They should introduce basic mathematical logic as well.
I read the article, it's all actually pretty reasonable. Although the idea of replacing calculus with something like "data science" is pretty terrible. As all mathematicians know, if calculus is replaced by anything it must be linear algebra.
I read the article, it's all actually pretty reasonable. Although the idea of replacing calculus with something like "data science" is pretty terrible. As all mathematicians know, if calculus is replaced by anything it must be linear algebra.
Insanity. Calculus was historically, and remains pedagogically, the first and most important case of escaping the limitations and rigidity of low degree equations that controlled algebra and geometry. It allows you to ask and answer many substantial questions on "arbitrary curves" and some surfaces/volumes, and to get the ball rolling in the direction of ever bigger and better theories encompassing everything in science. Linear algebra is a dinky autist subject by comparison if limited to what you can do in a basic class.
Calculus is not only an important subject in math. It is also crucial to physics, chemistry, and engineering. Leetcoders earn so much does not mean these basic subjects are no longer important.
Lagrange, Euler, Gauss, and probably Riemann did not know what is "rigorous analysis proof of calculus". They still produced so many brilliant works. I don't think the issue is about rigor. The issue is that teaching calculus actually is not that easy, and high school teachers usually do not have the ability to teach calculus in a not-that-messy way. (To be honest, even many math PhDs can not teach calculus in a not-that-messy way.)
Anyone who has any strong opinion about calculus class one way or another is spending too much time thinking about the curriculum. Students who become mathematicians never take these classes in university. They’re just for engineering students who’ll fail to understand anything (but will still get an A), and they will never need anything from the class other than what they can look up.
I don't think the issue is about rigor. The issue is that teaching calculus actually is not that easy, and high school teachers usually do not have the ability to teach calculus in a not-that-messy way. (To be honest, even many math PhDs can not teach calculus in a not-that-messy way.)
Preach, brother.
There's a certain know-how of concrete elementary mathematics that gets lost in today's educational approach that produces mostly "professional idiots", and many literal idiots among schoolteachers.
I read the article, it's all actually pretty reasonable. Although the idea of replacing calculus with something like "data science" is pretty terrible. As all mathematicians know, if calculus is replaced by anything it must be linear algebra.
Insanity. Calculus was historically, and remains pedagogically, the first and most important case of escaping the limitations and rigidity of low degree equations that controlled algebra and geometry. It allows you to ask and answer many substantial questions on "arbitrary curves" and some surfaces/volumes, and to get the ball rolling in the direction of ever bigger and better theories encompassing everything in science. Linear algebra is a dinky autist subject by comparison if limited to what you can do in a basic class.
commentary like this is why math education isn’t left to mathematicians
[...]Insanity. Calculus was historically, and remains pedagogically, the first and most important case of escaping the limitations and rigidity of low degree equations that controlled algebra and geometry. It allows you to ask and answer many substantial questions on "arbitrary curves" and some surfaces/volumes, and to get the ball rolling in the direction of ever bigger and better theories encompassing everything in science. Linear algebra is a dinky autist subject by comparison if limited to what you can do in a basic class.
commentary like this is why math education isn’t left to mathematicians
Students like to see a purpose, a punch-line. What do any of the proposed calculus replacement subjects have that compares to, e.g., modeling gravity?
[...]commentary like this is why math education isn’t left to mathematicians
Students like to see a purpose, a punch-line. What do any of the proposed calculus replacement subjects have that compares to, e.g., modeling gravity?
Number theory: quadratic reciprocity Linear algebra: some application to image processing OR linear algebra method in combinatorics Mathematical logic: Goedel's theorems
[...]Students like to see a purpose, a punch-line. What do any of the proposed calculus replacement subjects have that compares to, e.g., modeling gravity?
Number theory: quadratic reciprocity Linear algebra: some application to image processing OR linear algebra method in combinatorics Mathematical logic: Goedel's theorems
So "dinky autistic by comparison" was right? You want high school students without a special math interest to be impressed by quadratic reciprocity? Why should they care about a "symbol" that detects squareness mod p?? Or formal logical systems?
[...]Insanity. Calculus was historically, and remains pedagogically, the first and most important case of escaping the limitations and rigidity of low degree equations that controlled algebra and geometry. It allows you to ask and answer many substantial questions on "arbitrary curves" and some surfaces/volumes, and to get the ball rolling in the direction of ever bigger and better theories encompassing everything in science. Linear algebra is a dinky autist subject by comparison if limited to what you can do in a basic class.
commentary like this is why math education isn’t left to mathematicians
Indeed, much better left to the frumpy post-menopausal women that seem to dominate faculties of education. After all, it’s been left to them for several decades now and elementary and high school math education is better than ever! (C.f. the JB of Stanford email in which she asks if inequalities ever arise in connection with data science. Just the person who should be in charge!) or maybe we should give integrative biologists or whatever a chance?
This discussion is funnier when you realise Americans are taking calculus in college. The rest of the world is studying this stuff at 16 and in America 18-20 year olds are complaining that a non-proof based calculus course is too hard and they want to learn statistics instead.
This discussion is funnier when you realise Americans are taking calculus in college. The rest of the world is studying this stuff at 16 and in America 18-20 year olds are complaining that a non-proof based calculus course is too hard and they want to learn statistics instead.
The US high school calculus classes (Advanced Placement BC, don't know about IB) are actually pretty good by international standards. Of course the students and teachers in those classes are much stronger than the average for US.
This discussion is funnier when you realise Americans are taking calculus in college. The rest of the world is studying this stuff at 16 and in America 18-20 year olds are complaining that a non-proof based calculus course is too hard and they want to learn statistics instead.
I've taught first year service courses in calculus in both the US and Europe. There's no essential difference, though probably the bottom of the barrel is lower in the US, because of muh diversity. Asia is probably different. I haven't worked there.
Calculus is not only an important subject in math. It is also crucial to physics, chemistry, and engineering. Leetcoders earn so much does not mean these basic subjects are no longer important.
Lagrange, Euler, Gauss, and probably Riemann did not know what is "rigorous analysis proof of calculus". They still produced so many brilliant works. I don't think the issue is about rigor. The issue is that teaching calculus actually is not that easy, and high school teachers usually do not have the ability to teach calculus in a not-that-messy way. (To be honest, even many math PhDs can not teach calculus in a not-that-messy way.)
Intro Calculus should always be taught in tandem with Intro Physics. Provides immediate application and intuitive understanding of what the math actually means.
Calculus is not only an important subject in math. It is also crucial to physics, chemistry, and engineering. Leetcoders earn so much does not mean these basic subjects are no longer important.
Lagrange, Euler, Gauss, and probably Riemann did not know what is "rigorous analysis proof of calculus". They still produced so many brilliant works. I don't think the issue is about rigor. The issue is that teaching calculus actually is not that easy, and high school teachers usually do not have the ability to teach calculus in a not-that-messy way. (To be honest, even many math PhDs can not teach calculus in a not-that-messy way.)
Intro Calculus should always be taught in tandem with Intro Physics. Provides immediate application and intuitive understanding of what the math actually means.
Indeed, and when doing oral exams in basic analysis, I always ask students "explain the statement of this theorem in terms of driving a car".
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