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This post is prompted by two 17 year old boys, Cam and Thomas, who are about to enter year 13, the final year of High school in New Zealand. They are both academically capable, with highly educated parents. And both boys are struggling with a dilemma – should they take Calculus or Statistics at school this year. I suspect their maths teachers are pushing for calculus, whereas their parents appreciate the value of statistics.

Let’s take a look at the alternatives and see if we can help. (This makes no pretense of being a balanced view – that’s what comments are for!) Note that this is based on the New Zealand curriculum, which has a recently introduced strong emphasis on statistics. The assessment structure for this includes a full statistics subject in the final year for the first time in 2013. New Zealand is in the somewhat lonely position of leading the world in this area; statistical societies in other countries are watching. (And for you in the Northern Hemisphere who may be feeling confused, it is currently our summer holidays, and school starts back in early February.)

Calculus is “proper” mathematics. It is elegant, and neat, and you get right answers. You don’t have to write sentences. Ever! Most of the problems are nice and theoretical, so you don’t have to deal with “word problems”. The teachers like Calculus, and fight over who gets to teach it. They feel confident in what they are doing. They have taught it for years and don’t need to do anything new. There are oceans of on-line videos, games and resources to help students. Khan academy videos are useful. But you don’t need to have access to the computer room to do calculus. Parents are more likely to know calculus (though well forgotten) than statistics. Calculus is needed for important subjects such as engineering, physics and… Hmm can’t think what else! Oh yes – more calculus. It is a good mental discipline that helps with problem-solving skills. It can be pretty fun if well taught. Besides people tell me that statistics is the easy option for people who can’t do calculus.

Statistics relates to life. It is messy and often the answers aren’t clear, so interpretation and thinking are important. You will need to write reports and express yourself on paper. This will help you develop your critical thinking skills and communication skills. You have to understand contextual material such as biology, economics or sport. Innovative teachers are excited about the changes in the curriculum, and are embracing the new material as an opportunity to learn and develop themselves as well as you. As New Zealand is leading the world by introducing resampling, randomisation, bootstrapping and time series analysis at high school level, the on-line resources are few, but those extant (and in our pipeline) are focussed for your use. Parents are not familiar with statistics, but will find what you are doing interesting. You get to do most of your calculations on the computer, just as real statisticians do. You will never find yourself asking “Why do we need to learn this?” because it is obvious how it is a part of your life. You will be better able to discern truth from lies on the internet. You will find yourself looking at the world differently.

Statistics is needed for many subjects: psychology, biology, engineering, management, marketing, medicine, sociology, education, geography, geology, law and journalism. It also widens the possibilities in the study of arts subjects such as History and English.

Here is our advice – all students who possibly can, should take statistics. Those who are planning to be engineers, physicists, maths teachers or statisticians (yes!) should take calculus as well. Simple really!

What about my own sons – the jazz pianist and the movie maker – what would I have advised them at this point? Statistics all the way. Neither one had use for calculus, nor the aptitude, but both would have benefited from statistics.

I’ll let you know what Cam and Thomas decided.

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## 26 Comments

Hello from Canada! Let me toss in a couple additional pro-statistics remarks. Note I’m coming from the viewpoint of the Ontario Curriculum in Canada, where the last year of “University Level Math” in high school involves “Advanced Functions” in semester one and “Calculus and Vectors” in semester two… and/or “Data Management” which is effectively a probability and statistics course. Thus a course students might toss in instead of a spare (or maybe take as a second math in Grade 11). And I teach that one. With that said:

1) Reasoning with statistics and randomness is something humans are not very good at… we tend to invest in things like “lucky numbers”, despite our logical brains telling us otherwise. We should at least acknowledge our own personal difficulties here, and a statistics course is one way to start thinking about it.

2) We now live in an age where we have access to more data than ever before. What is it telling us? What is it NOT telling us? Is a study done on 30 students in California really something we can generalize? How scientific are the numbers being reported in the media? More to the point, do we ever really think about this – because we should. (Particularly if you’re planning on going into advertising, so you know how to manipulate people…?)

3) There are experts we can turn to for help with calculus. (And websites that can potentially do it for us…) And while there are experts we can turn to for help with statistics, I would argue that we tend NOT to, and moreover, that it’s more difficult for a computer to predict how many people in a room might like apple pie, as opposed to the value of pi. Statistics is somehow seen as “easier”, which is dangerous because it’s NOT. It’s DIFFERENT.

A student at our school once wanted to take one math in school, and another as a night course, and asked a guidance counsellor for advice. He was told the data course “was the easier one”, so he took that in the evenings. He later came to me saying “I’ve been following everything in Advanced Functions fine, but some of this data analysis is really confusing.” I like to make the analogy that Statistics is no more an easier math than Biology is an easier science. (Which of course means that it may be easier for some people!)

Now, not to knock Calculus, of course. As far as the pure mathematics goes, it’s awesome, and I agree, taking both would be ideal. But I think Arthur Benjamin put it best in a TED Talk (from the US) a few years ago, which I’ll link to below. It’s less than 3 minutes long, worth a watch, and I play it sometimes as an introduction to my course:

http://blog.ted.com/2009/06/29/a_formula_for_c/

Thanks and thanks for the link. Very inspiring.

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The choice between Statistics and Calculus is tricky, but for those who might wish to be future statisticians it is easy – Calculus every time. And I say that as a university professor of statistics. The biggest problem that I see in students studying statistics at second-year (200) level and above is poor mathematical skills. In part a good knowledge of calculus is useful in itself, for example to understand some very practical ideas in likelihood theory. However, more important is the additional practice in algebra and basic mathematical manipulations that is enjoyed by those students who have studied Calculus.

I mostly agree. The best subject choice for future statisticians and operations researchers is BOTH subjects. We wouldn’t tell a Chemistry student not to take Chemistry because they need Physics!

My comment wasn’t meant to imply that choosing both isn’t best! It’s just that almost all the students that I see coming to university have selected just one. If it is either/or then it has to be calculus for the future statisticians (and other mathematical sciences).

I would support taking Statistics too, except if you wanted to become a Statistician or any other applied mathematical science specialist.

Thanks Nicola.

Yes, do both if you can.

It is great that NZ students can do two math subjects.

When I taught Year 13 in NZ the experienced math teachers did not want to teach Stats at all, and it fell to us junior ones to teach it. (Their loss, our gain.)

It is important, I think, to have a non-linguistic subject like Calculus. It is a life-boat for dyslexic types, as well as acknowledging multiple intelligences.

It is certainly an interesting time to be a maths teacher, and for some it is rather daunting. It will take a while before people get used to the idea of two subjects.

they should take calculus. statistics only makes sense if one has already had at least two years in a university in an applied field. or if you are referring to theoretical statistics, then one should take calculus as the latter has measure theory and real variables as a prerequisites..

Thanks for commenting. I think you are correct if you are referring to theoretical or mathematical statistics, and you are talking about the minority of students who go to university and can do mathematics easily. Cam and Thomas are both in that group. For other people, I think applied statistics, as outlined in the GAISE report is more useful. I talk about this in an earlier post, http://learnandteachstatistics.wordpress.com/2012/08/06/stats-not-algebra/

I am a phd student in Statistics (in Australia and France) and went to high school in NZ, finishing in 04. Taking both subjects was perfect, the subjects are so different that it doesn’t feel like you are doing the same thing all day, and if they are interested in further statistics at any stage, a good understanding of calculus is extremely useful. If they do both they will find themselves much better prepared for university anywhere in the world (and will be easily able to compete for scholarships in Australia). One more thing – it is invaluable to take the level 4 scholarship exams for both these subjects! I received much higher scores in the level 4 exam than level 3, the format is different and usually better suited for gifted/mathematically able students.

Best of luck!

Thanks for your input, Zoe. Best wishes with your PhD!

As a PhD student (part time) in Statistics, I’d advise, if you can only take one – “take the one with the best teacher”. Otherwise, if intending to study in statistics – calculus is definitely a priority in my mind. One thing I do regret from my undergraduate days is not taking more maths (pure maths) papers. That said, I was already double majoring in computer programming (another ‘essential’ subject for statisticians in my humble opinion) and statistics so additional maths papers would have been hard to fit in, but still – calculus, linear algebra, and other such courses provide good solid foundations for statistical theory to then ‘fit’. Applied statistics can suffer for lack of theory.

My 2c worth. 🙂

Hi David. Thanks for your 2c worth (though with inflation it should probably be $2 worth.) For people like you, who are clearly competent at mathematics, and for Cam and Thomas, this is probably true. However you may be missing the other non-mathematical aspects of statistics. It is a different way of thinking, that mathematicians sometimes fail to get their head around. I say more about this in an earlier post, http://learnandteachstatistics.wordpress.com/2012/08/06/stats-not-algebra/

If a well prepared student is forced to choose only one, he or she should take the calculus. This is true, even if he or she envisions a career in statistics. Statistics can be started in uni later without any high school background in statistics. In my opinion, the main ideas of statistics require a very sophisticated reasoning that most high school students aren’t ready for. HS statistics are mainly taught by teachers trained in mathematics, which is different from statistical training. Even university students taught by professional statisticians struggle with these ideas. Oldies such as me can remember the days when statistics wasn’t even taught as an undergraduate major, but was picked up in graduate school after a first degree in math.

Hi Bill

Thanks for commenting. All true, especially the “oldies” bit. 😉

Before computers we could only really learn the theory of statistics, but these days you can get a better picture of what is happening in data without the need for the mathematics. As Cobb said, “Mathematical understanding is not the only understanding.” As students become acquainted with the concepts of variation and randomness, data and evidence earlier in their schooling, it is hoped that they will not struggle as others have.

[…] There’s also an interesting discussion of stats vs calculus over at Nicola Petty’s blog. […]

I agree with many of the comments IF the student is going into a mathematical field, including statistics. I think Arthur Benjamin’s very important point is that for students who will never take another math-oriented class after high school, statistics is more important. I agree with that.

I’m impressed with New Zealand for taking the lead on this.

I say this as a statistician who took calculus in high school and college, majored in psychology, then got a masters in applied stats in grad school (way too many years after learning calculus).

And while calculus is very important for graduate level stats, it’s not important for intro stats. Algebra is, though. For a couple years after I finished grad school, I taught intro stats. One year was at a community college. Between my first and second semester teaching, they dropped the requirement that students needed algebra as a prereq for stats. So all the students who thought algebra was too hard took statistics. That was a disaster. (I’m still not sure how they got out of high school without passing algebra).

Karen

What separates statisticians from others who use statistics is that we approach the problem with the logic of a mathematician and the practicality of someone who knows that decisions have to be made. The latter requires maturity and experience and is difficult to teach to high school students. Mathematics can be taught to such students surprisingly well, perhaps because experience can be replaced by assumptions. This suggests that if a choice has to be made, I would always recommend calculus over statistics.

Having said that, I question whether calculus should always be the “advanced” mathematics. Modern mathematics, including statistics, has many other core components such as finite structures (leading to designs in statistics) and graphs (network models) etc that can equally teach one of the core things that we hope a high school student gets out of mathematics – logic and the recognition of a proof.

[…] Statistics or Calculus? Do both! (learnandteachstatistics.wordpress.com) […]

[…] There’s also an interesting discussion of stats vs calculus over at Nicola Petty’s blog. […]

Do you have any self-instruction book or website recommendations that offers free instruction for an adult who, decided not to go to college after high school, and years later is re-entering school and is contemplating (and needing to) take a Statistics class to fulfill the IGETC requirement? I am terrified, absolutely terrified of math and to prove how much I suck at it, I failed Geometry in high school (which I am deeply ashamed of) and that’s sort of where my math classes ended. Did I say that I am terrified of math? But I know I need to take Stats (or Calculus) and most of the stuff I am reading online is suggesting Stats over Calculus. I have zero interest in math, and the thought of having to take a math class induces panic and fear of failure. Please help.

I cant separate the two! Calculus is great as it is the first ‘real’ Maths I ever studied. But Stats is also great. I made an online course https://www.udemy.com/alevelstatistics/ which you may find useful.

My daughter wants to major in math and become an eengineer, hopefully to work at Boeing.. she started her freshman year in algebra 2 and her class this year as a senior was IB HL calculus 2. I believe in her IB program she would have gotten all the problem solving and writting in her other classes. I feel she would be better off taking calculus 2. She received a grant from the University of Washington to major in math. I guess they thought so too.

Absolutely – that’s pretty much what I said in the post. Engineers need calculus. However, she will also need statistics at some point – Boeing even use our materials! That’s why I suggest that taking both is a great idea. And congratulations to your daughter.