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When I was in high school, I chose to take standard-level IB math instead of higher-level IB math. The standard-level math focused on probability and combinator

When I was in high school, I chose to take standard-level IB math instead of higher-level IB math. The standard-level math focused on probability and combinatorics, whereas higher-level was focused on calculus (you had to take calculus first). I appreciate the opportunity to have learned about these other subjects, which are arguably more useful in everyday life (and I went on to be a lawyer and a startup founder, where advanced calculus would not have been especially useful). It also meant my schedule was somewhat easier, since the standard-level class was not as challenging, and I was more mature by the time I took calc AB as a senior. I'm glad my parents realized that getting as far down the calculus path as possible was not the only goal, and suggested this path for me.

kqr 3y ago
I've always been surprised that probability and statistics are not getting more stage time in school. It's one of the most practically useful areas of mathematics, and also one of the least intuitive so people with little training get it wrong all the time.
- goeiedaggoeie 3y ago
  My 13 year old is doing some basic probability already at school, something I did not get exposure to until I was considerably older.
- lern_too_spel 3y ago
  To learn many topics in statistics, you need calculus. The reverse is not true.
  - kqr 3y ago
    You mean to prove many theorems in statistics, right? You can learn and use plenty of statistics with very few weeks of calculus.
    - lern_too_spel 3y ago
      If you can't prove something, even informally, you aren't doing math. Memorizing and applying magic formulas (especially in "math" and physics classes) is a big problem with the curriculum.
      - hdctambien 3y ago
        I agree. Algebra based Statistics is one of the things that makes people say "Math is a religion". There is a lot of "just trust me" in statistics when you don't know calculus. I suppose you could switch Probability & Statistics to "Just Enough Calculus" & Statistics to make it a less religious experience... but that also sort of defeats the "nobody really uses Calculus" mentality.
    - patrick451 3y ago
      How do you define a PDF without an integral? I guess you can work exclusively with the discrete PMF, but then you have no Guassians, which are central to probability and statistics. How do talk about non-linear transformations of random variables, for which you need a Jacobian?
      - kqr 3y ago
        You can explain density as mass with arbitrarily small steps, yes. The Gaussian is the limit of many small binomials. With some graphical demonstrations to go along with it, I've had much success getting people to fruitfully use these concepts. You also don't need a Jacobian, just the general concept of "How much does this change when we adjust this parameter in this direction". I'm not saying it's easier without calculus. By virtue of being more knowledge, the ability to use calculus will always be easier than not having it, all else equal. My argument is about opportunity cost. In my experience, people can get really good intuitions and tools around probability and statistics in the same time that they would otherwise learn the fine details around integrals and Jacobians -- and they'll find much more use for it.
      - wjnc 3y ago
        Obviously you’re right. But we are talking kids here. There is so much to learn in statistics at basic to intermediate level without algebra. Many social scientists or in the modern age data scientist go through life with cookbook statistics and some code examples. Sure, it lacks rigour, but intuition especially for kids breeds interest and then the subset that is mathematically inclined can go on to do statistics with all rigour.
- hdctambien 3y ago
  I think it all depends on where you went to school and possibly who noticed you while you were there. I took 2 years of Probability and Statistics in Highschool in 1998-99 and 1999-00 at a school with 200 students. At the 4000 students school I taught at a few years ago we offered AP Probability and Statistics (had have been for at least 10 years, but probably much longer than that). In both situations, you could (and many did) take Stats without Calc. Most times when people say "schools should teach X", many schools are (and have been) doing it (taxes, car maintenance, carpentry, gardening). Just maybe not your school ... or maybe nobody told you that it was a possibility at your school... Or maybe it's not at your school, but it is offered at another school in your district... Or maybe it's just not offered at your school. Because there is an AP exam associated with Stats, it is fairly easy to get the class made as long as there are students that want to take the class and enough teacher slots to accommodate that. If a school is understaffed in the math department and class sizes are nearing 40, then you probably won't find a Stats class there.
Fomite 3y ago
I followed the same path - it served me well in life, but man did my university assume when you were taking Calc 1 that you had already taken calculus in high school mess me up.
nraf 3y ago
Ah… IB must’ve been why I found the discrete mathematics subject at university so much easier than my peers did - I’d already been exposed to a lot of it.
unixhero 3y ago
IB?
- gnicholas 3y ago
  International Baccalaureate. It's like AP, but internationally accepted. To get the full diploma, you have to take three standard-level tests and three higher-level tests.

kqr 3y ago

I've always been surprised that probability and statistics are not getting more stage time in school. It's one of the most practically useful areas of mathematics, and also one of the least intuitive so people with little training get it wrong all the time.

goeiedaggoeie 3y ago
My 13 year old is doing some basic probability already at school, something I did not get exposure to until I was considerably older.
lern_too_spel 3y ago
To learn many topics in statistics, you need calculus. The reverse is not true.
- kqr 3y ago
  You mean to prove many theorems in statistics, right? You can learn and use plenty of statistics with very few weeks of calculus.
  - lern_too_spel 3y ago
    If you can't prove something, even informally, you aren't doing math. Memorizing and applying magic formulas (especially in "math" and physics classes) is a big problem with the curriculum.
    - hdctambien 3y ago
      I agree. Algebra based Statistics is one of the things that makes people say "Math is a religion". There is a lot of "just trust me" in statistics when you don't know calculus. I suppose you could switch Probability & Statistics to "Just Enough Calculus" & Statistics to make it a less religious experience... but that also sort of defeats the "nobody really uses Calculus" mentality.
  - patrick451 3y ago
    How do you define a PDF without an integral? I guess you can work exclusively with the discrete PMF, but then you have no Guassians, which are central to probability and statistics. How do talk about non-linear transformations of random variables, for which you need a Jacobian?
    - kqr 3y ago
      You can explain density as mass with arbitrarily small steps, yes. The Gaussian is the limit of many small binomials. With some graphical demonstrations to go along with it, I've had much success getting people to fruitfully use these concepts. You also don't need a Jacobian, just the general concept of "How much does this change when we adjust this parameter in this direction". I'm not saying it's easier without calculus. By virtue of being more knowledge, the ability to use calculus will always be easier than not having it, all else equal. My argument is about opportunity cost. In my experience, people can get really good intuitions and tools around probability and statistics in the same time that they would otherwise learn the fine details around integrals and Jacobians -- and they'll find much more use for it.
    - wjnc 3y ago
      Obviously you’re right. But we are talking kids here. There is so much to learn in statistics at basic to intermediate level without algebra. Many social scientists or in the modern age data scientist go through life with cookbook statistics and some code examples. Sure, it lacks rigour, but intuition especially for kids breeds interest and then the subset that is mathematically inclined can go on to do statistics with all rigour.
hdctambien 3y ago
I think it all depends on where you went to school and possibly who noticed you while you were there. I took 2 years of Probability and Statistics in Highschool in 1998-99 and 1999-00 at a school with 200 students. At the 4000 students school I taught at a few years ago we offered AP Probability and Statistics (had have been for at least 10 years, but probably much longer than that). In both situations, you could (and many did) take Stats without Calc. Most times when people say "schools should teach X", many schools are (and have been) doing it (taxes, car maintenance, carpentry, gardening). Just maybe not your school ... or maybe nobody told you that it was a possibility at your school... Or maybe it's not at your school, but it is offered at another school in your district... Or maybe it's just not offered at your school. Because there is an AP exam associated with Stats, it is fairly easy to get the class made as long as there are students that want to take the class and enough teacher slots to accommodate that. If a school is understaffed in the math department and class sizes are nearing 40, then you probably won't find a Stats class there.

Fomite 3y ago

I followed the same path - it served me well in life, but man did my university assume when you were taking Calc 1 that you had already taken calculus in high school mess me up.

nraf 3y ago

Ah… IB must’ve been why I found the discrete mathematics subject at university so much easier than my peers did - I’d already been exposed to a lot of it.

unixhero 3y ago

IB?

gnicholas 3y ago
International Baccalaureate. It's like AP, but internationally accepted. To get the full diploma, you have to take three standard-level tests and three higher-level tests.