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dereksurfs

x-post: Teach Probability and Statistics before Calculus. Your thoughts?

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I listened to a very short but interesting TED talk by mathematics professor Arthur Benjamin called "Teach Statistics before Calculus!" 


 


Even before this I was thinking of adding P&S into our math program.  My son is very interested in practical applications of math in daily life and I find Probability and Statistics so practical. In addition there is so much more available to students now with Massive Open Online Courses (MOOCS) such as:


Carnegie Mellon's Intro to Probability and Statistics






 

It seems like it would not be that hard to find a decent intro to P&S.  I'm just curious what your thoughts, plans or or efforts might be in this area?

 

I posted this on the High School board as well since I'm not sure at what age I would potentially introduce this.

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This article about Calculus and Stats by AMSTAT might interest you. It gives a quick overview of non-calculus stat and calculus required stat. http://magazine.amstat.org/blog/2013/07/01/calculus-and-statistics/

Example of calculus being use for prob and stat (from page 9). http://www.cengage.com/resource_uploads/downloads/1439049254_242719.pdf

 

I was from an intergrated math system similar to MEP. Calculus was taught concurrent with Prob and Stats. I'll probably do the same for my kids.

 

Maybe you can look at the AoPS intro to C&P textbook as well as the AP stats textbooks and see what your son prefer. You can also use the MEP Prob and Stat modules as introduction.

 

Ruth (lewelma) would probably be able to give you a better explanation using calculus for stats.

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DH had me buy Chances Are.. for him and we'll probably use that as an 'intro' or overview for all of the kids. I definitely have AoPS C&P textbook on the list for at least one of the kids, but not sure if I'll use it for all of them. 

 

There is a little of this in their regular high school math and whether we go deeper will depend on each kid, their math progression, and their interests. DH tries to get the kids interested in his probability work with dice, but they tend not to bite.  :lol:

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DH tries to get the kids interested in his probability work with dice, but they tend not to bite. :lol:

Gin rummy and poker played without chips when I was a kid got my cousins and I hook on probability. Even the solitaire game did spike the interest on the chances of where the Aces are hiding.

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This article about Calculus and Stats by AMSTAT might interest you. It gives a quick overview of non-calculus stat and calculus required stat. http://magazine.amstat.org/blog/2013/07/01/calculus-and-statistics/

Example of calculus being use for prob and stat (from page 9). http://www.cengage.com/resource_uploads/downloads/1439049254_242719.pdf

 

I was from an intergrated math system similar to MEP. Calculus was taught concurrent with Prob and Stats. I'll probably do the same for my kids.

 

Maybe you can look at the AoPS intro to C&P textbook as well as the AP stats textbooks and see what your son prefer. You can also use the MEP Prob and Stat modules as introduction.

 

Ruth (lewelma) would probably be able to give you a better explanation using calculus for stats.

 

Thanks, Arcadia.  I'll take a look at MEP's Prob and Stats modules.  But where would I find them?  Do they occur during calculus as you described your integrated math?

 

BTW, Ruth answered on the HS boards and is very much in favor of a taking a survey course before taking calculus based statistics.  She had some very interesting comments regarding the use of calculus and stats in both school and STEM careers.

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I think probability and statistics are more important to most people in our real lives than calculus. STEM definitely needs calculus, but just trying to decide whether to _____ or _____ depends on an understanding of P&S. Looking at a newspaper right here, I'd say few of the articles need a sense of calculus to be able to evaluate the information, but many, and many of the adds, could use P&S. So, I have not figured out how we will do it, but I do hope to get to P&S before, or if necessary instead of, calculus. 

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I think probability and statistics are more important to most people in our real lives than calculus. STEM definitely needs calculus, but just trying to decide whether to _____ or _____ depends on an understanding of P&S. Looking at a newspaper right here, I'd say few of the articles need a sense of calculus to be able to evaluate the information, but many, and many of the adds, could use P&S. So, I have not figured out how we will do it, but I do hope to get to P&S before, or if necessary instead of, calculus. 

 

Yes, Pen.  I fully agree and thus have been wondering 'how' I will pull this off which each child.  I think it may be easier with some who are ahead in their math sequence.  But regardless now that I've received input from other families I have seen creative ways to do both.  Some even take P&S in parallel with other primary math courses during HS.  Or they squeeze it in as a Semester course, during Summer, etc...  There some which are shorter courses I've noticed including some of the MOOC courses I listed above.  

 

BTW, Heathermomster recommended this book which looks like a great reference at the very least: http://www.amazon.com/Statistics-Plain-English-Third-Edition/dp/041587291X/ref=wl_it_dp_o_pC_nS_nC?ie=UTF8&colid=2UIQR8SU0BTJ0&coliid=I1MR415W3XQ789

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I'll take a look at MEP's Prob and Stats modules. But where would I find them?

 

Year 8 - unit 10 prob, unit 20 stats http://www.cimt.plymouth.ac.uk/projects/mepres/book8/book8.htm

Year 9 - unit 6, 8, 16, 18 http://www.cimt.plymouth.ac.uk/projects/mepres/book9/book9.htm

Year 10 - unit 5, 8, 9 http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/allgcse.htm

Year 11 & 12 - all the statistics and further statistics modules -> 21 modules altogether http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/alevel.htm

 

My estimate is that I had finish what is called PreCalc here by my 10th grade. So differentiation and integration has been mastered already.

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My older ds took stats and pre-cal his senior year of high school (private).  He took calculus 1 & 2 at college and will take stats his jr yr (req. for his major).

 

I hope younger ds will take calculus and stats for his senior yr of high school (public) which is next year IF the school offers stats (don't this yr). 

 

EDIT: Yes, I agree with Ben about every student taking stats and NOT necessarily calculus. 

 

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I'll repost here what I wrote on the high school thread.

 

My daughter majored in Classics/Latin and minored in Geology at college.

I (not she) was vaguely regretful that she did not take Calculus as she had to forgo taking several Geology classes which had a Calculus prerequisite; however, she commented several times that she was grateful for having taken Statistics as that knowledge has been useful.  In fact, she named Statistics as one of the two most valuable classes she took in high school!  The Statistics class she took was an AP class offered by Pennsylvania Homeschoolers.

Regards,
Kareni

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