Teaching statistics before calculus?

[Greg Bernhardt]

Here is a short (and old) TED talk where a mathematics professor suggests we teach stats and probability in depth before teaching Calculus because it's math that is more relevant to a wider range of people. Have we got our math curriculum wrong? Thoughts?

 

[axmls]

I absolutely would love if statistics was taught extensively to every student. In this day and age, where half the news stories out there involve some kind of statistic, it's simply necessary to have a population that understands statistics, sort of like Sagan's "living in an increasingly technological world where fewer people understand technology."

Unfortunately, statistics isn't often taught well. Regardless, it's so important that people be taught when to recognize bad statistics or when it's clear statistics are being used to stretch the truth.

 

[Diaz Lilahk]

Here is a short (and old) TED talk where a mathematics professor suggests we teach stats and probability in depth before teaching Calculus because it's math that is more relevant to a wider range of people. Have we got our math curriculum wrong? Thoughts?

The fundamental issue of mathematics teaching is not the order with which the content is taught but the content itself. By and large the content that is taught is the routine manipulation of ready made functions, regardless of whether it is algebra, geometry, trigonometry, calculus or statistics. The reason that this is the case is that this is the only mathematics which is politically acceptable from the standpoint of our high schools being transcript/diploma mills for entry into college, which is itself a gatekeeper to the corporate workplace. If deeper thought was taught and assessed it leads to outright rebellion on the part of the major stakeholders of the public k-12 enterprise, namely the students and parents. Before long, pressure is exerted on administrators who then transfer it to teachers.

Consider this, our high school Algebra/Pre-calculus courses should be capped off with an extensive treatment of the theory of interest. It is fairly comprehensive in terms of utilizing the mechanics of Algebra and it is even more important to our everyday lives than statistics, so why is it given only the most superficial treatment? It is too difficult and requires a algebraic competency which is beyond the abilities of the vast majority of our students precisely for the reasons stated above.

 

[late347]

Finnish high school curriculum teaches probability and statistics in course, which is situated as a pre-calculus course.

courses for higher math in high school
1.functions and equations
2. polynomial functions
3, geometry
4. analytic geometry
5. vectors
6. probability and statistics
7. calculus I (mainly derivatives, limits)
8. root- and logarithm functions
9. trigonometric functions, and sequences and series
10. integrals

optional courses (advanced courses; if I recall correctly at least one is recommended such as: the eleventh or the twelfth or the thirteenth)
11. number theory, and logic
12. advanced numeric and algebraic methods
13. calculus II (advanced calculus course)
14. rehearsal course

 

[late347]

for the lesser advanced mathematics curriculum in high schools there is also probability and statistics being taught (as far as I know)

1.) Finnish high schools have two math pipelines generally speaking. Regular and advanced mathematics. (unless you are , in a private high school, in which case the curriculum may differ, I think)

2.) Or if you were homeschooled at high school... but homeschooling is more rare in Finland than USA. Kids are allowed to take the high school finals after home schooling, after all.

3. Or if you already chose trade school instead of high school. Trade schools have different curriculum compared to highs schools I think.

 

[chiro]

Teaching statistics properly requires quite some training and the only thing that can be taught is a very superficial view of statistics.

If people are going to interpret statistics properly then they will need a lot more than a one or two semester course on it.

 

[Andy Resnick]

Here is a short (and old) TED talk where a mathematics professor suggests we teach stats and probability in depth before teaching Calculus because it's math that is more relevant to a wider range of people. Have we got our math curriculum wrong? Thoughts?

I've heard of this before, and discussed it with my Math colleagues. There is merit to teaching more/better statistics in High School, no question.

 

[gleem]

Statistical thinking will one day be as necessary a qualification for efficient citizenship as the ability to read and write.
--H.G. Wells

Teaching statistics properly requires quite some training and the only thing that can be taught is a very superficial view of statistics.

If people are going to interpret statistics properly then they will need a lot more than a one or two semester course on it.

Quite so.

Clearly a couple of semester courses in statistics does not make a person a statistician. But at some point as has been previously noted people today must have a basic knowledge of the concepts and methods of statistical analysis. They must appreciate the misuses of statistics , the error in interpretation of data, that correlation does not imply cause and effect and the down right use of statistics to mislead. It is not just about definitions , procedures and formulas. I do not think that a good elementary statistics course with the aim of adequately preparing a person to appreciate the value and danger of statistical inference can be taught by just any math teacher.

 

[Mark44]

In this day and age, where half the news stories out there involve some kind of statistic, it's simply necessary to have a population that understands statistics, sort of like Sagan's "living in an increasingly technological world where fewer people understand technology."

59.3% of all statistics are made up on the spot...

 

[chiro]

I see what you are saying gleem but the thing missing is context.

One can't really have that context without going a bit further and when you have a superficial form of a logic then regardless of how good that logic is it will be interpreted superficially as well.

Take correlation can be different from causation as an example.

The thing of this has more to do with how much variation (and co-variation) exists between the processes and this involves more than just co-variance and correlation.

If people learned this and then said "Well the rule says this so don't believe it" then you have people parroting something they don't understand and using it in ways they don't really comprehend and (which is worse of all) making inferences that they aren't really in a position to make.

One of the worst things you can do for people is give them a superficial, non-comprehensive form of a logic and get them to think that it isn't superficial.

It's a dangerous thing for people to think they know something when they don't and then apply it to the world around them because they will have not enough doubt and way too much confidence and make assertions and inferences that may be out of line for what should be done.

For the above reason I'd rather people just admit they don't understand things as opposed to thinking they did because they took an introductory course and now suddenly they think they can make interpretations on logical systems that they themselves don't understand.

This post is not just for statistics but for any logic and it's a really bad idea to get someone thinking they are an expert when they really aren't in a position to even decide whether they are or not. To really know something takes a lot of work - and that is something small. Encouraging people to think they are in a position to make decisions and comprehend a situation they can't is a dangerous and outright irresponsible thing to do and I certainly would not encourage that myself.

 

[mfb]

For the above reason I'd rather people just admit they don't understand things

Yeah, but how often does that happen if the topic is not directly politics but with political implications?
Knowing that you don't know things needs some education as well. Also the knowledge that you can easily make up statistics that sound great until you look at the details.

 

[Andy Resnick]

<snip>Encouraging people to think they are in a position to make decisions and comprehend a situation they can't is a dangerous and outright irresponsible thing to do and I certainly would not encourage that myself.

That sounds nice and neat but is completely untenable. People go through their day continuously making decisions based on incomplete information, and even more, people engage in many activities of which they are not an expert. Is it irresponsible of me to have a garden, since I am not a master gardener? Of course not.

I suppose you would ban procreation...

 

[chiro]

I'm saying it has to be put in its proper context.

One of the worst things you can do for someones intellect is to get them to believe something they aren't.

Incomplete information always exists and that is a certainty - but that doesn't mean it's an excuse to just say superficial logic is ok.

Politics is a screwed up system anyway and causes so many problems when it comes to decision making so that alone is already bad enough as it is.

If you are gardener you don't want to apply pesticides and weed killer incorrectly since you might kill all of the healthy and wanted plants.

Same thing with statistics - you don't want people taking their new found knowledge and making inferences that would destroy far more truth than it creates.

 

[Andy Resnick]

One of the worst things you can do for someones intellect is to get them to believe something they aren't.
<snip>

Who am I to tell someone who they are or what they can (or can't) do?

Edit- let me elaborate a bit more, because now we are getting to the actual rationale for formal education: evaluation of student efforts by experts. Indeed, I do tell my students what they can or can't do within the context of my class.

Education should not have a 'value'. I realize this is contrary to societal trends during the past several decades, especially in higher education. Currently, a college degree is often treated as a commodity- something that is purchased by a customer, sold by the institution, and confers some sort of value- future job earnings, prestige, etc. When education is treated as a commodity- something that can be bought and sold and has value (monetary or otherwise)- institutions are transformed into service industries with all the concomitant negative associations- customer satisfaction requirements, administrative oversight of academic functions, accountability requirements, etc. Only by resisting the commodification of education can educators truly ensure that students have an opportunity to gain proficiency and master skills.

On one hand, the goal of introducing basic statistics earlier in the math curriculum can be phrased in terms of 'educational commodity' by producing smarter consumers- consumers of *information*. But fundamentally, providing formal instruction of statistics at any level should be the same as any other formal education exercise- student efforts are evaluated by experts. One may be tempted to argue that (for example) a junior-high school teacher is not a sufficient expert to provide proper evaluation, but that's clearly a false argument since with few exceptions, no primary school educator has a PhD degree (or even a MS degree in something other than education).

Educational curricula must be adaptable to accommodate changing needs. One current need is for the adult population to have appropriate intellectual tools to critically evaluate biased information- news feeds, press releases, etc. Schools are in a essential position to provide the necessary evaluations to *prevent* someone from growing up thinking they are more of an expert than they in fact are.

 

[axmls]

One of the worst things you can do for someones intellect is to get them to believe something they aren't.

Is this your view of education? Don't educate, because if you don't teach them enough to be experts, then you've done more harm than good?

Guess I shouldn't have taken any literature classes, lest I fall into the trap of thinking I can have opinions on books without years more of training.

The entire point is that in the modern world, people need to understand at least vaguely that not every statistic they read is the complete truth. They need to know the common techniques used to mislead people.

 

[chiro]

My value is to get people to differentiate the limits that an education can provide.

I'm all for education but when people take it out of context things can go very sour.

Identifying context (which is the main point here) is far more important to having that context retained and it's often lacking in people's minds based on the effort it actually takes to clarify it.

If you don't have that context you create people that think in a more absolute way and that contributes to poor logic, reasoning and inference.

As educated people surely you must understand this.

 

[MarneMath]

My only quam with this is that in my experience, most students end up taking a statistics course before they ever take a calculus course. I think the problem is that if you study STEM, then the inverse is true, so the professor has a view that that is the norm. I, on the other hand, know far more people who have taken Intro to stat methods or business stats or econometric stats, or some other name for stats before ever taking a calculus course (if they ever do take a calculus course).

While I understand completely that there is a portion of students whose end goal is to take calculus in high school, I don't think that ends up being the majority of high school students. I could be wrong though.

 

[chiro]

The calculus is definitely necessary for the calculation aspect but I think most people in this thread are debating the sort of conceptual offerings as opposed to doing the "nitty gritty" stuff you would need to make any sort of real thorough assessment.

If you are wondering how you could do it without calculus you could just get lots of statistical tables and get the student to use them rather than do the calculations with the calculus techniques - and that is exactly what a lot of introductory statistics courses do.

 

[brainpushups]

Today's SMBC reminded me of this thread

 

[gleem]

That may explain why I am such a poor consumer. So are we all (physicists/mathematicians) poor consumers?

 

[BiGyElLoWhAt]

Does not having money constitute being a poor consumer?

 

[mpresic]

I was educated in a NY State high school in the 1970s and we had concepts of probability mostly in our precalculus course after geometry. I enjoy probability but think of the unintended consequences, good and bad. Gambling is fascinating, but do we want students to know you should always split aces and eights when playing blackjack. We can give rise to great poker and dice players.

I am being somewhat facetious but at least the students (and adults) might find out the real meaning of the often misused term "double down". In blackjack, double down means you get one card and you either win or lose based on that one card. You have also put twice the money in the pot. Major political leaders and parties are said to double down when they are reemphasizing the negative attributes of their opposition, and they continue over and over again to "double down" (incorrect usage). If the party was really doubling down, they could only do it once, and their failure would lead to an immediate win by their opposition, This would certainly limit their ardor to double down. Could you imagine one candidate party gambling and losing two consecutive elections (immediately) rather than just one.

Aside over. Probability and statistics can get pretty deep and the professor discusses the move to digital (probability) over continuous (calculus) but probability and statistics treats continuous distributions, as well, for example the ubiquitous and important Gaussian distribution. Because some concepts are counterintuitive, the subject runs the risk of being "touchy feely"; more so than calculus.

I think probability would be fun to teach, and useful. Growing up I knew more adult family members and friends who went to Vegas, than Cape Canaveral/Kennedy. Most often adults tried to convince me to bet on red after black came down 5 times in a row. I reminded them (usually unconvincingly) the roulette wheel still contained the same number of slots for red as black for the next spin. (They wrestled with this puzzle)

By the way do we teach students the Monty Hall problem. We can start a lot of arguments.

I have to disagree about the politics involved in the choice of curriculum. I would like to see linear programming in the curriculum, rudiments of game theory in the curriculum, a little spherical geometry would be good, but the sad truth is there is just to much to teach high school students and choices have to be made. Compound interest is usually taught in the precalculus year when I went to school. Maybe it still is.

At least one does not have to teach, linear interpolation in trig and log tables, as was done when I went to school. Many other topics have been supplanted by the computer and pocket calculator. This frees up some time.

 

[gleem]

Today we have the statistics of polls. What can we teach our children with regard to this seamiling important statistic.

 

[andrewkirk]

Another vote in favour of teaching stats and probability here!

I'm not so concerned about whether it is taught before or after calculus, as long as it is taught! In countries like mine (Australia) where the vast majority of children finish high school, it is only necessary that it be covered before the end of high school. That could be before or after calculus. There are some advantages in doing at least basic calculus first, in order that the notion of expected value and the relationship between PDFs and CDFs can be properly understood.

Of course, in order to teach it, something needs to be dropped, to make way for it. That's easiest in advanced curricula. In my state (NSW), the highest level of high school mathematics has twice the number of contact hours that standard maths has, and includes complex numbers, conic sections, polynomials and advanced integration. Much as I love all those beautiful subjects, I concede that they are used by only a tiny minority of people in post-school life, whereas stats and prob would be of regular use. So it would be easy to swap stats and probability into the advanced maths curriculum.

For standard level maths it would be more difficult, because there are fewer topics that would be uncontroversial to cut. It would depend on what topics were in the curriculum. But I think most study of integration techniques could be dropped. All that's really needed for a high school graduate is to know that it's the reverse operation of differentiation and that it can be used to give areas under curves and other cumulative amounts. Learning all the fancy techniques can be left to university.

 

[bhobba]

Another vote in favour of teaching stats and probability here!

Its what they do in Australia and in the IB program.

It's taught in conjunction with calculus.

Thanks
Bill

 

[houlahound]

I think the norm is in statistics teaching...HAW HAW.

why is the calculation of the average taught to every student on the planet when it is the most misleading measure of central tendency and the median which is more useful typically only taught in electives.

Not sure how accurate that is but on average... Oh too much, cracking myself up.

 

[mfb]

The median can be misleading as well.
If I go purely by the median day, all days are without rain, I never go to the supermarket, and I work every day but never get paid.
Take an average day, and it rains 0.xx times, I go to the supermarket 0.xx times, I work on y% of the days and I get paid on average z Euros per day.

 

[brainpushups]

I'm reminded of Aaron Levinstein's famous quote "Statistics are like a bikini. What they reveal is suggestive, but what they conceal is vital."

If the argument is to teach probability and statistics so that more people can be better at making informed decisions then I think the efforts would be better spent on teaching critical thinking. A few well-constructed conceptual lessons on identifying pseudoscience and bogus claims can go a long way with students. I can imagine that, for students not interested in math or science, that lessons on critical thinking may even have more long-term benefit than an entire course in probability and statistics.

 

[axmls]

A few well-constructed conceptual lessons on identifying pseudoscience and bogus claims can go a long way with students.

This! I have had (high school) teachers that use pseudoscientific (read: completely false) sources when they teach! My school, at least, and many others, have never realized how important it is to teach students the art of healthy skepticism. One lesson on fact checking and skepticism is worth 100 lectures on anything science.

People forget that science isn't a list of facts. It's a way of thinking.

 

[Dale]

a mathematics professor suggests we teach stats and probability in depth before teaching Calculus

That is how it is done in my local public school system.

 

[newjerseyrunner]

I think statistics are more important to the everyday lives of the working class than calculus. Those of us who actually use calculus are few and far between, but everyone should understand the concept of normal distribution and bell curves. The fact that The Lottery is even a business shows a clear need for statistics education in the USA. Gambling is also getting more popular, especially casinos. I think this will be very bad for the society as a whole.

 

[houlahound]

The level of math required for life in the modern world for most people, in fact the vast majority is very basic.

Neither of my parents went to high school, my grandparents never went to any school. They all own or owned investment properties, ran businesses ... lived very well indeed.

My dear ol mother just this month designed a beautiful kitchen with a tape measure and computer and hit the submit button. Done it dozens of times. She buys and sells property, houses any shares. Does not know what calculus or algebra are. Only knows basic arithmetic.

it is a well built, well equipped modern kitchen you will find anywhere. Arrived on a truck in flat packs and was assembled easily and every measurement was perfect.

The hardest part was choosing the colours.

Educators IMO way overstate the level of math required for the life in today's society.

 

[bhobba]

People forget that science isn't a list of facts. It's a way of thinking.

That was Feynmans lament.

Students were often taught rote answers rather than how to think with it.

The IB program really tries hard to reverse that, but I don't know of others.

Thanks
Bill

 

[bhobba]

I think statistics are more important to the everyday lives of the working class than calculus.

True.

But like a Foreign Langauge the thinking skills it enhances is of value.

I like what the IB program does and what we do here in Australia - its taught together. We have a separate math stream for those that do not want to do calculus, but personally I would discourage students from taking it. Already there is concern where I am far too many people are taking the soft option. Universities have even had to change the way they teach stuff eg in economics a bit of calculus makes teaching some things easier but since students don't have it they have to go the less elegant route. When I did HS everyone almost without exception did calculus - even those in the arts stream. Now its a lot different and IMHO its a worry.

Thanks
Bill

 

[Dr. Courtney]

In the US there is a tension between producing more scientists, engineers, and medical professions on the one hand and providing a better general math education to all the other professions.

All scientists, engineers, and medical professionals (at the dr level) need calculus and physics. The inability to pass calculus and physics is a huge bottleneck in the number of graduates who can move on into these fields. The lack of STEM grads is more likely to have an economic impact than the suboptimal abilities of other folks in stats.

While it may make sense to throw stats at all the other majors, STEM majors (including pre-med, pre-vet, pre-pharm, and pre-dental) really do need calculus.

And in the physical sciences and engineering, they really need calc-based stats, which means they need calc first.

 

[bhobba]

And in the physical sciences and engineering, they really need calc-based stats, which means they need calc first.

Well said.

I did my degree part time while I did a pretty dead end job in the public service. It didn't really worry me but some people I knew thought my talents were being wasted and every now and then would contact people in the PS hierarchy and I would pop up for them to look at my qualifications.

I well remember one guy looking at my subjects and he saw Mathematical Statistics 1A, 1B, 2A, 2B and said what's that? Do you do things like the t-test? Of course. Then what is this mathematical thing? Its code-word for uses calculus. His eyes glazed over and said I need to speak to someone. He went away then came back and said - not sure if that's of any value here. I internally shook my head but didn't say anything. As soon as I finished my degree left for elsewhere. Sad really.

Thanks
Bill

 

[Astronuc]

Here is a short (and old) TED talk where a mathematics professor suggests we teach stats and probability in depth before teaching Calculus because it's math that is more relevant to a wider range of people. Have we got our math curriculum wrong? Thoughts?

There are some applications of probability and statistics that can be addressed with algebra, e.g., counting discrete events of a finite population such as the number of coin tosses that are H or T, or roll of a die, or dice, and the probabilities of the number of times a number appears, or a combination of numbers appears.

https://www.mathsisfun.com/data/
https://www.mathsisfun.com/data/probability.html

At some point, calculus is necessary in order to deal with probability theory and continuous distribution, probability density functions and so on.

I remember learning a little of chance or probability in 4th grade science (genetics) and later in 10th grade biology, which was a year before I took a formal calculus class. I had actually bought a book on calculus in 10th grade and was studying it on my own, with my father's encouragement. It was clear to me that I needed calculus to study physics.

 

[Dale]

Several posts about the anti-vaccination crowd have been deleted. Please keep the discussion polite and do not reopen the anti-vax topic in this thread.

 

[Loowee]

Here in the Philippines, the K-12 curriculum was launched nationally only last month (June 2016). In the current curriculum, kindergarten students are introduced to statistics and probability concepts. The topics build up slowly from grade to grade culminating in combinatorics in grade 10. Calculus is taught beginning grade 11 culminating in integral calculus in grade 12. That looks good on paper. I sure hope the private schools that dared to open senior high (grades 11 and 12) are up to the challenge. Public schools have to offer senior high whether they like it or not. Before the advent of K-12, high school was only up to fourth year (grade 10). Grades 7 to 10 are now called junior high school.

We Filipinos usually think that (our) public schools are not good, with a few exceptions like the University of the Philippines. Private schools have a better reputation. I came from a rotten private school (with no reputation at all).

When I was in my beloved but rotten high school, we studied algebra in the second (grade 8) and fourth (grade 10) years; statistics, business math and taxation in the second year; geometry in the third year; and trigonometry in the fourth year. My alma mater was a Chinese school until 2000. In 2001, the Chinese curriculum was removed and the school became exclusively English. In the Chinese curriculum, calculus was taught along with trigonometry in the fourth year. I never learned calculus in high school because I did not take the Chinese classes.

Two of my nieces migrated to Canada when they were 5 and 6. My sister, their mother, was surprised that Canadian children could not read well at that age. I was surprised as well. I expected more from a developed country. Socialization is more important than learning to read at a young age in a developed country to produce well-rounded people.

Educated Filipinos (allow me to emphasize “educated”) learn to read and do arithmetic at an early age. That is why I was against the K-12 curriculum which seems to be the standard worldwide.

Some schools (in any part of the world) teach advanced subjects which the majority of schools do not include in their curriculum, e.g. graduate-level subject in an undergraduate degree. Are these early “inductees” better than the regulars?

I searched the Net for a federal K-12 standard but so far found only the standard course of study of mathematics for North Carolina public schools. North Carolina already has statistics and probability by the sixth grade. As proven by earlier poster/s to this thread, statistics is taught in a number of American high schools before calculus.

Look at us Filipinos. Our beloved country, the Philippines, apparently has had a relatively high standard of language and math education long before K-12 rocked our education budget, yet our country is poor. The Philippines remains one of the most corrupt countries in the world. Make no mistake: I may pass on malignant remarks about my country, but I will always love her more than any other in the world.

Is it really that important which math is taught first in your country? I expect there is corruption anywhere even among your ranks. However, I do love the creed you live by, “that all men” – and women – “are created equal…”

It is good that schools in countries like ours are given the freedom to choose which subject to teach first.

If I were to choose though, I would choose statistics first, not because local curriculum made me take it first anyhow, but because statistics is more practical for any citizen, with or without a college degree – this essentially quotes “it's math that is more relevant to a wider range of people.”

I do not mean to lecture. Just my two cents. Thank you for the indulgence.

 

[Dr. Courtney]

I do not mean to lecture. Just my two cents. Thank you for the indulgence.

I appreciate the level of detail and the personal insights. And I never mind a bit of preaching from the heart.

My view is somewhat skewed from having served in an administrative position at the Air Force Academy that had a close-up view of our nation's need to improve STEM education and especially STEM majors.

Lack of stats is not the bottleneck in producing the needed numbers of STEM majors. Lack of Calculus (and good enough pre-calc to succeed in Calc and Physics) is the bottleneck. Many more aspiring majors and careers in science, engineering, and medicine are stopped cold by the inability to succeed in Calculus and Calc-based Physics than weaknesses in stats.

 

[Diaz Lilahk]

Lack of stats is not the bottleneck in producing the needed numbers of STEM majors. Lack of Calculus (and good enough pre-calc to succeed in Calc and Physics) is the bottleneck. Many more aspiring majors and careers in science, engineering, and medicine are stopped cold by the inability to succeed in Calculus and Calc-based Physics than weaknesses in stats.

Yet again, I think we should be a little careful with this. In the high school where I teach there is a drive on the part of students to get to BC Calculus as quickly as possible. The ultimate goal is to complete it by the end of junior year so that they can have it on their transcripts and since no one gets below a B, well then they have among "the most rigorous courses" on their transcripts with a pretty decent grade. What I have observed as a teacher of algebra and calculus based physics of these students is that their calculus knowledge is extremely superficial and their knowledge of algebra, geometry and precalculus is the same. The problem solving skills are practically non-existent. What is worse is that they see themselves as being successful in mathematics. Very few of them are actually prepared for a rigorous STEM major unless they are willing to acknowledge and fill in a lot of gaps in their knowledge. I would argue that they are far better off getting a rigorous pre-calculus education involving proofs of elementary algebra, geometry and trigonometry accompanied by sophisticated problem solving, ala https://www.amazon.com/dp/0395524326/?tag=pfamazon01-20 than they are having a standard calculus course.

 

[Dr. Courtney]

Yet again, I think we should be a little careful with this. In the high school where I teach there is a drive on the part of students to get to BC Calculus as quickly as possible. The ultimate goal is to complete it by the end of junior year so that they can have it on their transcripts and since no one gets below a B, well then they have among "the most rigorous courses" on their transcripts with a pretty decent grade. What I have observed as a teacher of algebra and calculus based physics of these students is that their calculus knowledge is extremely superficial and their knowledge of algebra, geometry and precalculus is the same.

Yeah, I agree. When I was on the USAFA faculty, we saw lots of students with As and Bs in AP Calculus who could not even pass the pre-calc exam and get placed in Calculus.

Grade inflation is horrible, and every high school teacher who awards As and Bs in AP Calc who shouldn't even be in the course should be fired for fraud.

I'm talking about students needing real mastery, not a grade in a course.

The problem solving skills are practically non-existent. What is worse is that they see themselves as being successful in mathematics.

Yeah, I've had a lot of students get to my physics courses who could not even solve algebra based kinematic problems (projectile motion, etc.) yet they thought they were good at math because of their high school grades. But the fraud of the teachers who passed them does not remove the real need for competence in Algebra, Trig, and Calculus. I stopped confusing real competence with having passed courses a decade ago.

Very few of them are actually prepared for a rigorous STEM major unless they are willing to acknowledge and fill in a lot of gaps in their knowledge. I would argue that they are far better off getting a rigorous pre-calculus education involving proofs of elementary algebra, geometry and trigonometry accompanied by sophisticated problem solving, ala https://www.amazon.com/dp/0395524326/?tag=pfamazon01-20 than they are having a standard calculus course.

There is no need for Calc in high school. I believe a 30-35 on the ACT in math much more than a grade in any high school course, including AP Calc. But I've known high schoolers to score in this range on the ACT in math with nothing more than an honest and rigorous Algebra 2 course.

 

[Diaz Lilahk]

Grade inflation is horrible, and every high school teacher who awards As and Bs in AP Calc who shouldn't even be in the course should be fired for fraud.

Who will do the firing? The very people who encourage and endorse the behavior. I think you are largely blaming the wrong people. I know personally that the only grade which I hold a line on is an A+ and to a lesser extent an A, below is my grade distribution for my AP Physics courses this year - pay close attention to the number of drops. Every other letter grade should be a full grade to two grades lower, and everyone below a B should have failed the course.

Grade Total
A+ 3
A 9
A- 10
B+ 9
B 8
B- 9
C+ 3
C 1
C- 0
D+ 0
D 0
D- 0
F 0
Drops 30

Now you have to realize that my grade distribution was not politically acceptable particularly the number of drops and I was told point blank to decrease the rigor of my course and that my grades were too low. Had these students actually earned the grades they deserved, there is no doubt in my mind that I would have been fired this year, and I still may be fired next year. Now you can argue that I should just walk out, but I can tell you that it is the same if not worse elsewhere. In fact, in all the places this is the school where I had the most academic freedom. Furthermore, I am without question considered the toughest teacher in the department when it comes to content and grades and have had the reputation of being an extremely tough teacher in every place that I worked. The problem is at a higher level and I really think a lot of this could be solved if admission offices required submission of AP tests/scores. Another thing that needs to happen and if teachers were forced to submit their final grades to the College Board to audit and run a correlation between AP scores and student grades, schools AP programs would then be put on probation if there is a large disparity.

Anyhow I want to tie this back to the original thread, which is teaching statistics before calculus. I think it is really important for someone like the person who gave the Ted talk, Arthur Benjamin, to spend a few years as a high school math teacher so that he can get an idea of whether this type of proposal would have any impact at all.

 

[Dr. Courtney]

Who will do the firing? The very people who encourage and endorse the behavior. I think you are largely blaming the wrong people. I know personally that the only grade which I hold a line on is an A+ and to a lesser extent an A, below is my grade distribution for my AP Physics courses this year - pay close attention to the number of drops. Every other letter grade should be a full grade to two grades lower, and everyone below a B should have failed the course.

Grade Total
A+ 3
A 9
A- 10
B+ 9
B 8
B- 9
C+ 3
C 1
C- 0
D+ 0
D 0
D- 0
F 0
Drops 30

Now you have to realize that my grade distribution was not politically acceptable particularly the number of drops and I was told point blank to decrease the rigor of my course and that my grades were too low. Had these students actually earned the grades they deserved, there is no doubt in my mind that I would have been fired this year, and I still may be fired next year. Now you can argue that I should just walk out, but I can tell you that it is the same if not worse elsewhere. In fact, in all the places this is the school where I had the most academic freedom. Furthermore, I am without question considered the toughest teacher in the department when it comes to content and grades and have had the reputation of being an extremely tough teacher in every place that I worked. The problem is at a higher level and I really think a lot of this could be solved if admission offices required submission of AP tests/scores. Another thing that needs to happen and if teachers were forced to submit their final grades to the College Board to audit and run a correlation between AP scores and student grades, schools AP programs would then be put on probation if there is a large disparity.

Anyhow I want to tie this back to the original thread, which is teaching statistics before calculus. I think it is really important for someone like the person who gave the Ted talk, Arthur Benjamin, to spend a few years as a high school math teacher so that he can get an idea of whether this type of proposal would have any impact at all.

I feel your pain. I've suffered a couple non-renewals of my contract because I would not bow to pressure to pass students who did not deserve to pass and otherwise refused to gift grades. I've known other physics and math teachers who experienced the same thing. No doubt the admins who pressure faculty bear the greater guilt, but my conscience has never allowed me to trade unearned grades for a paycheck.

The phenomena is widespread, but it is not ubiquitous. I can say with great certainty that there was no gifting of unearned grades (or pressure to do so) when I taught at the United States Air Force Academy, and my wife has the same experience and testimony when she served on the Physics faculty of the United States Military Academy (West Point). A very dear longtime friend bounced around quite a bit due to his refusal to award unearned grades, but now he is happily teaching (Math and Physics) at a special school for math and science and reports that there is no pressure to gift grades at his current institution.

Who will do the firing?

A few years ago, my wife and I realized that as parents, we had to do it, and the only way to ensure a quality education in science and math for our own children was to pull them from the public schools and home school them.

It has taken some effort (and is still dicey), but we've also had some success finding good teachers (for our teens) in college dual enrollment programs who maintain a high level of academic rigor and do not seem to be gifting grades.

But if grades are routinely gifted, the discussion of Calculus vs. Stats is arranging the deck chairs on a sinking ship.

 

[houlahound]

I perceive a real pressure at the undergraduate level to get and keep butts on seats even at the expense of what is best for the student long term, the economy, the course quality...etc.

Faculties want to exist, to exist they need butts on seats.

There are accusations around that some universities let the standards slide downhill to capture full fee paying in advance foreign students, it is seen as a special market that raises revenue to subsidize the fees of domestic students and creates cash for infrastructure and research.

Of course I doubt any uni admins would agree.

 

[Dr. Courtney]

I perceive a real pressure at the undergraduate level to get and keep butts on seats even at the expense of what is best for the student long term, the economy, the course quality...etc.

We address this issue in some detail in this paper:
https://arxiv.org/ftp/physics/papers/0612/0612117.pdf

Abstract: As education systems move toward business models of operation, there is a strong tendency to misidentify the student as the customer. Misidentifying the student as the customer leads to interpretation of the course credit or degree as the product. The true product is the additional knowledge, skill, and ability that course credit and degree should represent. Consequences are potentially disastrous, because the notion that “the customer is always right” can lead to the perceived product (course credit or degree) meeting the desires of the misidentified “customer” (student) rather than the real product (value added to student) meeting the standards of the properly identified customers (future employers and taxpayers).

Faculties want to exist, to exist they need butts on seats.

Sure, but they do not need the absolute maximum numbers of butts in the seats.

My experience is that holding the line on academic rigor is a game of chicken. Once students realize they really need to work hard to reach their grade goals, they will work hard and earn the grades. But they will avoid working hard until they are really convinced they need to. Sometimes, a faculty member needs to have high rates of Ds, Fs, and Ws for a semester or two until word gets around and the students start working.

There are accusations around that some universities let the standards slide downhill to capture full fee paying in advance foreign students, it is seen as a special market that raises revenue to subsidize the fees of domestic students and creates cash for infrastructure and research.

This is part of it at some schools. But at other schools, it's a simple numbers game: the state money to the school depends on the number of students in the seats. If there are other nearby schools (driving distance) that will gift grades, a school that won't gift grades will lose enrollment and dollars to the ones that will.

 

[Dale]

Can we bring this back around to statistics vs calculus rather than a generic critique of the education system?

 

[houlahound]

Statistics is a huge field, can someone post specific topics in a logical order, would you include the null hypothesis, what year level.

Is mathematics modeling statistics? It forms the basis of almost all gov public policy that affects everyone.

 

[Andy Resnick]

Statistics is a huge field, can someone post specific topics in a logical order, would you include the null hypothesis, what year level.

Is mathematics modeling statistics? It forms the basis of almost all gov public policy that affects everyone.

I think the Common Core curriculum lays it out very well, the 'null hypothesis' is introduced in 6th grade and Baysean methods are discussed in High School:

Kindergarten: Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

1st grade: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

6th grade: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Summarize and describe distributions.

7th grade: Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models.

8th grade:Investigate patterns of association in bivariate data.

High School: Summarize, represent, and interpret data on a single count or measurement variable. Summarize, represent, and interpret data on two categorical and quantitative variables Interpret linear models. Understand and evaluate random processes underlying statistical experiments. Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Understand independence and conditional probability and use them to interpret data. Use the rules of probability to compute probabilities of compound events. Calculate expected values and use them to solve problems Use probability to evaluate outcomes of decisions.

 

[Dr. Courtney]

I think the Common Core curriculum lays it out very well, the 'null hypothesis' is introduced in 6th grade and Baysean methods are discussed in High School:

Kindergarten: Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

1st grade: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

6th grade: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Summarize and describe distributions.

7th grade: Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models.

8th grade:Investigate patterns of association in bivariate data.

High School: Summarize, represent, and interpret data on a single count or measurement variable. Summarize, represent, and interpret data on two categorical and quantitative variables Interpret linear models. Understand and evaluate random processes underlying statistical experiments. Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Understand independence and conditional probability and use them to interpret data. Use the rules of probability to compute probabilities of compound events. Calculate expected values and use them to solve problems Use probability to evaluate outcomes of decisions.

What percentage of students who will pass the assessments for these learning objectives do you reckon will really be competent with them?

I see a lot of very good standards in science and math. But then I see most students who reach college with high grades in each subject nowhere near the level of competence their grades would indicate.

Coursera and ALEKS both have excellent statistics courses that I've overseen high school students taking.

I would trust success in those to have actually delivered mastery of the learning objectives (outlined above) much more than I would trust the competence of most students coming out of a common core assessment framework.