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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 High School math plan.  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?
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This is what we did/do:

DS did AoPS Intro to Counting and Probability in 7th grade; it is an easy one semester course.

We are covering some statistics with science lab when we do data analysis.

With DD (who did not do C&P), we covered combinations/permutations and some basic stats during test prep for the SAT2 Math.

We did not do a complete course in discrete statistics.

 

I prefer my students to have calculus early because of the practical applications in physics (and because of the related constraints on the science sequence.)

I would actually prefer doing statistics after calculus, because then you can work with continuous probability distributions. DD covered some basics in connection with Modern physics. A complete calculus based statistics course has to wait until she is in college; we did not have enough time in high school.

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This is what we did/do:

DS did AoPS Intro to Counting and Probability in 7th grade; it is an easy one semester course.

We are covering some statistics with science lab when we do data analysis, and a few things when prepping for the SAT2.

We did not do a discrete statistics course for math.

 

I prefer my students to have calculus early because of the practical applications in physics (and because of the related constraints on the science sequence.)

I would actually prefer doing statistics after calculus, because then you can work with continuous probability distributions. DD covered some basics in connection with Modern physics. A complete calculus based statistics course has to wait until she is in college; we did not have enough time in high school.

 

Yes, I like the idea of introducing non calculus based probability and statistics courses such as AoPS's intro to C&P.  I am considering that among others.  I think that is what Arthur Benjamin was referring to for HS students.  Obviously one should not attempt a college level calculus based P&S course prior to calculus.  ;)  I can also see time being a limiting factor.  So it's important to balance out Probability and/or Statistics with other goals.  Another consideration may be STEM directed vs. non-STEM focus.  

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My older son took AoPS C&P last year (9th) as a semester elective and liked it so much that he is taking AP Stats now as a 10th grader (and loving it). This is definitely a STEM-oriented student.

 

He will not take calculus until his senior year. This is completely due to reluctance on my part...and honestly, it is probably a mistake. Once upon a time, I read "The Calculus Trap" article on AoPS's website and took it to heart, but now I'm not sure it was the wisest decision for this particular student. Like Regentrude and snowbeltmom indicated, delaying calculus limits the science sequence options.

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I don't have high school kids, but I do have an engineering degree and dh has a master's degee in engineering.  We both had to take statistics in college, mine was an undergrad class, that at the time the entire college had to take and dh's was a grad level class.  Neither were calc based, but i had completed calc 2 or maybe even 3 when I took it.  It was extremely easy for me and then when my dh took it, I realized they covered about the same material in the upper level class.

 

After having the upper level math classes there just wasn't anything to the statistics classes other than maybe a little new vocabulary.  In a lot of ways the economics class that I took was the same way.  They were both easy A's in college for me.  I don't know that something like statistics would have made calc easier to understand or not.

 

I did take a business calc class before taking calculus and that was really helpful because it was a lot of real life applications of calculus and the professor I had for it was excellent.  She was part of the reason I changed from a Psychology major to an engineering major.  Assuming you have covered some of the basic statistics already like mean, average, std deviation, ect. it might be worth looking into a business calc class, IMO.

 

ETA:  Neither the undergrad or the grad statistics classes were calculus based and this was at a fairly well known engineering school about 15 years ago.  In 10 years of working in engineering, I have never had a need to use calculus based statistics.  i have used some basic statistics though.

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ETA:  Neither the undergrad or the grad statistics classes were calculus based and this was at a fairly well known engineering school about 15 years ago.  In 10 years of working in engineering, I have never had a need to use calculus based statistics.  i have used some basic statistics though.

 

For a physicist, OTOH, calculus based statistics is essential. Continuous probability distributions occur in thermodynamics and quantum mechanics, and are absolutely vital in statistics mechanics. Sadly, many students are not adequately prepared from their math classes, and their physics instructor needs to spend class time to remedy the shortcomings.

 

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After having the upper level math classes there just wasn't anything to the statistics classes other than maybe a little new vocabulary.  In a lot of ways the economics class that I took was the same way.  They were both easy A's in college for me.  I don't know that something like statistics would have made calc easier to understand or not.

 

***

 

ETA:  Neither the undergrad or the grad statistics classes were calculus based and this was at a fairly well known engineering school about 15 years ago.  In 10 years of working in engineering, I have never had a need to use calculus based statistics.  i have used some basic statistics though.

 

FWIW, at my college there was more than one type of stats course within the economics dept.  The regular stats course was not calc-based, but the honors stats course (which I took) and econometrics were both calc-based.  (Thus for a long time I was so confused about how a college stats course could possibly be taught without calc as a prerequisite  :tongue_smilie:)

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I don't think it is critical what order you do it in, but I do feel strongly that every child should have some basic statistics under their belt before they graduate. I believe stats is more practical and useful than calculus for many people. Statistics is so often used as a scare tactic and I want my children to be able to understand what is being said.

I took several calc classes for my Chemistry degree but no statistics. When working though, the computers did the calculus but I used statistics every day.

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Derek, the order does not matter. I personally would not teach calculus based stats as a first stats class anyway. It would be like taking calculus based physics as your first physics class -- you are likely to lose track of the concepts because you are buried in the details of the calculations.

 

Statistics is not about calculating, the computers do that, rather it is about thinking about the data. Sure it is easy to run a t-test on data that has been collected for that purpose, but where statistics gets tricky is when the data has been collected without a statistical test in mind. My sister just did a bio masters and her advisor had her collect data without planning the stats first. She had only 8 claws, but took multiple samples from each claw and took measurements over time. She also removed tissue in some but not all the claws and at different times in the experiment, had three different levels of drugs, three different response variables, and non normal data. Her measurements had such a high degree of error just because of the sampling equipment that we could not even use percentage change which would clearly have been useful. It was a mess! Calculus does not help here, being familiar with numerous options does, because you can see the big picture, know what questions need to be asked, and then you can look the details up in a book.

 

My main point is I think you need to think about your goals. If a student is passionate about statisitcs or physics, clearly calculus based stats in high school can be a good option, but to just be an educated adult, it is not, because with limited time in this world you cannot be both a generalist and a specialist (think medical doctors). My goals for my kids are to understand as many possible types of tests as possible so that they can interpret the stats in the news or research papers that they read. This translates into a survey class. They do not need to be able to calculate all these types of stats, so I am not looking for a calculus based class. There will be time for that later if they want to persue it. But to have their first and possibly only stats class be calc based, means that they will have the trees and no forest, and I don't think that kind of knowledge will be very useful in a field like statistics.

 

FWIW, I have taken 8 university stats classes, done a four year statistical modeling project, and worked at Statisitcs NZ and the Ministry of Health as a multivariate statistician ( so quite a large range of topics in biology, economics, and medicine) and I have never used calculus based statistics. Clearly some fields need it, but the majority don't. I will add however, I don't consider myself a statistician because of my lack of deep understanding. So happy to be overruled by others more experienced.

 

I don't have a book to recommend as we are not there yet, so hopefully others will link to some good ones.

 

Ruth in NZ

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Derek, the order does not matter. I personally would not teach calculus based stats as a first stats class anyway. It would be like taking calculus based physics as your first physics class -- you are likely to lose track of the concepts because you are buried in the details of the calculations.

 

Statistics is not about calculating, the computers do that, rather it is about thinking about the data. Sure it is easy to run a t-test on data that has been collected for that purpose, but where statistics gets tricky is when the data has been collected without a statistical test in mind. My sister just did a bio masters and her advisor had her collect data without planning the stats first. She had only 8 claws, but took multiple samples from each claw and took measurements over time. She also removed tissue in some but not all the claws and at different times in the experiment, had three different levels of drugs, three different response variables, and non normal data. Her measurements had such a high degree of error just because of the sampling equipment that we could not even use percentage change which would clearly have been useful. It was a mess! Calculus does not help here, being familiar with numerous options does, because you can see the big picture, know what questions need to be asked, and then you can look the details up in a book.

 

My main point is I think you need to think about your goals. If a student is passionate about statisitcs or physics, clearly calculus based stats in high school can be a good option, but to just be an educated adult, it is not, because with limited time in this world you cannot be both a generalist and a specialist (think medical doctors). My goals for my kids are to understand as many possible types of tests as possible so that they can interpret the stats in the news or research papers that they read. This translates into a survey class. They do not need to be able to calculate all these types of stats, so I am not looking for a calculus based class. There will be time for that later if they want to persue it. But to have their first and possibly only stats class be calc based, means that they will have the trees and no forest, and I don't think that kind of knowledge will be very useful in a field like statistics.

 

FWIW, I have taken 8 university stats classes, done a four year statistical modeling project, and worked at Statisitcs NZ and the Ministry of Health as a multivariate statistician ( so quite a large range of topics in biology, economics, and medicine) and I have never used calculus based statistics. Clearly some fields need it, but the majority don't. I will add however, I don't consider myself a statistician because of my lack of deep understanding. So happy to be overruled by others more experienced.

 

I don't have a book to recommend as we are not there yet, so hopefully others will link to some good ones.

 

Ruth in NZ

 

Thanks, Ruth.  I was hoping someone from a STEM research and statistics background would chime in. Obviously certain courses are required to fulfill educational requirements such as calculus to get into the higher level sciences.  But probability and statistics seems so much more practical not only in conducting research and performing data analysis but in everyday life.  Many students will take calculus and never use it in their professional lives even if in STEM careers.  But I can't imagine too many not using some form of statistics along the way. 

 

Your recommendation for taking a precursor to calculus based statistics makes perfect sense to me, the same way one takes an intro to physics before calculus based physics.  It's important to be able to see the big picture and understand the 'whys' before crunching numbers and working formulas.

 

Thanks for your input,

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My DD did Courera's Passion Driven Statistics before Algebra I was finished.  It was a wonderful class in that it tried to do a few things well, rather than go over every possible statistics method in a superficial way, and the prof was terrific.  If that one comes up again, jump on it.  It's more like a quarter of math than a semester or a year, but the payoffs from that class have been amazing in terms of how she looks at collecting science data, reading about stats in the news, etc.

 

It was basically selected topics from the OLI class you linked to, though I have no experience with the OLI class.

 

--Janet

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My older son took AoPS C&P last year (9th) as a semester elective and liked it so much that he is taking AP Stats now as a 10th grader (and loving it). This is definitely a STEM-oriented student.

 

He will not take calculus until his senior year. This is completely due to reluctance on my part...and honestly, it is probably a mistake. Once upon a time, I read "The Calculus Trap" article on AoPS's website and took it to heart, but now I'm not sure it was the wisest decision for this particular student. Like Regentrude and snowbeltmom indicated, delaying calculus limits the science sequence options.

 

Jetta, its nice to see that love and appreciation for math.  Statistics was fun for me in college.  I can see how those who like math would enjoy its practical nature, even at an earlier age.  Did he find AoPS C&P difficult?  How would its level of challenge compare to AoPS Algebra?

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FWIW, I have taken 8 university stats classes, done a four year statistical modeling project, and worked at Statisitcs NZ and the Ministry of Health as a multivariate statistician ( so quite a large range of topics in biology, economics, and medicine) and I have never used calculus based statistics.

 

Ruth, I bow to your expertise and want to make it clear that my statistics knowledge is very limited, and so, maybe my question is  a stupid one. But I can not imagine that you are saying you have never dealt with any continuous probability distributions and only discrete data sets.

But as soon as it gets into continuous distribution, even something as simple as the Gauss normal distribution (which apparently is supposed to be covered in the new standards?) requires calculus if one wants to understand it and not simply use as a black box equation that fell from outer space and that I can use for plug and chug.

In order to obtain the coefficient in front, I need to calculate the integral, so that I can normalize and makes sure the total probability equals one. I also need to integrate to see that the sigma happens to be the standard deviation.

If I don't have calculus, all I can do is hand my student a function and say "This is so, believe me".

What am I missing?

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Ruth, I bow to your expertise and want to make it clear that my statistics knowledge is very limited, and so, maybe my question is  a stupid one. But I can not imagine that you are saying you have never dealt with any continuous probability distributions and only discrete data sets.

But as soon as it gets into continuous distribution, even something as simple as the Gauss normal distribution (which apparently is supposed to be covered in the new standards?) requires calculus if one wants to understand it and not simply use as a black box equation that fell from outer space and that I can use for plug and chug.

In order to obtain the coefficient in front, I need to calculate the integral, so that I can normalize and makes sure the total probability equals one. I also need to integrate to see that the sigma happens to be the standard deviation.

If I don't have calculus, all I can do is hand my student a function and say "This is so, believe me".

What am I missing?

 

Not Ruth, but was wondering this as well.  Admittedly its been a 'looong' time since I've taken calculus and I've also never needed it outside of school in my professional life as a software engineer.  So I did a quick look up of your question and found a great, short tutorial on Khan Academy:  https://www.khanacademy.org/math/probability/statistics-inferential/normal_distribution/v/introduction-to-the-normal-distribution

 

Obviously there may be more involved than this.  But if a student could understand the big picture as explained for a normal distribution would it really require 1+ years of calculus first before applying it to statistics?  Could some of this be learned even earlier in Pre-Calc perhaps?  Maybe at this point you are saying it doesn't matter because this *is* already calculus?

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But as soon as it gets into continuous distribution, even something as simple as the Gauss normal distribution (which apparently is supposed to be covered in the new standards?) requires calculus if one wants to understand it and not simply use as a black box equation that fell from outer space and that I can use for plug and chug.

 

Never a stupid question, especially from you. Let me restate, I do not consider myself a statistician.  I am a biologist. And I also have not taught statistics, only done lots of it.

 

In biology, medicine, and economics (at least the questions that I have answered), you are asking if the location of two populations are different or how two populations are associated.  For hypothesis testing, there are numerous tables in the back of any stats book that you can use to determine if your test statistic is greater than the critical value depending on your desired significance levels. These things have already been calculated.  I have never needed to find the exact probability of something happening, which is why I would not have calculated the area under a specific piece of the normal curve. All the probabilities I use reference the standard deviations.

 

I would not suggest that you would never want to take calculus based stats, I am just saying that if you are only going to take one or two classes in your life so that you can understand the news and the important scientific and social questions that face the world today, a large survey of the field (anova, regression, nonparametric, time series, etc) is much more important than a thorough understanding of how the statistics are calculated.  Yes, calculations lead to a deeper understanding, but there is just not time for everything.

 

This is just my experience, and I am happy to agree to disagree.

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If I don't have calculus, all I can do is hand my student a function and say "This is so, believe me".

What am I missing?

That was how one of my high school math teacher who is bad at calculus taught my cohort. Just get the parameters, look up the statistical tables and assume all is good. We kind of figure out the concepts ourselves.

What the student is missing is that it becomes more of a computation problem without the fun of understanding. It also makes it harder for a student to tell if the answer is wrong if the student does not have a rough idea of what the answer might be.

When I was in university, the business admin undergrads get to use SPSS for statistics while the engineering undergrads has to either use the statistics tables or just work it out.

  

 But if a student could understand the big picture as explained for a normal distribution would it really require 1+ years of calculus first before applying it to statistics?  Could some of this be learned even earlier in Pre-Calc perhaps?  Maybe at this point you are saying it doesn't matter because this *is* already calculus?

There is no precalculus where some of us come from :)
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In biology, medicine, and economics (at least the questions that I have answered), you are asking if the location of two populations are different or how two populations are associated.  For hypothesis testing, there are numerous tables in the back of any stats book that you can use to determine if your test statistic is greater than the critical value depending on your desired significance levels. These things have already been calculated.  I have never needed to find the exact probability of something happening, which is why I would not have calculated the area under a specific piece of the normal curve. All the probabilities I use reference the standard deviations.

 

I would not suggest that you would never want to take calculus based stats, I am just saying that if you are only going to take one or two classes in your life so that you can understand the news and the important scientific and social questions that face the world today, a large survey of the field (anova, regression, nonparametric, time series, etc) is much more important than a thorough understanding of how the statistics are calculated.  Yes, calculations lead to a deeper understanding, but there is just not time for everything.

 

This is just my experience, and I am happy to agree to disagree.

 

I do not even think we actually disagree ;-)

Maybe we are simply looking at different goals.

 

(I abhor using any tables or formulas if I do not understand how they are derived, LOL. I would, for example, if somebody talked about "normal distribution",  want to know what the formula for the probability distribution is, why it has this shape, what exactly the coefficient in front signifies, why the one parameter in the exponent is equal to the standard deviation, before I would feel comfortable applying this creature. )

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When I was in university, the business admin undergrads get to use SPSS for statistics while the engineering undergrads has to either use the statistics tables or just work it out.

 

 

I made my sister do her statistics for her masters in Biochemistry by hand. :001_smile:  And there were quite a few of them!  They were, however, nonparametric, so lots of ranking and no calculus.  I told her that she would understand the stats so much better if she was not just reading printouts.  When they asked her about her statistics at her defense, they quit asking once they found out she had done them by hand. 

 

I have definitely considered teaching the calculating of statistics by using nonparametric stats.  My nonparametric class was by far the best, most interesting stats class I ever took.  The calculations were very very easy to do and thus really helped me to understand statistics. I was never buried in the details.

 

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Jetta, its nice to see that love and appreciation for math.  Statistics was fun for me in college.  I can see how those who like math would enjoy its practical nature, even at an earlier age.  Did he find AoPS C&P difficult?  How would its level of challenge compare to AoPS Algebra?

 

Baseball fanatics (like my son) especially love the practical side of stats. ;-)

 

It is hard to answer your question about the difficulty level because we approached these two courses (c&p and algebra) with two very different attitudes. C&P was a semester math elective; my intent for that course was more "exploratory"...to introduce my son to topics he would not experience in the traditional math sequence just to see if something interested him. So with that intention, it was okay if he didn't completely grasp a topic or was not able to work a problem or whatever. I assigned all the regular problems but would let him pick and choose among the challenge problems. So C&P was low-key, low-stress...and thus, highly enjoyable to him. (He is doing Number Theory this year in the same way).

 

Algebra was a different animal. I wouldn't let him move an inch if there was a problem he couldn't work or a topic he didn't grasp. We spent a year and half on Algebra I using 3 different texts (including AoPS). This boy KNOWS algebra inside out backwards forwards. So he might say that algebra was more difficult...but only because his mom was a taskmaster during it. LOL!

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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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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

 

Kareni,

 

Thanks for the tip on that class.  I just looked it up and it looks great including the teacher who worked as a research engineer for 20 years prior to homeschooling!

 

http://www.aphomeschoolers.com/cgi-bin/choose.pl?class=statistics

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Thanks for the tip on that class.  I just looked it up and it looks great including the teacher who worked as a research engineer for 20 years prior to homeschooling!

 

http://www.aphomeschoolers.com/cgi-bin/choose.pl?class=statistics

 

You're quite welcome, Derek.  Carole Matheny is a great teacher.  She also posts here on the board as  Blue Hen.

 

Regards,

Kareni

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I second the recommendation for Carole Matheny's class!

 

My dd added her class as a 4th PA Homeschoolers Class last year--for fun, because it looked interesting against my "better" judgment.  Not only did she absolutely love it, but it has opened up so many doors for her in college.  She was one of only 2 freshman that were allowed to take an honors 400 level economics--intro to stats class last semester.  (She had gotten AP credit for a statistics department course, but not the corresponding econ course)  Mrs. Matheny's course definitely prepared her well for this more mathy statistics course--she definitely had an easier time than most in the course because of having the background in Carole's course.  The professor even encouraged her to continue on this semester with an honors version of his econometrics course he is teaching for the first time this semester specifically so that students can get into the course before senior year.  It is considered mentored research where she will work closely with this professor on an independent research project for the 2nd half of the semester, and the statistics package (stata) that she is using in both courses is apparently an extremely valuable/marketable skill for a kid who wants to get involved with economics research.  

 

There are corresponding statistics courses in many of the social science departments at her university (poly sci, psych etc) that are prerequisites for the upper level research courses, so I can't imagine a more valuable course than AP Stats even outside the STEM track.

 

Blue Hen, if you see this, Kelly says thank you!  There was something you made her learn like the back-of-her hand that resulted in her scoring 26 points above the median on her first quiz (review of probability) in this tough econometrics course!

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I second the recommendation for Carole Matheny's class!

 

My dd added her class as a 4th PA Homeschoolers Class last year--for fun, because it looked interesting against my "better" judgment.  Not only did she absolutely love it, but it has opened up so many doors for her in college.  She was one of only 2 freshman that were allowed to take an honors 400 level economics--intro to stats class last semester.  (She had gotten AP credit for a statistics department course, but not the corresponding econ course)  Mrs. Matheny's course definitely prepared her well for this more mathy statistics course--she definitely had an easier time than most in the course because of having the background in Carole's course.  The professor even encouraged her to continue on this semester with an honors version of his econometrics course he is teaching for the first time this semester specifically so that students can get into the course before senior year.  It is considered mentored research where she will work closely with this professor on an independent research project for the 2nd half of the semester, and the statistics package (stata) that she is using in both courses is apparently an extremely valuable/marketable skill for a kid who wants to get involved with economics research.  

 

There are corresponding statistics courses in many of the social science departments at her university (poly sci, psych etc) that are prerequisites for the upper level research courses, so I can't imagine a more valuable course than AP Stats even outside the STEM track.

 

Blue Hen, if you see this, Kelly says thank you!  There was something you made her learn like the back-of-her hand that resulted in her scoring 26 points above the median on her first quiz (review of probability) in this tough econometrics course!

 

Excellent review, Nancy.  And hearing her enthusiasm and the results in college speak for themselves.  That is really cool regarding those doors opening up for her in the advanced course and potential research exposure!  I had never thought about using the PA Homeschoolers classes that seriously until you both mentioned the stats course here.

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I second the recommendation for Carole Matheny's class!

 

My dd added her class as a 4th PA Homeschoolers Class last year--for fun, because it looked interesting against my "better" judgment.  Not only did she absolutely love it, but it has opened up so many doors for her in college.  She was one of only 2 freshman that were allowed to take an honors 400 level economics--intro to stats class last semester.  (She had gotten AP credit for a statistics department course, but not the corresponding econ course)  Mrs. Matheny's course definitely prepared her well for this more mathy statistics course--she definitely had an easier time than most in the course because of having the background in Carole's course.  The professor even encouraged her to continue on this semester with an honors version of his econometrics course he is teaching for the first time this semester specifically so that students can get into the course before senior year.  It is considered mentored research where she will work closely with this professor on an independent research project for the 2nd half of the semester, and the statistics package (stata) that she is using in both courses is apparently an extremely valuable/marketable skill for a kid who wants to get involved with economics research.  

 

There are corresponding statistics courses in many of the social science departments at her university (poly sci, psych etc) that are prerequisites for the upper level research courses, so I can't imagine a more valuable course than AP Stats even outside the STEM track.

 

Blue Hen, if you see this, Kelly says thank you!  There was something you made her learn like the back-of-her hand that resulted in her scoring 26 points above the median on her first quiz (review of probability) in this tough econometrics course!

 

Nancy,  Thank you so much for sharing this! Your *review* definitely put a huge smile on my face this morning.  I'm not sure what it was that I had her learn in probability like the back-of-her-hand.... perhaps the difference between independent events and mutually exclusive events, or perhaps how to check if two events are independent.  Wonderful, wonderful news.  Congratulations to Kelly too.

 

 

Carole

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  • 3 years later...

 

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 High School math plan.  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?

 

 

Hi Derek.

 

It's been over 3 years since you started this discussion, but since I am considering having my son do statistics next year and calculus his senior year, I wanted to see what you chose to do. Did you have your son take statistics first? If so, would you do it again?

 

Thanks!

Kim

 

 

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Hi Derek.

 

It's been over 3 years since you started this discussion, but since I am considering having my son do statistics next year and calculus his senior year, I wanted to see what you chose to do. Did you have your son take statistics first? If so, would you do it again?

 

Thanks!

Kim

 

Hi Kim,

 

I find it interesting that you found this old thread. I had to re-read part of it to remember the context. In looking it over I am still impressed with the great feedback received from the hive members on this particular topic. In response to your follow-on question, I definitely plan to have our oldest take P&S while in high school. However, as some others have suggested, I am not as concerned about the order. Our son will take AP Calculus next year, then P&S his senior year. Our dds may take it in the opposite order. Regardless, they will all take it during high school because I think its a very important aspect of their education.

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