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> I could probably be convinced to jump on that bandwagon [dump calc, replace with stats] I think, really, that the opposite needs to be done. Math curriculum

> I could probably be convinced to jump on that bandwagon [dump calc, replace with stats] I think, really, that the opposite needs to be done. Math curriculums would do better to focus more on getting "the foundations" right. Starting with algebra, geometry, trigonometry and real analysis (calculus), and pursuing it rigorously for college-bound students. There should be a focus on mastery rather than covering a wide variety of stuff quickly. Too many students get to college with a mathematical foundation that looks like Swiss cheese-- with many holes in basic skills: like fractions, exponents, trig (yes, even if they took calc in high school).

tomnipotent 7y ago
Why should geometry and trig be "the foundations" while statistics is not? Because that's the way it's always been? Sounds like a horrible reason to keep things the same.
- jacquesm 7y ago
  For the same reason that the concrete or blocks partition under your building is the foundation: the one supports the other.
- hdctambien 7y ago
  Geometry is really used to introduce proofs. Turns out its easier to get teenagers to understand a proof if you can actually see its results. I think that's a pretty good foundational skill, but I admit that it isn't obvious from the students point of view why that would be or that that is what they are even learning. In Texas the Geometry class is designed to "strengthen their mathematical reasoning skills in geometric contexts. Within the course, students will begin to focus on more precise terminology, symbolic representations, and the development of proofs" [1] In Texas Trig is taught in Precalc, which makes sense if you are going to take Calc which makes sense if you are going to go on to study engineering or physics or mathematics. But neither of those classes are required in Texas. You could just as well take Algebra 1, Geometry, and AP Stats. [1] http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.html http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.ht...
  - phkahler 7y ago
    I was wondering why people hadn't suggested having a choice. Go Texas!
- alxlaz 7y ago
  Ever tried to teach an introductory Physics class without using geometry, trigonometry or calculus? (Edit: for that matter, teaching statistics to students with limited exposure to calculus is not a very successful endeavour, either...) There are a lot of things that mathematics is fundamental to besides data science, and schools need to address the requirements of all children, not just those who want to write (a very limited range of) software when they grow up.
  - samastur 7y ago
    I wish I could upvote this comment more.
  - aeternum 7y ago
    I hated calculus until learning Physics. It was so abstract and seemed useless. I'd much rather be presented with a problem, like how far did this ball travel, then learn calculus as a tool to solve that problem. I agree with you though that attempts to teach Physics without calculus are sorely misguided. It's ridiculous to force students to memorize kinematic equations that can be trivially derived from each other.
    - shkkmo 7y ago
      I got lucky enough to be able to take both Calculus and Physics concurrently from the local University rather than taking Physics without calculus from my high school. It almost seems like they should be taught as a single interdisciplinary class.
  - wwarner 7y ago
    Not really an argument. Spolsky didn't suggest leaving out geometry. Trigonometry and calculus can be shortened and taught to prepare a student for statistical reasoning, which includes plenty of trig and calc. And finally, what makes the way physics is taught so sacred? Introductory physics doesn't bear much resemblance to what physicists have been talking about for the past 100 years or so, precisely because the student lacks the statistical reasoning that modern physics requires.
  - 7y ago
lootsauce 7y ago
Disagree. I find that there is a lot of supposed value in everyone learning all the foundations but I often wonder how much money, time and potential for other outcomes has been wasted on everyone being forced to learn things they never use. This is totally verboten to say I suppose but languages are very much like this, and so is much of maths. Not saying the options should not be there or the classes should not be full of kids, just that the sense that its "of course" a good idea for everyone to get these same foundations is overly prescriptive and ignores all the other possibilities and the lack of value most people actually gain from them.
ssully 7y ago
I know this discussion is focused on Math, but I think most students get to college with a general foundation that looks like Swiss cheese. I think it's just a result of good education being hard to apply generally, and students lack of interest in certain topics.
satya71 7y ago
I studied many years of calculus. Guess how many times I've used calculus in my electrical engineer career. 0. When needed, I use a math package instead. Statistics, on the other hand, I encounter daily, but don't have the expertise to handle well. I know, I could study, but easier said than done.

tomnipotent 7y ago

Why should geometry and trig be "the foundations" while statistics is not? Because that's the way it's always been? Sounds like a horrible reason to keep things the same.

jacquesm 7y ago
For the same reason that the concrete or blocks partition under your building is the foundation: the one supports the other.
hdctambien 7y ago
Geometry is really used to introduce proofs. Turns out its easier to get teenagers to understand a proof if you can actually see its results. I think that's a pretty good foundational skill, but I admit that it isn't obvious from the students point of view why that would be or that that is what they are even learning. In Texas the Geometry class is designed to "strengthen their mathematical reasoning skills in geometric contexts. Within the course, students will begin to focus on more precise terminology, symbolic representations, and the development of proofs" [1] In Texas Trig is taught in Precalc, which makes sense if you are going to take Calc which makes sense if you are going to go on to study engineering or physics or mathematics. But neither of those classes are required in Texas. You could just as well take Algebra 1, Geometry, and AP Stats. [1] http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.html http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.ht...
- phkahler 7y ago
  I was wondering why people hadn't suggested having a choice. Go Texas!
alxlaz 7y ago
Ever tried to teach an introductory Physics class without using geometry, trigonometry or calculus? (Edit: for that matter, teaching statistics to students with limited exposure to calculus is not a very successful endeavour, either...) There are a lot of things that mathematics is fundamental to besides data science, and schools need to address the requirements of all children, not just those who want to write (a very limited range of) software when they grow up.
- samastur 7y ago
  I wish I could upvote this comment more.
- aeternum 7y ago
  I hated calculus until learning Physics. It was so abstract and seemed useless. I'd much rather be presented with a problem, like how far did this ball travel, then learn calculus as a tool to solve that problem. I agree with you though that attempts to teach Physics without calculus are sorely misguided. It's ridiculous to force students to memorize kinematic equations that can be trivially derived from each other.
  - shkkmo 7y ago
    I got lucky enough to be able to take both Calculus and Physics concurrently from the local University rather than taking Physics without calculus from my high school. It almost seems like they should be taught as a single interdisciplinary class.
- wwarner 7y ago
  Not really an argument. Spolsky didn't suggest leaving out geometry. Trigonometry and calculus can be shortened and taught to prepare a student for statistical reasoning, which includes plenty of trig and calc. And finally, what makes the way physics is taught so sacred? Introductory physics doesn't bear much resemblance to what physicists have been talking about for the past 100 years or so, precisely because the student lacks the statistical reasoning that modern physics requires.
- 7y ago

lootsauce 7y ago

Disagree. I find that there is a lot of supposed value in everyone learning all the foundations but I often wonder how much money, time and potential for other outcomes has been wasted on everyone being forced to learn things they never use. This is totally verboten to say I suppose but languages are very much like this, and so is much of maths. Not saying the options should not be there or the classes should not be full of kids, just that the sense that its "of course" a good idea for everyone to get these same foundations is overly prescriptive and ignores all the other possibilities and the lack of value most people actually gain from them.

ssully 7y ago

I know this discussion is focused on Math, but I think most students get to college with a general foundation that looks like Swiss cheese. I think it's just a result of good education being hard to apply generally, and students lack of interest in certain topics.

satya71 7y ago

I studied many years of calculus. Guess how many times I've used calculus in my electrical engineer career. 0. When needed, I use a math package instead. Statistics, on the other hand, I encounter daily, but don't have the expertise to handle well. I know, I could study, but easier said than done.