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This guy is one of my favorite TED speakers, and he makes a strong argument for exactly this: https://www.ted.com/talks/arthur_benjamin_s_formula_for_chan....

⬐ susiecambria

Thanks for sharing! (writes the girl who barely passed pre-calc)

Reminds me of Arthur Benjamin's talk on focussing on statistics instead of calculus.

http://www.ted.com/talks/arthur_benjamin_s_formula_for_chang...

It's easy to recognize that the author's arguments could apply just as well to any academic subject: literature, history, you name it. ("We should just teach 'citizen reading', where students learn to read recipes and furniture assembly instructions.")

But the real surprise to me is his ignorance of actual college math curricula. He says, "Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art". I don't know about his college, but the math requirement where I teach can be met with courses such as "Math in Art and Nature" or "Liberal Arts Mathematics". It's not as if his suggestions there are novel! But here's the kicker: for both of those classes, proficiency in algebra is a prerequisite. It turns out that you can't really describe those topics that he likes without actually using some math.

On the other hand, I have come around to agree that statistics is more broadly useful than calculus. Here's a TED talk by one of my old math professors making that case: http://www.ted.com/talks/arthur_benjamin_s_formula_for_chang...

⬐ daleroberts

I don't get that TED talk. For example, how are you meant to properly understand the ubiquitous Gaussian distribution without learning Calculus first?

⬐ NyxWulf

Even if people don't learn to "properly" understand the Gaussian distribution, basic understanding of the nature of variation and the difference between random events and something that indicates an actual change in an underlying system would be immensely useful to people.

You don't have to know all of the fundamental underlying ideas of any concept before it has practical utility.

⬐ Steuard

I may not entirely understand your question. My wife has taught statistics college statistics many times (including Gaussian distributions), and her classes have never had a calculus prerequisite.

Are some topics easier to understand if you already know calculus? Sure. (I assume she has to do the same sort of brief "area under a curve" explanations there that I have to do when I teach algebra-based physics.) Can you understand the topic in greater depth using calculus? Of course. But for a first exposure to basic statistics I think you can mostly dodge the issue.

(And really, apart from already knowing the concept of an integral, does knowing calculus really buy you much when studying Gaussian distributions? You can't even do those integrals! That frustration might be even more annoying to a calculus student than to others.)

⬐ Evbn

Experimental research papers in medicine, and decision making in business, are in a shambles, due to people learning and then misapplying the trappings of statistics, slamming Gaussians everywhere in plug-and-chug SAS sessions, without understanding the mathematical justifications for model selection.

⬐ Steuard

Absolutely. So wouldn't it be neat if premedical students and business majors had already seen a thorough stats class in high school, so that their college-level stats classes could spend less time on the basics and more time on those subtleties?

(Speaking as someone who's taught calculus-based physics to premedical students, I think it's important to recognize that most folks who've taken a year of calculus really have not internalized those concepts enough to be fluent in applying them. I think it would take a particularly strong math background for someone to really understand the mathematical justifications for statistics, so I suspect class time would be better spent warning students about pitfalls than on hoping that they will draw meaningful conclusions from formal derivations. Heck, medical students are required to have taken calculus, but lots of them (evidently including a journal editor, peer reviewers, and 163 followup papers) apparently don't even know what an integral is: http://fliptomato.wordpress.com/2007/03/19/medical-researche... .)

⬐ kaiwetzel

I've taken an introduction to statistics course with social science students and based on that experience, I can relate to what you are saying, 100%.

However, I think there is a broad group of students[1] for which a significantly earlier exposure to calculus would be beneficial and make learning statistics (and physics) a lot easier or at least faster.

When I took introduction to statistics as a math major, I found the subject extremely confusing because the discrete and continuous case where taught completely disconnected and useful anchors for understanding such as basic measure theory and Lebesgue integration where left out. That's certainly a good way to teach for many but for some it doesn't work.

A similar case was physics for me (classical mechanics in particular). From grade 5 to 10 (after which I avoided the subject) there was little insight gained (e.g. heavy things fall down, there may be some friction, memorize all those seemingly random formulas and if you use a long lever, make sure you pick a strong material). Then I was exposed to an introduction to physics course at university (for non-majors) and the revelation that all those random formulas have a strong grounding in just 3 general principles and can then be developed with some help from calculus was liberating. Just too late in my case. Maybe I would have loved physics and actually study it, had they told me in 7th grade that there is something tying all of it together, and the ultimate goal of the class was to reach that summit. Just trying to show the other side of the coin which should be integrated into the way math and science is taught in schools in my opinion :-)

[1] Say, the top 5-10% of middle school students.

⬐ Steuard

Oh, don't get me wrong: I was served very well by today's standard math sequence. I learned fascinating stuff in precalc, and calculus was a revelation and a profound joy. Prof. Benjamin's argument favoring statistics instead was a tough sell for me.

But I'm a theoretical physicist. As much as I hate to say it, structuring the entire standard math curriculum so it works best for kids like me (or even for the top 10% of students) just isn't reasonable. (Ideally, a solid gifted program could fill that gap.) I think that we agree on that.

I'd like to think that there are ways of introducing concepts from physics or statistics that do highlight the underlying structure of the field, even if the students don't yet know all of the math they'd need to work through the details themselves. If I find a perfect way to do it, I'll let you know!

⬐ bunderbunder

One approach I've seen and thought was interesting is the course schedule offered at the Illinois Math and Science Academy.

Their pre-calculus courses have been somewhat radically reorganized into a curriculum called "mathematical investigations" which orders the topics according to more of a practical progression. So, for example, bits of linear algebra are pulled all the way up into precalc because they're useful in geometry, and will also work better with the science curriculum. Perhaps physics teachers inheriting students who already understand vectors, for example.

Then the calculus curriculum is split into two tracks, one more basic, and a more intensive one for students who anticipate going into fields that require more calculus.

⬐ ceras

> It's easy to recognize that the author's arguments could apply just as well to any academic subject: literature, history, you name it.

The impact algebra has on graduation rates makes it unique. Something is clearly wrong: either we're teaching algebra ineffectively, or we're expecting too much and preventing students who are otherwise capable from graduating high school. It's important we figure out what's wrong and fix it. Without knowing the core problem, his proposal is no less valid than any other and, as a novel and controversial idea, might inspire research toward a real solution. I'm glad he wrote the piece, whether or not algebra should actually remain a mandatory subject.

I have a younger sister who is currently going through the High School system in Canada, and as the son of a Teacher and an Engineer (both of Russian upbringing), education is a constant hot topic at family gatherings. While we are not experts on these topics, I'll share some of the opinions that we've reached.

The education in North America (not necessarily the US alone, I live in Canada) is significantly lagging behind the rest of the world when it comes to mathematics. This should come to no surprise to anyone who has studied with anyone outside of this country. The Asian and Israeli kids (I am singling them out as I lived in a predominantly immigrant heavy Jewish/Asian neighborhood of Toronto, so I only have them to compare against) in my High School classes consistently scored higher than those born in Canada in all math courses, and this continued throughout my undergrad.

This widening gap between high school and college math is most prominent here, as compared to Europe, the Middle East, and Asia. In my humble opinion, this is largely due to our policy of "no child left behind" when it comes to Education and, as a secondary cause, due to Teachers teaching the "Fear of Math" (I'll get to that later).

As a society, we are constantly attempting to make sure that all our kids have an equal opportunity at success in life. Pursuing this endeavor, we have decided that rather than recognizing that everyone has different strengths and weaknesses, we should level the playing field. But how do we level this field? We simply adjust to the lowest common denominator. We want our children to score higher on the standardized tests, and when the scores are low, we simply make the tests simpler. This lowers the bar so that the weakest links in a particular subject area can keep up (it also allows politicians to get reelected and show how "great" of a job they're doing).

I think this is inherently wrong. First, not everyone needs to be educated with the same level of intensity on a particular subject area. Second, you are preventing "super stars" in particular areas from ever developing since they will never get to grow to their full potential. Integration is too hard for some Grade 12's? Let's remove it altogether. My sister, who is a decade my junior, will never learn even derivatives in high school. Algebra and geometry? Gone. My dad's high school ended in grade 10, and by the end of Grade 10 they have learnt derivatives, integration, and the importance of the natural logarithm. How many of us in our 20's can say the same thing? Yes, the drop out rate was higher, and if you didn't push yourself the system sure as hell did not care, but this is also the system that sent a man who shares my first name into space.

As a society, we have gone soft. We are babying our kids into believing that everything is roses. It made me furious when even as early as Grade 4, my sister would come home with a poor mark and say that it's ok because she "did her best". Really? What do kids really know about doing their best? of course if she truly did her best it would be ok and often when I see someone truly struggling to grasp a concept that they can't I feel both sympathy and have great respect for them, even if they fail. But at such a young age, there is no way that anyone knows what "their best" is, and this constant statement from her teachers is certainly not helping. In fact, I've never heard of "doing your best" until I immigrated to Canada.

And then, then there's the teachers. Oh the teachers. Few people are as important to a society's success as the teachers of children. They are in a direct position to influence and train our minds at a very important stage. And yet, they are underpaid and disrespected, such that only "those who can't do, teach" has become an unfortunate reality in many school systems. This is of course (and luckily) not always true, as some of my closest friends have dreamt of being teachers for as long as I can remember prior to ever beginning their Bachelor's degrees. In a high school environment the situation is also not as terrible as in the elementary schools as the teachers have at least specialized in the subjects they are now teaching.

However, in the elementary school, the situation is in fact worrisome. Class coordinators (those that you spend most of your day with), teach practically everything from Math, to English, to History, at least until grade 5, and sometimes even through middle school. As such, they are in a particularly strong position to put the fear of _____ into you. Generally, this happens to be the "Fear of Math". The teachers may in fact be great educators of English, and may have a very strong foundation in early childhood education, but quite often, these same teachers are the ones who were not great at math growing up, and so they subconsciously teach their own fear and lack of understanding to the kids. I've seen this first hand from kids who are afraid of math without having even tried, and it used to baffle me, until I talked to some of my Math teachers in high school and they explained this concept to me (yeah, I was a nerd growing up and still keep in touch with some of my teachers ;)

I realize that I place a lot of blame and offer few solutions. The truth is, I don't really have many solutions, if I did I would be trying to implement them. I think the position of teacher should be highly respected -- as much as a Doctor and/or a Lawyer or even an Engineer. I think this can only be achieved if teachers are not as heavily underpaid as they are today... I think that the policy of "no child left behind", is fantastic, but it needs to incorporate the realization that not everyone is the same.

Finally, I think that Arthur Benjamin's formula for changing math is something everyone should spend 3 minutes, watch, and think about: http://www.ted.com/talks/lang/eng/arthur_benjamin_s_formula_...

I'd like to apologize to my sister for singling her out in this post, she is a great kid with a good head on her shoulder's. I'd also like to apologize to any teachers that I have inadvertently offended -- I have nothing but the greatest respect for you and your profession. I have been BLESSED by having teachers who did not tell me to just "do my best", but rather challenged me at every turn.

⬐ netcan

As someone who has been through the education system in Israel, I am very suspicious of anyone claiming anything about Israeli high schools is better.

The state of education there is terrible & getting worse. It is common for high school students to go to private tutors who in 5-10 sessions can do more for them then school does in 2 years.

⬐ yurisagalov

I haven't gone through their high school education system, but I studied with plenty of kids who went through it. I don't know if they went to tutors to be honest, since it never came up, but many of those who came to us in grade 10 were much further ahead of those of us in grade 10 in the field of mathematics.

As someone who did study in Israel until the end of grade 6, I can safely and without exaggeration say that when I started grade 7 here, the material we were covering in math was equivalent to what I learnt in grade 5. In fact, I was advised to skip grades, but my parents decided not to advance me as my English was quite poor at the time.

⬐ netcan

When was this?

⬐ yurisagalov

13 years ago :) Keep in mind, I'm not saying that the High School education system in Israel isn't going to hell and back. It very well may be. The purpose of my post was to discuss Canadian/North American education...My comment on Israel was largely anecdotal in relation to how those kids do in the Canadian high school education system...

⬐ netcan

Well, if they are doing any worse then Israel, they are in trouble. Israel requires math to graduate, but the level is not high. It was my experience that the level is set such that a relatively unmotivated & unintelligent teenager can pass without listening in any classes by doing some preparation in the weeks before.

BTW, I went in the other direction about that time & age as you.

⬐ yardie

I am wary of comparing one states education system to another. Not every country is created equally and although it looks easy to look at some raw numbers and state this country is doing better than this country. Most of these comparisons tend to not look at the overall picture.

The developed countries that have the lowest scores tend to have high levels of immigration. Predominantly this is Canada, the UK, and the US. While programs such as the US "no child left behind" has been an educational disaster, this has been a problem for years. Schools have a limited, and shrinking, budget. The student population isn't getting any smaller so as an educator your options are to cut funding to a bunch of smart, but bored students, or cut funding to the lowest levels. In one instance you might be denying the next Bill Gates. In another you might be keeping someone from turning to a life of crime.

Usually from the same immigrant families, they will complain about the education their children receive in the host country but if pressed to send the children back, even if just for school, most would rather take their chances in their new country.

⬐ None

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