4 ms·

jeez, what kind of 11th and 12th grade curriculum teaches topology, real analysis etc...? Is this a syllabus for math whiz kids?

ecshafer 4y ago
The "High School" Curriculum is basically an undergraduate mathematics degree.
- Workaccount2 4y ago
  I can't tell if they believe they have cracked the code that makes learning these concepts accessible or if they are suffering from a severe case of expert syndrome, totally unable to put themselves in the shoes of a novice.
  - jayro 4y ago
    Through trial and error and the application of some rarely employed, but highly-effective educational strategies like active learning, distributed practice, mixed review, mastery-based learning, interleaving, layering, etc., you end up with a pace of learning that's a little shocking. I realize it's hard to believe -extraordinary claims require extraordinary evidence and all that, but that's what got us started having our 8th-graders take the AP Calculus BC exam as as an outside, objective measure.
  - yamtaddle 4y ago
    Opt-in educational programs of all sorts are usually heavily selection-biased toward students that are well-motivated and generally exceptionally easy to teach—good support from home, probably above-average SES, above-average IQ, et c. Which doesn't mean such programs are useless, just that they're typically far less effective if you try to apply them to a representative slice of the overall student population.
    - jayro 4y ago
      It's true that the students in the school program are high-aptitude, but something like 70% of the students in the middle school where this all started are on the federal free and reduced lunch program (low SES) along with a couple of the top kids in the original cohort, who I taught personally and they were amazing.
      - lupire 4y ago
        > 70 % of the students in the middle school where this all started but > a couple of the top kids in the original cohor Are their parents from a tight-knit immigrant community, highly educated in their previous country, with economic prospects in the US dimmed by language barrier and professional certifications that got dropped at the border?
- jayro 4y ago
  Yeah, pretty close, although it's not like most universities will allow students to skip straight to graduate school. Our first cohort of students just graduated this past year, so we're just now getting a sense of how this is likely to play out. My son, who's majoring in CS, is starting with 300 (junior-level) courses in both math and CS - although the departments were happy to allow him to start even deeper in the curriculum if he wanted. Another student, who collaborated with one our our math PhD instructors on some original research that's about to be published, is starting with at least one graduate math course this year (the last I heard, anyway).
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jayro 4y ago
Well, it turns out that when you have mathematically-talented students completing Calculus in 8th-grade, and move on the Linear Algebra and Multivariable Calculus in 9th, you eventually reach Real Analysis and Topology by the end of high-school - although, we haven't gone quite as deep in those particular subjects as the others mentioned. But we do comprehensively cover Differential Equations, Discrete Mathematics, Probability & Statistics and Abstract Algebra.
- lupire 4y ago
  Honestly that looks like superficial rushing for rushing's sake. There is so much advanced and deep elementary math kids could learn.
  - jayro 4y ago
    I understand why it might seem that way, but it's really not. We've just put a premium on learning efficiency, and most math classes are highly inefficient - whether K-12 or university. Just imagine how much more quickly a student could progress through a course if they were to work one-on-one with an expert tutor 5 days per week. Quite a bit more quickly in most cases. Well, our system effectively serves as an expert AI tutor and based on our calculations is on the order of 4 times more efficient than a traditional math class. But I get the skepticism. I'd probably be skeptical myself.

ecshafer 4y ago

The "High School" Curriculum is basically an undergraduate mathematics degree.

Workaccount2 4y ago
I can't tell if they believe they have cracked the code that makes learning these concepts accessible or if they are suffering from a severe case of expert syndrome, totally unable to put themselves in the shoes of a novice.
- jayro 4y ago
  Through trial and error and the application of some rarely employed, but highly-effective educational strategies like active learning, distributed practice, mixed review, mastery-based learning, interleaving, layering, etc., you end up with a pace of learning that's a little shocking. I realize it's hard to believe -extraordinary claims require extraordinary evidence and all that, but that's what got us started having our 8th-graders take the AP Calculus BC exam as as an outside, objective measure.
- yamtaddle 4y ago
  Opt-in educational programs of all sorts are usually heavily selection-biased toward students that are well-motivated and generally exceptionally easy to teach—good support from home, probably above-average SES, above-average IQ, et c. Which doesn't mean such programs are useless, just that they're typically far less effective if you try to apply them to a representative slice of the overall student population.
  - jayro 4y ago
    It's true that the students in the school program are high-aptitude, but something like 70% of the students in the middle school where this all started are on the federal free and reduced lunch program (low SES) along with a couple of the top kids in the original cohort, who I taught personally and they were amazing.
    - lupire 4y ago
      > 70 % of the students in the middle school where this all started but > a couple of the top kids in the original cohor Are their parents from a tight-knit immigrant community, highly educated in their previous country, with economic prospects in the US dimmed by language barrier and professional certifications that got dropped at the border?
jayro 4y ago
Yeah, pretty close, although it's not like most universities will allow students to skip straight to graduate school. Our first cohort of students just graduated this past year, so we're just now getting a sense of how this is likely to play out. My son, who's majoring in CS, is starting with 300 (junior-level) courses in both math and CS - although the departments were happy to allow him to start even deeper in the curriculum if he wanted. Another student, who collaborated with one our our math PhD instructors on some original research that's about to be published, is starting with at least one graduate math course this year (the last I heard, anyway).

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jayro 4y ago

Well, it turns out that when you have mathematically-talented students completing Calculus in 8th-grade, and move on the Linear Algebra and Multivariable Calculus in 9th, you eventually reach Real Analysis and Topology by the end of high-school - although, we haven't gone quite as deep in those particular subjects as the others mentioned. But we do comprehensively cover Differential Equations, Discrete Mathematics, Probability & Statistics and Abstract Algebra.

lupire 4y ago
Honestly that looks like superficial rushing for rushing's sake. There is so much advanced and deep elementary math kids could learn.
- jayro 4y ago
  I understand why it might seem that way, but it's really not. We've just put a premium on learning efficiency, and most math classes are highly inefficient - whether K-12 or university. Just imagine how much more quickly a student could progress through a course if they were to work one-on-one with an expert tutor 5 days per week. Quite a bit more quickly in most cases. Well, our system effectively serves as an expert AI tutor and based on our calculations is on the order of 4 times more efficient than a traditional math class. But I get the skepticism. I'd probably be skeptical myself.