Why teach calculus?: Daniel Ashlock at TEDxGuelphU
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- Опубликовано: 9 июн 2024
- Professor Daniel Ashlock has a doctorate in pure mathematics from Caltech. He has been a math professor for 23 years and taught twelve different types first year math courses at four institutions for majors in math, hard sciences, general education, biology, and business. He has developed five different first year courses. He currently holds a chair in bioinformatics with the Department of Mathematics and Statistics where he is a Full Professor of Mathematics. He has prizes for teaching at the undergraduate and graduate level as well as for research. He has over 200 peer-reviewed scientific publications in mathematics, computer science, theoretical biology, computational intelligence, artificial intelligence, game theory, and automatic content generation for games. He is a senior member of the IEEE and serves as an associate editor for the IEEE Transactions on Evolutionary Computation, the IEEE/ACM Transactions on Computational Biology and Bioinformatics, the IEEE Transactions on Computational Intelligence and Artificial Intelligence in Games, and Biosystems.
This video was recorded at TEDxGuelphU - Inside Out in November 2013. TEDxGuelphU is a student-organized TEDx event held annually at the University of Guelph in Guelph, Ontario. Each year we highlight emerging ideas, movements and talent from the University and surrounding community. For more information visit our website at www.tedxguelphu.com.
In the spirit of ideas worth spreading, TEDx is a program of local, self-organized events that bring people together to share a TED-like experience. At a TEDx event, TEDTalks video and live speakers combine to spark deep discussion and connection in a small group. These local, self-organized events are branded TEDx, where x = independently organized TED event. The TED Conference provides general guidance for the TEDx program, but individual TEDx events are self-organized.* (*Subject to certain rules and regulations)
At the University of Guelph, he was my Set Theory Prof. in my 2nd year and Abstract Algebra Prof. in my 3rd year. He has an amazing personality, super intelligent and fun to be around. His method of exams were the seek-your-own-level test which I liked a lot.
I love Calculus! I never took it in high school or college . I'm teaching myself using a variety of types of resources. along the way I've been re-exposed to trig algebra and geometry and I'm doing it only for the sheer joy of doing it. I get to do it at my own pace and without competition. I highly recommend that you do it too....the intellectual rewards are infinite ☺
I've 'stumbled' onto it too, late in the game. Could you please link some of the resources that have helped you?
patrickjmt on youtube is a good one.
Pauls online notes is very good
17calculus
professor leonard
3blue1brown youtube channel. Explains linear algebra like noone before. And Physics Videos by Eugene Khutoryansky which covers also math topics.
lol bullshit
Had this guy at Guelph and he’s absolutely amazing. He’s one of the few profs I’ve had that emphasizes critical thinking and teaches the foundation you need to be able to truly make a connection to the topics at hand. This was a great presentation.
From the K-12 perspective, what I see is that math is not taught for understanding. Students memorize algorithms. They don't know why. They are taught certain keywords to look for to determine which algorithm to use. But, they're never asked to understand what is going on. So, they're helpless when asked to apply the math in my science courses, so I end up reteaching what should be fairly basic math.
I recall this from my own career. I wanted to be a math teacher, but just couldn't comprehend. No surprise, when I switched to Physics, I was then able to understand the math. Why? It wasn't a meaningless algorithm. It had context and application.
I feel like I'm a "victim" of this pedagogy BUT 2nd language learners like myself seem to respond and have SOME (or limited) success.
@@michaelvillanueva233 Im a second language math learner as well. For some reason i learn math better in english than in my own language. Quite bizarre
I love what he said about text books. He's a real fucking teacher. From one to another keep up the great work. Makes me proud
Excellent presentation. I assumed that mathematics stopped at calculus. Now, I know a world of infinite possibilities are out there.
I really love limits, specifically convergent limits. it's as if you're containing infinity in a box.
his shirt... is calculus... but in all serious, I LOVE these topics! and math!! and LIFE!! :D
Definitely one of my favourite talks!
I love Maths! Wish I had him as my teacher!! Fantastic insights.
Thanks for sharing,
Liked :)
I studied engineering and I've seen through the years that even when everybody support math and know the importance of math, the truth I've seen is that not everyone seem to have the brains to do math beyond basic calculations or is good in logic. But everyone agrees on blaming the teacher.
Good observation. I also felt similar while talking to classmates.
Excellent ideas. The level of the course determines difficulty, not the math subject. We should teach more math and integrate math in other subject areas. Use Jupyter notebooks as a teaching resource.
He is excellent
This title was misleading. I love calculus and thought that he would tell the audience why it is so interesting. Instead he discourages it.
I don't know what all the fuss with Calculus is about... We went straight to real analysis in my first semester...
Unfortunately, these changes cannot be made without math teachers who have a degree in mathematics. For some reason, "educators" in this country think it wise to have math taught by those who have only a passing understanding. Better education requires better teachers. Better teachers requires schools with actual standards. Actual standards can only be imposed by administrators who have a clue. Good luck finding those. For all these reasons and more, homeschooling for elite students is a must.
First of all this is the internet, so when you reference "this country" you demonstrate how provincial and self-centered your thinking is. And NO, there isn't an "educator" in any country that thinks math should be taught by people with only passing understanding. Schools struggle to find qualified math teachers for two main reasons: One is that people who have a strong knowledge of math are qualified to do much higher paying, and often less stressful jobs. The second is that some countries, such as the US (the country I assume you're referring to), have sectors of the culture that treat teachers with low respect and low prestige. Your comments serve as an example of this.
This is not the internet. This is the You Tube comment section for a talk about how math is taught in the USA. Perhaps you should watch the video before making such a comment. Also, notice, I did not dismiss the possibility there exist good teachers. Indeed there are some. However, the posture of government schools in the USA is not to reward excellence. Nor to allow academic freedom. No the "educators" force a one size fits all mentality where so often we find our curriculum is entirely geared towards proficiency in SOL tests, or in calculus the AP exams. I don't see this as a problem of society, it seems to me this is a problem created by the business of professional educators. Less the teachers, more the administrators. Simply put, if we had the right administration in schools then some teachers would lose their jobs. This rarely happens because we do not have standards. Standard number one: to teach math you must know math. If we don't even require an undergraduate degree in Math for highschool math teachers then it is very hard to implement creative redesign of curriculum. That is what this video was about, at least that what is what I remember from when I first watched some of it and then made my comment.
Sorry for the ad hominen attack, it is fair you limit the discussion to the US, although to my knowledge Calculus is introduced in the same sequence in all english speaking countries and the speakers critiques apply to all of them. Also, I agree with you that there is too much focus on testing and too little ability to fire bad teachers. Another thing about teaching is that all teachers are paid based on experience, but never on skillset. In other words, a math teacher is paid exactly the same as teachers of every other subject. I understand the sentiment behind this, but in every other sector skills are paid by market value. And the market value for a math major in finance and technology is astronomically higher than in education. So every school wants math majors, but many don't get the option. I don't agree that every math class in high school needs to be taught by a math major. Any science major should have a solid enough background to teach most high-school level maths. Even business and social science majors who can demonstrate subject knowledge are qualified to teacher lower level classes. I'm am not saying this based on some abstract philosophy, but from my personal experience as a math teacher with a math major who has worked with non-math major math teachers whom I believe deserve equal respect for their efforts to help students succeed.
I tend to agree it is possible a science major could teach math, but, I would limit that to fields which meaningfully require arithmetic in major course work. I'd still prefer math majors because philosophically they are more likely to teach math without short-cutting foundations. Now, I will say this, I will gladly take a science major over an education major. Your right about pay, but, I'd guess the issue is really more about academic freedom and respect. Neither of these are widely available because the system of public schools, thanks to the government and teachers unions, is geared to keep unqualified people employed and to put nice furniture in central offices. I'm glad you found some non-math majors who can teach elementary school math proficiently. I've taught a few thousand non-math majors calculus, linear algebra, etc. The percentage who can communicate mathematics meaningfully is very small. Yes, 20% can solve problems reliably, but, how many can really explain what they are doing. If they can't explain the nuts and bolts then in my book they shouldn't teach it.
I don't mean to attack your friends, but, if we are to raise standards there will be people offended. Credentials are only statistically useful, there are always exceptions both positive and negative. Anyway, fear not, no one listens to me.
Indeed. Far to many people miss out on the hidden beauty of maths. If you are aware of this and have mathematical (and the other core subjects by and large) skills greater than those offered by publicly funded teachers who's curriculum is virtually non adaptive, what justification is there to let them teach your child.
Thank you!!! How is your collaboration?
They should introduce the concepts of calc in 8th grade.
In a way, they do: as slope and area.
Did anybody NOTICE, in the two pictures that he showed in the end , one of which has "AUM" symbol in it . For those who don't know what is "AUM" , it is a holly symbol used in Hinduism.
I’ve taken three calculus course and Linear algebra. The latter is way harder for me
penny Zhang which one is the most difficult
I went through the same I think.
Calculus can be easily taught to high schoolers especially if you point out how it is applied to real world problems. This is no different than teaching algebra and showing how it is applicable to real world problems that matter to the individual. If you provide the context and applicability of the subject matter then that knowledge become immediately relevant to the individual who has always wondered about that topic.
One more thing. Math is awesome because you can always verify your answer by working the problem back to the given criteria. If you aren't taught this early on THEN you'll never know if you're right and you'll never have the confidence to challenge teachers to prove you wrong!
All subject matter can be made into a game. It's okay to make mistakes as long as you learn from them and you do them when you're practicing. Thats the whole point of homework! So that you're prepared when it comes time to demonstrate your knowlege and competency on a test. Being allowed to make mistakes is THE BIGGEST ADVANTAGE that the U.S. culture has on the rest of the world but that should not take away from getting the right answer when it matters.
Common core? Fucking burn that shyt already and toss the promoters and authors out on their arses too
Last rant. Parents YOU need to get yourselves educated so that YOU can supplement your kids knowledge with meaningful content. If your kids fail it is YOUR responsibility. Not the school! So if you don't know then fucking find out or don't have kids! And be vigilant regarding the HW and quality of that HW that is given to your kids. And be ready to challenge the teacher. Teachers hated me, especially math teachers, because I always challenged them and proved many of their answers were wrong(they didn't know cause they just pointed to the answer in the teachers booklet. Ugh. The blind leading the blind). But my kids became nuclear and mechanical engineers with slants to business because they didn't struggle with math thanks to my obsessive supervision and making math fun for them from the get go. It mattered to me just like the kings english and being able to write ideas coherently mattered to my wife.
Please support School choice for the benefit of our kids and making the best use of the involuntary property taxes levied on homeowners.
In India we learn Calculus in schools. In Russia in some of the best schools they also teach calculus.
Easily? Not true. Nothing easy about it
In Economics, we need Calculus. Without it most of the theories cannot be proved. However, in quantitative economics, we do not need it, we need linear and non-linear algebra..
This guy is a boss.
Indeed, a very insightful and inspiring professor. BAUD_RATE!
This is awesome video.. But i don't know why it didn't get So many views...
5:10 I could not have said it better.
Wonderful presentation, except that there is a mistake in the procedures at the beginning.
I took calculus in college and for me at least it was not bad. The concept of limits is fairly straightforward and not a difficult concept. I will however agree on many of his points, for example, the textbook rip off I have always said textbooks are sold by the mafia!! You have no choice on which one to buy and they change them every couple of years....math does not change....of course I love math, lol. SO I guess I am the weird one in the group.
Re; The purchasing of textbooks - e.g. new 'Calculus' Books' - The subject matter doesn't change - I couldn't agree w/ you more. Same goes w/ the Physics texts....
The universities are making a 'killing' on these books - Best advice - get your text (used) or study via 'online' classes - They're many! Last resort - go to your local library ~
you need to have really wonderful teachers for students to appreciate maths, maths is the queen of sciences but the treatment it gets is so bad.
i've studied all types of math in high school and in college , and i passed all exams with high grades , i still don't know what calculus is and what its used for(yeah sure other scientists use it and its great bla bla bla) or any other thing in math except the +=-x/ , thats all the math i need
The limit does not exist!
qt3.141516 at 8:43
If only people would think that maths and other really useful topics were as important as other really meaningly stuff such as what celebrities are currently doing. Not to mention how much more control people would have in their lives. Universities I've discovered are not really interested in number, unless it benefits them in a massive way. You would think that they are, and would listen to you because you had an idea, but they're full of bureaucrats whom are paid to administer, not so much improve.
What is the big problem with calculus? It is actually far easier than linear algebra or graph theory. I disagree with the speaker. Also, fractal pictures are nice but frankly pretty useless. Calculus and differential eqs. are the mathematics of the physical world, something people are forgetting as they disappear into their computer screens and get more and more obese as they look at nice fractal pictures. TEACH CALCULUS.
Fractal pictures can be used to test a certain GPU or CPU performance
@Tournel Henry I think you may have a misunderstanding of what linear algebra is.
On standardised test defence I will say sometimes we need to be drilled before we get to understand the drill. We learn to talk and walk before we understand physiology. A great teacher knows how to set tests that will prompt understanding instead of mere cramming. I have always advocated teaching history mathematics and including it in test. Math esp calculus is best appreciated from history perspective. About alternatives to math, I partly agree, math is one one the computational language but it shouold not be scrapped off as it is ubiquious esp in engineering. algorithmic treatment only does calculus on a computer but it is still calculus. Difference equations is just discrete calculus. It is a bit sad the professor attacks calculus yet he wrote a book on calculus. I find it odd that he thinks one can replace calculus with graph theory or linear algebra. True calculus is linear algebra but it takes advanced math(differential forms) to see that connection.
@Dirk Knight On another note, I share your views about not pushing math to all high school students, though I do feel that advanced math topics can be taught well with other methods, eg computer based math. The professor above(he most likely knows what he talking about) is trying to put a message that math can be talk in different languages. And this, I share his views. Calculus as is taught now is old way of teaching. Infact newton used the same method. I bet if he was around, he will laugh at us that we still teach the same method that he used when he didn;t have tools that we now have. Math is really essential in all sciences(even social sciences). What the professor is resisting is emphasizes on calculus(traditional) at the same time math phobia caused by it. He raather suggest other alternatives. My vivent believe is that advanced math can be taught to every child provided we change our methods of teaching and adopting computer based mathematics and emphasizing mathematical model building. You do not need to teach a child how a computer works before you teach them programming. Similar analysis is not essential before one can learn to use the derivative to build a model of a bouncing ball. Only when you want to know how the derivative works do we now turn to analysis just like we do in programming. In mathematiccal modeling we really have to hide mathematics and see only models.
My child study calculus when he is less 6 years old. some like slope,dy/dx,x^n' = nx^n-1. He feel it is easier than +-*/. Children study from newton's calculus and force is more efficient for understanding world.
Well there goes the 'Theory of everything'...
What is calculus
What? It looks to me like you were saying that you don't need it. Other than that, this was pretty good. One more comment: Just because standardized tests are faulty, doesn't mean they shouldn't be standardized. Maybe you just need a better test to standardize. And manage them better. What good is it if you get an "A" or an "F" and don't know what that means? You might as well get no grade at all.
It makes sense that an agency famous for budget screw-ups would deprive the math program first. Irony quantified. lol
I really wish that I understood calculus when I was in high school
@Dirk Knight When I was in high school, teachers didnt teach calculus. And then when I was colege, I get stuck because if calculus. I took EE degree.
@Dirk Knight but I am proud of my self now because I am really good at calculus now. I love calculus.
@Dirk Knight they didnt teach calculus in some of the high schools in here. Not all of the high schools.
@Dirk Knight oh. Where are you from? I'm from Indonesia.
@Dirk Knight I think third world country will catch up because this globalization era.
The problem with most maths teaching is that it is pointless. It has no objective.
If the course material seems purposeless, then nobody remembers it. With calculus, the objective could be to determine how much fuel a rocket requires to reach orbit, for example. Once you have a real world objective, people get interested and pay attention.
You are correct - It's called 'Optimization' and very few universities cover that topic (in depth) within a 1st or 2nd Calculus course - Same goes for O.D.E. They teach 'methods' but not a comprehension toward the real world. I agree w/ your post immensely ~
The problem with teaching the concepts using real-world objectives is that you loose the emphasis on how to derive your answer with formal logic and proofs.
Did he answer the question he started with? Why teach calculus?
Calculus is the mathematics of continuous change.
This is necessary for physics. Now, why teach physics? Well, our modern society depends on physics.
No physics -- no technology -- no modern society.
Right.....🙂
The thing is, Mathematicians don't want everybody to understand maths. If they did, it would be so.
12:25 is so poignant. I’ve constantly seen schools parcel teaching something across such a long period of time that you don’t even remember how to begin the problem by the end of the semester. And my entire college education was a pay to win Ponzi-scheme with McGraw-Hill as its thought leader.
Your one is the type you'd set a pack o' bullies on to drop him upside down in a waste bin with rumpled, calculus syllabi to fill in what air-spaces dare [sans bubble wrap] to ensure he's conscious for the duration, and give our scalar scholar newfound direction -- namely -- tumbling down the choicest "slope" of grassy negativity ye can find on the Cartesian College plane.
Can calculus solve why some people's can't do math.
Are you a backwards caveman? sheezze. Calculus is what everyone NEEDS now!
For me, calculus is way easier than liner algebra to understand, even if it is easier to do the home work in liner algebra. That being said, calculus is the key to real abstract-realistic thinking, and yes, it is hard, but it is important in my opnion for understanding math. If one so not develop an absract thinking he may do math, but i dout he can realy understand what he does. Sory for the spelling, english isn't my first language..
@Dirk Knight im not sure everyone can undrstend the fundemental theorem of calculus or the limit def. Try to ask a random student when execly a limit does not exist.. the idea of calculus is the limit def and all what comes from it, not deriving basic functions by knowing the formula.
Calculus becomes easy for those who practice it regularly. Its also quite interesting. So once students start practicing they get absorbed in it. But sometimes, even the best students dont know how to apply calculus or where to apply it.
I thank the Professor for enriching us with application part of calculus.
Welp..I think that was a great presentation, but I'm not sure
The ideas are good but insofar as changing the public school system the problem is the lament I just can't shake that I came up with when looking at the idea of sending humans to Mars from an ethically conscious angle: All too often, those who have the power, lack the wisdom; and those who have the wisdom, lack the power. The ones with the most power to change the system do not have the ideas and the vision that people like this guy have, and people like this guy tend not to have that political power to exert control. Or that people like Robert Walker, who understand the ethical problems with Mars missions and have good ideas for how we could do them better, do not have the power of people like Elon Musk, who mirroringly lacks quite so much sensitivity. Or that people like John Lombard, who has a very wise approach to how to deal with "development" (as in development of countries) and "helping" "poor" and minorities, lack the eminence of many international NGOs, who are stuck in the folly of the "white messiah"/"white paternalist" complex that disempowers and removes agency, and thus pride, from those they seek to help.
you don't make any sense. you are like "him".
not albert einstein
At university, I got an A in Calc 1, and a C in Calc 2, 3, Numerical Analysis (based on Calc 2), and a B in Real Analysis (which has some Calc 1 stuff among other things). I'm an Algebraist. Calculus is NOT my thing. Also, he called diff eq the "final math". that was the last course that I attempted to take (after graduating) and thus dropped. That professor was NOT a nice person and made fun of his students. I complained to the university.
Shepherd's Chapel Network !!!!!!! Pastor Murray is an Anointed Servant of GOD who teaches the Word of GOD with Authority!!!!!!!
Bro, take a health test. That fupa is off the chain.
Fast talking huckster.
OK he apparently realizes the apparent contradictions underlying calculus as taught,
meaning the 0/0 bit. He should be congratulated for that.
BUT he provided no answer "lest our brains get splattered on the ceiling". Then he started to show off by rapidly enumerating all the other kinds of math but explaining none.
He vaguely mentioned tangents touching a curve at one point ( a serious error actually) and "multiple infinities" and then stopped talking about calculus labeling it as "too hard".
That's a shame since he did identify the problem (along with Bishop Berkley over 200 years ago).
I venture to say he himself has not resolved the problem. In fact I am certain of it since calculus does not ask us to solve 0/0 since tangents do not touch a curve at just one point (both statements he did make). Calculus fortunately is not that cruel.
So what is the answer? Is there one? Yes there is. But first it means defining the tangent correctly with a non zero run. Next the concept of adjacent points which are dx apart and non adjacent points which are Dx apart. Then the concept of isolating the secant quotient's averaging error. All these ideas are then tied together. No more nonsense about 0/0. That is VERBOTEN (not fit in polite company).
Speaker should bear in mind that calculus was a truly new discipline and not just an extension of algebra and geometry and one cannot create a truly new discipline without breaking old crockery. Sir you will have to break some serious crockery.
Calculus is not hard and you get a lot of slgebraic practice. You should take calcilus and statistics. You keep lowering the standards, the Chinese are taking over anyways
Rubbish presentation. Managed to lose me in the first 30 seconds by diving in the Deep end with no intro or prep. Poor.
The introduction _was_ that quick lesson on calculus. There is a lot to cover in mathematics, so diving right into the lesson is par for the course in many presentations/lectures.
@@hankmann2508 This is a TEDx presentation. It is not a higher mathematics course. It needs to confine its content to a general audience.
This guy is just trying to show off
I still hate all mathematics, and think it should be taught only to people who will use it. There's no logic to math at all.
It’s only logic. There’s very little memorization. It’s really easy to retain the things you learn because there’s always a logical base to it. Every single concept in math has been proven to be true in 100% of cases. You’ve just never had any classes/exposure to mathematical logic, proofs, set theory, number theory, etc... That’s exacty the issue he adresses in the presentation; we start teaching kids very abstract concepts which they can’t possibly grasp without having a better foundation.
"There's no logic to math..." This is a complete misconception as math is logic. It's also highly correlated with intelligence as it deals with abstraction. Most people can't deal with abstraction which is fine, but don't consider yourself intelligent if you can't.