a wasted opportunity to acquire a working familiarity with actual tools that students might actually use in the future. The BASIC code is worse yet as it can't even be argued for as an exam-score-inflation trick; it's simply obsolete. Students learning coding ought to learn modern languages. The focus should be on what's best for the students. And this isn't it. The retro stuff belongs in a museum.

canada_dry 5y ago

This resource really isn't that great IMHO. For anyone (esp. children) to grasp a new concept it helps to have relatable problems that can be solved in gradual steps. After dividing up a cookie in Ch. 2 it continues further and starts to discuss proof via harmonics!

aryehof 5y ago

Let children be children, not experiments in the aspirations of parents and adults.

Atreiden 5y ago
Sometimes children seek this kind of stimulation. I used to love trying to solve 'advanced' problems. Making new connections, i.e. "wow, so THATS why that is the way it is" were some of my favorite memories. I did Math Olympiad as a kid not because my parents pushed me - on the contrary - I pushed on them (and my teacher) to get into the program. Obviously it's not for everyone, but I personally I would have killed to have started learning the 'interesting' stuff earlier in my life.
boringg 5y ago
How is this considered aspirations of their parents? One of the most thrilling things in life is to learn new skills and understand how the world works. My child loves to learn new things and is very excited when he does something new. I am sorry that you feel that way and maybe you personally did not like to learn new things. Don't cast your negative judgement on the enjoyment of others learning guised as "Just let kids be kids". You assume that people doing this are pulling a Beethoven's father or something. Check your assumptions.
boringg 5y ago
I'm also assuming here, but it does sound like you don't have children of your own.
koheripbal 5y ago
Don't educate people. Let them remain ignorant.

beardyw 5y ago

When I was 9, my next eldest brother of 16 was captivated by calculus at school and wanted to share it with me. Without algebra he managed to get across to me how it worked though I am sure I had no idea what the point of it was. Sadly I have little capacity for memorising anything so eight years later in my final school exams I was still using first principles. It didn't go too well.

jfmc 5y ago

During pandemic lockdowns I had the opportunity to teach my 7yo son maths at home. It does not work for all kids, but he showed a very strong interest in symbolic manipulation. School overemphasizes arithmetic and arithmetic algorithms ad infinitum (extremely tedious and boring!). Our work plan is simple: a problem each day (together when the concepts are new), immediate reward after he finishes, and increase difficulty once he is ready. After one year, we have just started trigonometric equations at home, while they are still working on simple multiplications at school. In the same way that some kids are good at sports, drawing, music, foreign languages, or playing videogames, some of them are very good managing abstractions. Those would be very happy learning calculus or other advanced mathematics, just for fun!

tmaly 5y ago

I will keep this for reference. It is a good starting point that I can build on with my kids.