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In a 3 minute talk on, mathematician Arthur Benjamin made the argument that it makes sense to give emphasis on statistics instead of on calculus in school, after students have been given a basic background on algebra and arithmetic. Statistics is something most people can use in their day to day life, if only they knew how to. In contrast, people who don't study maths after school hardly find any use of calculus in their daily lives. Obviously such people don't do calculus related jobs, but most of the people are in that category.

  • How can statistics be used in day to day life by common people if it is emphasized more in the school level? What will some concrete examples of this?

  • How should a two year post high school curriculum focusing on
    statistics instead of on calculus be designed to accomplish the

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Tim Gowers has an interesting post that you may find helpful on his weblog:…. – J W May 1 '14 at 16:43
I pretty much agree in the case of most students, but the problem is that whatever is considered to be more difficult will be sought after for college admissions purposes. However, there shouldn't be that much of a problem in even getting a Ph.D. in math if one waits until college to take a first calculus course, as I explain here (scroll down to where I wrote "Even a student planning to get a Ph.D. in math"). – Dave L Renfro May 1 '14 at 16:51
It is interesting to note that in… there are some links to courses combining statistics and calculus. – J W May 1 '14 at 20:12
But to REALLY understand statistics---yoiu need calculus! – kjetil b halvorsen May 4 '14 at 19:46
The phrase "day to day life" seems odd to me here. Obviously you can buy groceries and balance your checkbook without knowing calculus or statistics. If you're talking about people's professional life, then it depends completely on their profession. Engineering majors are the single largest group of students who take calculus. They need to understand calculus in order to do engineering. – Ben Crowell Dec 16 '14 at 2:00

4 Answers 4

A question arose earlier about "how is calculus applicable in students' daily lives?", and the fact is... it's not. We use basic arithmetic in our daily lives, and that's generally as far as it goes. Occupations aside, of course.

Statistical analysis, however, is pretty instantly applicable all over the place. You can use it to analyze how you spend your money, and use it to develop budgeting skills, and overall get a good economic sense.

You can use statistics to measure your workouts and your diet, and find out what gives your body the effect you desire. It could be weight increase or decrease, generating muscle mass. If you consistently log your behaviour and measure your results, you can analyze this and become an expert in managing your physique.

I started doing this, and while I won't go on too much of a tangent, I'm very pleased with the results on my body. I used very basic statistics like noticing periods of change in my weight, checking my log, figuring out my average caloric intake over that period (1-2 months), and jotting down the result. Started getting more advanced and did the same, give or take, over another period, and compared the standard deviations. End tangent...

My point is that basic statistics is immediately useful everywhere. Whether you're trying to increase your productivity, figure out how many hours of sleep render you rested and alert the next day, or even figure out what kind of diet makes your finger nails grow faster; statistics is the way to go. Simple logging and very basic, almost menial calculations, can give you sooo much information.

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Not to mention seeing through much of the fluff published in newspapers and spewed by random politicans... – vonbrand May 1 '14 at 19:56
@vonbrand - Absolutely. Learning the difference between correlation and causality changes your entire view on media. – Alec May 2 '14 at 8:47

The premise here is that we are limited by traditional curriculum of these courses. Continuous rates of change are essential to understanding the world. The machinery of calculus is not. Calculus, however is structured to focus on the later rather than the former. In fact I suspect that if you asked many calculus students basic conceptual questions about the nature of calculus, they would not do very well. Courses focus on what I will call "calculytic techniques" -- techniques used to compute derivatives and integrals. While for advanced students these can be fun puzzles, for many these are exercises in futility that seem to have no relation to the the concepts underlying calculus. Furthermore, I would argue that in an age of Ti-89's and Wolfram Alpha, we need to reevaluate how valuable teaching students these techniques actually is.

I would make the same argument for statistics. Statistics education can be equally befuddling for many students because it focuses on manual computation of statistics in a way that does not usually develop understandings of how to interpret statistics in context and how to understand the significance of that interpretation. Again, statistics curriculum is shaped by an age without technology, and we have to reevaluate it in the context of ubiquitous computational technology.

In this way, teaching statistics also does not solve the problem posed by the original author -- that students learn math that will be valuable for them. Fundamentally, our mathematics curriculum (at all levels) does not reflect what we want students to be able to do -- transfer mathematical thinking from one topic to another, one class to another or to their lives filled with work, games, and puzzles that all require mathematical thinking.

In all of the our courses at the high school level, we focus on content (and computation) at the expense of teaching mathematical problem solving skills to most students. In the age of the common core, there is more pressure than ever to do both -- teach skills and content, but I do not believe that this is fully possible. Students cannot simultaneously engage in developing transferable problem solving skills around content they are not fluent with. That, however, is a post for another time.

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The OP asks: how should a curriculum focusing on statistics be designed? I understand your goals and what you want to avoid, but what would the curriculum look like? What examples you would use? – Matt F. Jan 4 at 21:38

For high school math students, there are two basic "tracks." One leads to pre-calculus and calculus, etc. The other is called "general math."

Statistics makes a good "general math" study for students who don't want to pursue calculus. That is because it deals with things that are found in everyday life, such as the "averages" and "dispersions" of things like height, weight, grades,and other key attributes for high school students.

Calculus-bound students could also benefit from the study of statistics (and probability), but they can wait to take the calculus first, and then learn about integrating conditional density functions in probability, or differentiating normal equations in statistics.

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This almost answers the question "how can statistics be used?"...but how is it useful to compute an average height? – Matt F. Jan 4 at 7:56
@MattF.: Learning statistics and "how to compute and average height" might be a good "fallback" position for someone interested in math but is incapable of calculus. – Tom Au Jan 4 at 19:35

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