Arthur Benjamin: Teach statistics before calculus!
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- Опубликовано: 30 июл 2024
- www.ted.com Someone always asks the math teacher, "Am I going to use calculus in real life?" And for most of us, says Arthur Benjamin, the answer is no. He offers a bold proposal on how to make math education relevant in the digital age.
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Ad a math teacher, I couldn't agree more. I don't know how people get along without at least a basic understanding of probability. I find that my students love when we discuss the possible outcomes of an event. We spent nearly an entire period discussing how to calculate the odds of winning the lottery and the lesson was supposed to be American history. The best part about that lesson is hearing them wonder aloud why anyone plays the lottery given the odds against it.
On high school level, statistics is most useful mathematics for daily life. But for the students who are going to study physics and engineering, calculus is the must mathematics to be mastered.
Mori: I would disagree, if we include computer science under the heading of "engineering". I think probability and stats are usually more useful in CS than calculus is.
Arthur Benjamin is a combinatorialist himself, so this is not his personal preference, this is his objective opinion on how to get more people engaged with the subject. Good for him.
Love the passion in him
I agree mostly, but speaking from my experience, when I took stats in college it did help to have an understanding of calculus. Probability curves and standard deviations take on new meaning if you understand the calculus used in determining them. Perhaps a solution would be a study of both. Simple comprehension of limits, derivatives and integration coupled with probability, distribution curves, margin of error, etc. I realize the reason we don't really comes down to the immensity of both topics. Calculus took me six months to understand and stats 3 months. I feel both are great to understand, but you will never use everything you learned in either class.
Been teaching for 10 years. Still waiting for this switch to happen. :D
Here here. Seriously, a good point.
This is so true, i've never used calculus but i come across situations almost every day where statistics would be very useful.
You can teach some of the basic concepts of probability and statistics, without Calculus. But ultimately the more advanced ideas and theorems of Probability and Statistics require a knowledge of Calculus. If you just want to show students how to properly use various statistical formulas, and not worry about proving theorems, you need not bother them with rigorous Calculus.
Thank you! Someone had to say it
I think this is right. I have been thinking about this before seeing this. As long as you teach baby prob & stats. You don't see that much calculus in college classes like this. Marginality uses some integration and expectation and variance related topics use derivatives in certain topics. However, those are techniques that anybody can learn and be adjusted to elemantry problems. In my personal experience students should learn it along with the other classes. Maybe, once a week algebra 2 is baby stats, that would enrich much of their skills by building logical skills being that what they need. For instance, for nonlinear equations in stats you still gotta find a y intercept and solve for this one to find it, this implies undrrstanding the slope and averages of x and and y in nonlinrar functions given some data.
Love it! Please share with the math professors who educate math teachers! Good going.
I'm just going to go ahead and master both.
that is great man. I also love Arthur benjamin, so enthusiastic!
Yeah. When I took calculus, I also took physics with an emphasis on employing the maths for real world experiments, observations & measurement. It was fascinating to learn that way. That was the key to my becoming an engineer in a career that I've loved for decades. It's powerful to be able to predict the behavior of an imagined device that can become real & practical. Now, America has too few science-knowledgeable teachers; that's the problem.
thankfully im a music major studying soundwaves, digital processing and consumer trends so we use means and averages allot. electronic and acoustic music courses work with this math to shape waveforms in my class. i totally agree with this guy.
In the curriculum here in Alberta (curriculum is decided by the province) we get a bit of combinatorics and statistics at the gr. 12 level, though calculus is also an optional subject.
In response to saying that calculus isn't used, I think about rates of change all the time. I think of the interrelations between one object's flow or movement and another object flow or movement.
yay I love this guy. I had his TTC series on my comp XD
I agree with freesk8 because of the following observation:
It's 5 years since I was last in any form of institution with their own curriculum, not only consisting of things I find interesting.
But now I've noticed difficulties I didn't have before, and it's age related at 27. It's because school teaches us to take in new information and keep our minds in shape.
If you don't practice your mind and step up your game towards calculus, you'll eventually find yourself unprepared for challenges.
Makes sense.
I was thinking bout this the other day actually. I have pretty much forgotten everything i learnt in my maths class in high school cuz i don't use it and need it anymore. I was in the top 10% of my maths class but now i barely remember anything from calculus cuz in medschool you don't need it.
But next year i have to study statistics and probability in med school, which it would have had helped me a lot if my maths class would have thought me more of statistics than calculus!
What Arthur Benjamin doesn't realize is that if kids can do calculus, they can also do risk analysis and anything else. Probability comes easy to a calculus student, in fact the prerequisite for the probability course I took in college was Calculus III.
there's definitely some truth in this, but there's also a hidden danger in teaching stat without calculus, since calculus (then higher maths) lies in the core of both statistics and probability theory. so without teaching calculus, one runs into the danger of turning a stat class into a calculator exercise like the AP class i took in high school. i agree wholeheartly in his claim that statistics is a subject closer to our daily lives than calculus, but teaching statistics without calculus requires a teacher with extraordinary understanding of the material and communication skills in order to sidestep the calculus-based core theory while keeping the material interesting.
You have a very old fashioned view of statistics, if you think it has any base in calculus.
Modern statistics does not need the pure theory of the past. We no longer need to assume ridiculous things, like that a distribution is Normal, when it clearly is not, because our techniques only go that far. We have bootstrapping and jack-knifing, and similar methods -- what the talk calls "discrete" -- that have moved on from assuming perfect distributions.
Likewise, we have Monte Carlo methods in probability, that remove the need to "solve" everything as if it is an algebra problem.
It is simple to teach practical statistics early. Theoretical statistics is, like high level calculus, a branch of mathematics that few actually need to enter far into.
Mark Plant bootstrap etc are sampling methods used for computational simulations like monte carlo. these are all glorified calculations. sure, in practice no one can assume closed form distributions, and most methods these days do not do so. but the "why these methods work" is rooted in theory, and without calculus you can only go so far. therefore, as i said, if the goal is to teach students "how" to do statistics, then yeah, you probably don't need calculus, but if you want them to know "why", calculus is indispensable.
95% of people never need to know "why". A society is better off with people who understand a moderate level of statistics, without theoretical underpinning, than with people who spent so long on the theory that they lost interest. Hence you teach Statistics first, and only *later* back it up with Calculus for those who either need it or are interested. Which is the original premise of the talk after all.
As it happens, I'm a calculus teacher, and I love calculus. But I recognise that calculus is not a skill that most people need, whereas statistical understanding is a skill most people could benefit with.
Mark Plant learning the theory of anything is better because you never need to remember how. You just derive your own "how"
This should definitely have more views, this is great!
what? i want a ten minute video of this!!! this is a great idea!
You can have use for both calculus and statistics in everyday life and in dealing with practical scenarios. The key is to have the analytical capacity to go with the knowledge so you know how to phrase the problems you encounter in a way you can apply math to them.
I'd agree with him that basic statistics should take priority over calculus at highschool level, and that basic algebra is enough for "most people".
I am a structural and material engineer for building envelope design. The glass/aluminum/precast high rises you see in cities has a team of designers and regulators that design the skins of the buildings that we work and play in. Structural engineering relies heavily on beam/column theory which utilizes differential equations (calculus). Materials such as Glass are non-ductile and are limited by statistical studies of breakage based on sizes and design pressures (statistics). Etc...
here in australia you learn all of that stuff in a class which was called "applicable mathematics" when i did it.
It was actually the math level below calculus, but was compulsory if you also did calculus.
Statistics exists in reality more than Calculus. Statistics has become a part of our lives. Even though I struggle when learning Statistics, it still has a big impact on me more than Calculus.
Yes!!! I really wish I'd had a formal education in statistics.
i think math and the creativity involved is a highly personalized discipline. the problem with conventional education is that students are prevented from exploring and instead are all averaged, with anything unusual taking place considered a reason for disciplinary action.
@mitochondrie126 definitely the probability and statistics. Direct usage is tremendous. I myslef enjoy it.
Calculus is that part of mathematics where you take functions (f(x)) and you either differentiate them to look at the slope (rate of change) or perform the opposite operation which is integration (and calculates the area under the curve).
For example, if you get a GPS signal with the position f(t) of a car at each instant t, you can then calculate it's speed df/dt at each moment by differentiating once, and it's acceleration by differentiating twice.
That's ok but you couldn've said something about limits e.g. the area under a curve is basicly limits. Instentanious rates of change. See in Australia the government do not teach calculus to highschoolers until year eleven and we took descriptive statistics in year eight. One of my uni prefessors told me that the american system of education has lots and lots of differences to the australian ecducation system. By the way i'm not sure your working is correct when you say differenciate twice. I'm sorry no disrespect but i'm preparing to study maths at uni full time next year so we have to look at the proofs of these things very closely. Good luck hey
@@Neemsy30 true, but if you're using the first principles definition of derivatives as limits I would say you're doing real analysis rather than calculus. Similarly, if you're going back to the first principles definition to calculate integrals I would say you're doing measure theory rather than calculus.
good thing i took ap calculus AND ap statistics this past senior year :]
In my university before i could even touch statistics i needed to know: analysis (which is advanced calculus), measure theory (which is advanced analysis), then probablity hteory ( which builds upon measure theory) and only THEN statistics.. :))))))
@ubermajestix Actually, I wasn't talking about the speaker in the TED talk, I was talking about 444DeanMachine. This would have been obvious if RUclips was still laid out the way it used to be. Now that replies aren't indented and the comment with the most thumbs up is put at the top, comments like the one I posted are doomed to be misinterpreted.
Fantastic sir
Stats is is good tools
to know and use in about
any circumstance.
How to interpret data=
good skill to have.
In today's era of Big Data, Data Analytics etc. as far as getting a Job is concerned Statistics, Probability have more applicability compared to Calculus.
prisoneroftech absolutely not
i think the problem is that there are not enough inspiring maths teachers like Arthur!
Where did you get "more challenging" from?
This guy is so cool! He's really inspiring and I'm taking more math classes in school because of his talks and books.
The other way around, you cansimply know what the forces acting on a certain object are (e.g. sun's gravity acting on a comet), then use Newton's law to convert that into acceleration (F=m*a). You can then integrate twice (or solve a differential equation) to find the position. Hence, for example, you can predict the trajectory of the comet and decide whether or not to send Bruce Willis off to destroy it.
@xXisabella23Xx That's awesome! Hope you enjoy his class. :)
Totally agree. Just an understanding of calculus, even if one forgets the various rules after a time, gives a good understanding of change over time. And probability/statistics is just as essential for the reasons he gave.
It's 2009, and we are only using science and technology more and more as time goes on. Reducing curricula is ridiculous, and the US is already falling behind enough as it is.
While calculus is my absolute favorite branch of mathematics, Benjamin is dead right on this. I got my B.A. in mathematics without taking a single statistics course; this was a mistake. Later I realized I need statistics and took a course at a community college.
great..
There is a finite amount of time available in schools to teach stuff.
If you just keep adding more material to the curriculum teachers will have to spend less time on each subject, and hence students will end up being less proficient in the rest of the curriculum.
It makes sense that to increase emphasis on statistics one first needs to free some time elsewhere. Teaching less calculus makes sense.
If you can suggest other areas of the curriculum to prune, be my guest.
He is not saying Algebra would be replaced. He says everything AFTER algebra is preparation for Calculus. Algebra is still a fundamental precursor to Statistics.
It was a great impressive three minutes ever.
It does indeed refer to "speakers and learners," though I was deliberately referencing that statistic's wording in another TEDtalk, "Jay Walker on the world's English mania." I agree I should have been more exact, but unfortunately the character limit prevented that in my previous comment. Thank you for clearing up any possible misunderstanding, though it doesn't affect my basic point. (And fact-checking, not statistics per se, is what you should be advocating here.)
Gotta love studying for a bachelor, come major in statistics and probability!
Hear hear!
Love.
yes, it does. arthur mentions a change from continuous to discrete math. the entire wing of discrete random variables in probability and statistics can be studied without any calculus whatsoever. as far as continuous random variables go, the normal and t distributions require computers to calculate the areas swept out, since they dont have antiderivitives, so we dont basically let the computers do the calculus whenever we use them.
@prospectnyc I know you're comment was posted long ago, but I just wanted to say that he's my math teacher! :)
The average student might not take calculus, but he's saying all/most preparation is for calculus-which is why so many students bow out as quickly as possible.
But if statistics was the high end goal, then algebra-the killer for most non-mathematical students would possibly be replaced with probability. Which provides far more useful and engaging real world examples than figuring out the distance between train a and b if a was traveling at
@saltonsea2 I am pretty sure this professor was referring to rudimentary statistics.
I think you meant "appalled", and if so I totally agree with you!
Also...
It's disgraceful the number of teachers in elementary schools who teach math with so little confidence, let alone excitement!
Students should never stop asking, "When will I ever need this?" and they deserve answers!
I know what two standard deviations from the mean means, its algebra 2.. the one before precalc...
Can anyone please helpl me because i'm told that so much of inferencial statistics comes from the rules and proofs of calculus so if you know more than me please give me a reply because all of this realy does interest me. Preparing to study maths full time at uni next year folks
so what does 2 standard deviations from the mean mean?
Take a stats class and you'll find out ;) [StatQuest videos on RUclips are also very good]
OMG I am genious!!!!
I figured this out myself months ago!!! I am not mathematician just amateur and little of scientest.
@Tzadeck this is a TED talk, which, until recently was an invite only conference for rich, smart or famous people, so they are not a "general audience" and the video was not made exclusively for youtube. And how does "kids should learn statistics in high school instead of calculus" not make sense? Data rules our world and understanding statistics means understanding data. I totally agree with Mr. Benjamin's point in the video.
Mmm... I totally agree with him. Statistics was the most useful thing I learned in math past grade 9, it affects our lives much more than calc. I began learning statistics after watching a TED talk about it... before that I only knew it as 'that class college kids hate taking'.
Forced to choose I would chose Statistics, but calculus is incredibly valuable and useful and it synergizes with statistics and is in fact foundational to the development of statistics.
Overall, we need to do a much better job of making math relevant to our students. Most problems given should be word problems and we need to do a better job of writing those word problems in relevant ways.
@ser132 ±2 standard deviations from the mean explains about 95 percent of the data.
Maybe it's the fact that my school sucked, but when I was taking math in high-school there seemed to be two very distinct types of students. 1) Those who thought AP Caculus was too easy and were taking university math classes their senior years and 2) Those who just barely pass geometry and never take another math class. To whoever answers (I'm curious that's all) what is the minimum math requirement for HS in your state, and does the majority of the student body find it easy or hard to achieve?
As a computer scientist and engineer, I have studied both and use statistics all the time in work and for personal use, but rarely use calc. As a matter of fact, I have not used calc in such a long time, I no longer can really do it. The only thing I think he is not addressing is that calc is used in high level statistics, so I'm not sure you can really just avoid calc completely.
How many complex calculations do you need compared to the number of randoms or statistics? Not many, they're so far away from most ppls lifes (exept for students of who most don't understand the topic anyway).
I don't think, however, that it is a choice between an interpretation and nothing, in exchange for the time we spend in History courses, we give up the opportunity to learn other thing. I think very little history is retained after the course ends, and memorizing dates is actively destructive.
I would need to see studies showing that PE positively affects health, I am very skeptical toward this claim.
I accept your point regarding modern history, this would be an improvement, you are correct.
Weird I was seriously just thinking the exact same thing yesterday
Yes, i think he is right.
Not in every province. In Ontario, calculus and vectors is at the top of this pyramid of math education with data and stats left largely as an optional course.
Calculus is simply more valuable to more subjects (science, engineering, commerce, economics). This is why it is and should be favoured over stats.
thats awesome
It's impossible to get any but the most shallow educations in probability/statistics without knowing basic calculus. Try explaining the Central Limit Theorem, arguably the most important result in statistics (basically, the explanation for why the normal distribution a.k.a. "bell curve" pops up everywhere), without reference to limits (which you learn in a high school calculus class): not possible.
You're right, i didn't know, (about Outliers) the black swan is a norm for me.
Ted does make a lot of sense. If you want to prove laws you need calculus and to prove theories you need statistics. In social sciences we only have have theories. any thing other than pure science has to rely on statistics for its emperical ratification (validity)
People who take applied stats and probability are baffled by the sheer amount of complexity that they only learn enough to pass the class. They never understand the fundamentals of the material that they are learning, they just learn how to apply it to the problem they are working on. They are hard pressed trying to relate what they have learned to the real world, how many freshman in a community college know how to use the binomial distribution related to life.
What does “two standard deviations from the mean” mean?
Reading a fundamental statistics book can ask your question. The concept of your question is very simple.
I would half-agree. I think there should be a balance of statistics and calculus. The meat and bones of calculus are important for statistics itself, but maybe the rest could be sidelined.
The other problem is that students are not told or given practical uses for calculus and these other branches of mathematics than students would be more interested and maybe a more hands on approach on applying calculus students would be interested in leaning mathematics.
This guy is on to something... Just go to Amazon and look at the list of the popular books on Statistics versus the popular books on Calculus. I personally love Calculus but was never able to use it in real life.
I think his point was for education of people in general. Of course for engineers and mathetmaticians we'll have to know calculus. But for other fields they are better off learning probability and risk. It's hardly a shortcut considering most Americans don't learn Calculus anyways.
Wow. In Freshman year? We learn calculus at school in Australia.
Especially true now!
He's right, in my country, where i used to live, math there like something that Im never gonna to use it in my life ... seriously.
But by the way, anything that we learn, is something that we will use somehow in our life. And u have a choice to learn Caculus or Statistics. Depend on your major later on.
Behzat Rasuli gönderdi beni❤
:)
I would rather learn about calculus... because I'm a physics/astronomy dork :)
I took AP calculus in highschool and I have yet to use it at all. In fact, I've forgotten most of it. I even had a dream last night that I screamed at my old calculus teacher saying, "WE ARE NEVER GOING TO USE THIS INFORMATION IN OUR LIVES!!!"
Totally agree, far more applicable :)
Alaska, more specifically Juneau (southeast). Up here you only have to take geometry and pass the high school qualifying exam sophmore(?) year and that's all you need for the math requirement. Without delving into anything political or racial, the standard CAN'T be any higher, and so no university in Alaska will deny a prospective student based on math ability. Hell, I got accepted to UAF and there was no math qualification...or required essay (needed the ACT scores and transcripts though).
I agree to a lot of comments here. Statistics should be learned with a full understanding of what it is and with all the depth it has. Hs statistics that is taught to most of students is easy, because none of the students would understand what it is, without a strong mathematical knowledge base.
Statistics does need to be emphasized. However in order to understand later topics at least Calculus II is needed. There would also need to be an earlier introduction to discrete mathematics in high school if not middle school. Majors like economics, psychology, education, and business should have better math requirements. Often they just need one calculus course and/or one statistics course. This is insufficient if you want to produce graduates with any kind of competency in statistics.
Everyone's entitled to their opinion. For me, though, I think he's got a very valid point. Well made, too
is there more then calculus and statistics?
@Tzadeck I kinda agree with you, but there is a positive site of it: if I dont know what Kantian logic is and it interests me, I'll Google it.
Epistemology is actually a word that sound complicated but the concept should be known by an average college or high school student. Peace.
History, PE, and many English courses.
But, aside from my disdain for these fluff courses, I think that restructuring the way we teach to better match the way we learn, would more than compensate for the strain of additional courses.
Calculus is one path, statistics is another. I use the fruits of calculus on a daily basis. I also studied statistics, and this is useful in another set of circumstances. One should not be taught over the other. It is like saying that literature should be the path of language arts and not technical writing.
Well i dont know about all high schools, but in my high school we have to learn about probability and statistics in Math B. But now they are changing Math B and i don't know if the curriculum will tech probability but the current method has implemented probability into a class that most students take. I wish they would just leave the curriculum alone.
I floundered in Calculus classes. The problem is that why I asked "When will I use this in the real world?" the teacher told me to shut up and stop being a smart ass.
I needed to know why the information was useful, because otherwise it was worthless.
RUclips, can someone tell me when a guy like me (just a normal guy who doesn't build or explode anything) will ever use calculus based mathematics in my daily life?
he makes a very good point...i think ill show this to my teacher
Education is not about utility.
It is about developing your ability to think for yourself.
Learning calculus builds your mental powers in ways that are totally unrelated to calculus.
It's like professional athletes lifting weights in the off-season. They do this in spite of the fact that they never lift weights during a game. But lifting weights makes them stronger. Same with calculus. It makes your brain more capable and that power is used in many different ways each day.
Well said Dr. Benjamin.