> You seem to always shoulder students with the burden of suffering a math deficit, whereas it may be the school's curriculum and/or teachers and/or the whole culture of a high school that starts closing these doors.
That?s not true. Most of my years here were spent studying curriculums, in detail. I blame the schools and curriculums for not nurturing the students who are good in math. The only students that actually continue on after school and use and apply this gift. The little bit of math that the other students pickup is soon forgotten.
> "Math dependent degree" includes a lot of them, including just about anything healthcare related. Maybe 3% want to be math majors, whereas 40% seek a math-dependent major.
Arithmetic dependent, probably, but not math dependent. And certainly not pure math dependent.
> Some students have just never had the benefit of an optimized learning environment. They have every potential to catch up and surpass, and yes, that potential is as yet unfulfilled. Not unusual.
I am not saying that is not true. But this is not the course I would point that ?some? to. This course is not designed for the student that found their calling, even if they just found their calling. Can this course help a late student find their calling? Maybe, but I would design it quite differently. Similar topics but very different treatment. This course lacks a crucial element. It doesn?t prove to the student that they are really good at this, and that is what a calling is.
> That doesn't mean it's wrong to ill advised to steer them to courses like Devlin?s.
My point was that Devlin?s course wasn?t actually a ?course?. The topics are good for the stated purpose, but the treatment is off. You?d have to read the textbook I guess. And I?ll wait for the course in February to make a final judgement.
> Making sharp distinctions between pure and applied mathematics is not essential.
Making sharp distinctions is always essential. And this one isn?t complicated. I like pure math, but my colleagues and I didn?t find our calling in solving everyday technical problems from pure math. I am talking about engineers, software engineers, financial analysts, the list goes on. That is why they call it ?applied? math. Can you also study pure math? Yes, but it obviously isn?t a requirement for everyday problem solving because the vast majority of people solving everyday problems don?t have a lick of pure math in them. To say it is a different path is an understatement. When Lou makes comments about engineers not knowing ?math? my first thought is ?Who doesn?t know that?"
> Textbooks are very often formulaic, having you find roots of this and that polynomial, slopes of this and that line. What may not fall out of such formula-based learning is any confidence of being able to solve "generic problems" that life my pose.
That depends on the textbook. Unfortunately, the textbooks of today are so remedial in design that they never get to the enjoyable part of applying all these new skills and insights to a compendium of problems like our textbooks did. They are so focused on the majority of students that are not good at math that they never get to the pace that occurs with students who are good at math. Because of the algebra mandate, the purpose of math education in secondary school has changed from choosing math as one of your life's pursuits to just learning some math. And this has had a large impact on qualified students finding their muse. It was easy in our day, you could be good at math, like you could be good at music, you could be good at sports. Now you can only be good at music or sports, but not math.
> At some point in a student's career we let them know about "numerical recipes" and the fact that whole books of them are out there for consultation.
Let?s not paint a rosy picture where there isn?t one. Numerical recipes is not a best seller. And schools are not turning out as many math artists as they once were that could appreciate ?Numerical Recipes? or even understand it.
> Those who use mathematical techniques to grapple with problems are less in need of great memorization skills than great research skills.
The evidence I see is that you can?t have one without the other. There is no shortcut to being smart and good at what you do. You need the reasoning and you need the memorization. I have never seen someone make it with "research skills". Those candidates stand out right away.
> Where are the cookbooks? How do you match a problem to an algorithm? Those are skills too, beyond proving.
Now you are agreeing with me on the difference between applied and pure math. But there are plenty of cookbooks out there, in everything. And I use them all the time, but you have to be smart to know where to look and how to apply them. Again, there is no shortcut to being smart and good at what you do. The lack of google was never a barrier to being smart and good at what you do before the internet, so how can it be an enabler of the same? It isn?t.
> Finding the theorem and realizing it's relevance, locating the right recipe in the library, is all part of what one needs. Good road maps. Overviews. Most K-12 textbook math is fairly bereft of such concept maps.
No. If this were true then over the years I would have seen a steady surge in qualified candidates for the technical positions we post for. I have seen a study surge in the breadth of expertise in the qualified candidates but no surge at all in the number of qualified candidates. A sharp decline in fact.
Think about what you are saying.
Has not the internet made research incredibly more easy than our day? Certainly you remember the before time. Before the internet.
If road maps and research had anything to do with conquering these technical fields, wouldn?t we have seen a surge rather than a decline?
Being smart and good at what you do is the key. That is what needs to be nurtured. Not excuses.