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I agree in principle that statistics education should be given to all students. The problem I have with the proposal is that I have very little confidence that
by chongli 3y ago
I agree in principle that statistics education should be given to all students. The problem I have with the proposal is that I have very little confidence that teachers are prepared to provide a rigorous and thorough statistical education.
For an example, the replication crisis in the social sciences. These studies, containing flawed statistics, are carried out by social scientists with PhDs who have been required to take courses in statistics designed for their discipline.
If they can’t get the statistics right, how can we expect it from teachers with far less education?
- klodolph 3y ago> If they can’t get the statistics right, how can we expect it from teachers with far less education? Because it’s their job—and if the statistics curriculum is mandatory, then the teachers might spend inservice days developing statistics curriculum, going to workshops to learn how to teach statistics, etc. Teachers will develop statistics curriculums and share them with each other. With NSF grants, you can fund teacher outreach programs, put statistics exhibits in science museums, etc. A lot of teachers will struggle to teach various subjects. That’s why we have support networks in place, to help develop curriculums and provide training for teachers. I know that the support network has a lot of problems—but many teachers would struggle to teach, say, biology, history, or algebra, too, without support.
- chongli 3y agoI think what's far more likely is that the curriculum-writers will see it as an opportunity to dumb down the math. They'll make it into a very basic course on study design and data collection, with a handful of descriptive statistics thrown in so the students have something to do with their scientific calculator's STAT mode. Will they teach discrete and continuous probability distributions? The binomial, Poisson, and normal distributions? Dependent and independent random variables? Bayes' Theorem? Measures of statistical significance and hypothesis testing? Chi-squared and student-t distributions? Confidence intervals and p-values? Maximum likelihood estimation? Highly doubtful, since many of those topics are built on top of university-level calculus.
- vgatherps 3y agoPeople who have some understanding of study design and data collection would be in a much better spot to understand and interpret day-to-day news / “information flood” than those who have done a lot of calculus-based probability. You can go all the way through rigorous measure-theoretical probability and come away with almost nothing useful for interpreting a study. Most problems I see with moderns statistics aren’t of the form “ohhh, they fooled you by using a subtly wrong statistical metric to ascribe significance” but “the way the data was gathered/interpreted is fundamentally wrong and made to mislead”
- dr_dshiv 3y agoSome of the problems come from statistics itself. “All models are wrong, but some are damn hard to interpret.” Let’s make that a corollary to Box’s statement about the utility of models. Why does so much statistical analysis take place without even an expectation of human comprehension? It’s just magical sigils for most papers. Many midlevel statistical practitioners suffer from a holier than thou complex, where a “correct” approach to statistical analysis might buy a little more precision at the expense of a lot of comprehension. Box plots or Bar charts with error bars, using randomized data collection. That’s like 90% of the interpretive value right there. Statistics is a UI for math and it could use improvement if we expect so much from it. See Brett Victor’s “Kill Math” for more context on why we should expect more from our mathematical interfaces. http://worrydream.com/KillMath/ http://worrydream.com/KillMath/
- cutemonster 3y ago> "Math" consists of assigning meaning to a set of symbols, blindly shuffling around these symbols according to arcane rules, and then interpreting a meaning from the shuffled result. The process is not unlike casting lots. Form that Brett Victor. Wow
- cutemonster 3y ago@dr_dshiv Edit: Sorry about the bad quote, I should have included the prefix "When most people speak of Math ...". And the negative comment about the blog post. Now I've read / skimmed all of it and it was interesting, I hope the new methods he wants to use for teaching maths will work fine. (I'm sceptical, but still seems like worth to give it a try.) I think his project title does his project a disservice: "Kill maths"? That sounds silly to me. And how it starts -- I got annoyed and stopped reading (until I went back two days later). Another more positive project title maybe could be "Maths for everyone" or "A new approach for teaching maths"?
- wisty 3y agoThis is kind of like blank slate thinking though. Not all topics are equally easy to teach and assess in a deep way, with limited time and resources. Statistics is IMO a lot like security. Unless it's at a very high level, just follow a basic check list and don't do anything creative. Calculus is more like algorithms - you can get to deep and creative levels at an earlier stage.
- jampekka 3y agoA big problem is that people do creative stuff but use the basic check list.
- dv_dt 3y agoIf we decide that statistics are more necessary in earlier education there is nothing stopping us from building a system with more teacher training for stats education.
- mp05 3y agoMy first real stats course was a 300-level engineering stats class that kicked my ass pretty well. The class had a calc 3 prereq I found the computation generally the easiest part. Truly grasping the topic takes patience and work but it's pretty rewarding. That said, it must be difficult to find genuinely insightful instructors who can make the material remotely interesting because good god it's necessary.
- KMag 3y agoSorry, what's calc 3? I wasn't aware there was a standard linear progression of calculus courses. Is "calc 3" complex variables? Diff Eq?
- Jensson 3y agoI think Americans do calc 1 which is the basic derivatives and integration you typically learn in high school, then calc 2 which is more like a college calculus course, then calc 3 is multi variable calculus.
- KMag 3y agoI don't recall if multivariable was pushed in at the end of my differential and integral calculus course or at the beginning of my differential equations course. It's possible it was also somehow tucked into my linear algebra course (though, I doubt it). In any case, we did cover multivariable as a pretty straightforward extension of single-variable calculus, without making it a separate course. Do I likely have some huge blindspot as a result of not spending a full course on multivariable calc? (All of my formal education was in the U.S., for what that's worth. Though, it was an accelerated magnet program teaching middle school students algebra and trigonometry and covering geometry, calculus, linear algebra, and differential equations in high school.)
- Jensson 3y agoDid you cover Jacobian matrices and how to to calculate and classify local extremes in a multivariate function? Do you remember saddle points? If not you did miss multivariate. The main thing you lose then is you don't know how to apply calculus on non linear coordinates like spherical coordinates and so on. It is useful for data analysis if your data is easier to work with after a non linear transformation, but if you don't work with that sort of thing then probably not very useful.
- anonylizard 3y agoTeachers not being skilled enough for a high school subject is not a problem in 2023. By the time the curriculum gets reformed, it'll be like 2025. By which time students can ask GPT5 for any statistics question. Statistics is so unbelievably broadly useful at low levels, compared to calculus. Understanding 1. Selection bias 2. Normal distribution + standard deviation 3. Central limit theorom Is a massive help in modern society. You don't even need any math equations, just understanding them on a rough conceptual level would help.
- steve_gh 3y agoAnd you think GPT-5 will be trustworthy on any contentious issue?
- bluescrn 3y agoPerfect for schools aiming to indoctrinate rather than educate. If we encourage them to let AI do their thinking for them, there's much less need to worry about wrongthink...
- ykonstant 3y ago>By which time students can ask GPT5 for any statistics question. Will students get unlimited free access to GPT5?
- blharr 3y agoGPT4 is already well above the level of reliability and accuracy of any of my high school teachers.
- CrazyStat 3y ago> For an example, the replication crisis in the social sciences. These studies, containing flawed statistics, are carried out by social scientists with PhDs who have been required to take courses in statistics designed for their discipline. > If they can’t get the statistics right, how can we expect it from teachers with far less education? This isn’t really a statistics education issue, much like Enron wasn’t an accounting education issue. Social scientists abuse statistics because the incentives are all aligned with abusing statistics. To get a good job you have to publish lots of papers. To publish you have to have statistically significant results. To get into top journals you need surprising results. You see other people in your field playing fast and loose with their data and getting rewarded for it. Why not exclude that one problematic subject from your data analysis? Without them the p-value (from a regression on a carefully chosen eight of your eleven measured variables) drops to .038, and you can publish... It’s not that nobody thought to teach the scientists about corrections for multiple comparisons or the dangers of picking observations to exclude as outliers based on what gives you the result you want. They learned all those things. But it’s so much harder to get results when you’re not willing to play games with the data, and they need results. The people who do try to play by the rules wash out, either by choice after getting fed up with the fraud they see all around them or by failing to publish N papers in top journals.
- chongli 3y agoWhy aren't we cleaning house? If the social sciences are roughly comparable to Enron then shouldn't they suffer the same fate?
- CrazyStat 3y agoIt’s like a country where bribery is endemic. Everybody’s used to it, it’s just the way things work. It’s very hard to stamp that out.
- verall 3y agoEnron left millions of people without power while poor social sciences research convinced millions of people that priming is real. They're both wrong but I'm not sure they're so comparable
- Arnt 3y agoThinking back to my own statistics at university… how do you even teach statistics without a lot of other math first? Analysing data is similar. I'm all for it, it's clearly useful on the days when my main working tools are slack and powerpoint, but it's not clear to me how teach that without math. One of my math textbooks even had the word "analysis" in its title. ("Calculus and analytic geometry" perhaps?)
- seanhunter 3y agoYou can absolutely teach basic statistical literacy without too much other maths and certainly without any higher maths. That’s how it’s done in schools in other countries - for example here is the statistics component of the maths GCSE for one of the exam boards in the UK (the others will be similar) https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300/subject-content/3.6-statistics https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics... GCSE starts after the third year of secondary school in the UK so most people will have completed their GCSE in the year they turn 16. Then 16-18 year olds wanting to study STEM subjects go on to do maths A-level, which includes more topics that in the US would be considered precalc as well as some calculus, more probability and statistics and some mechanics. Here’s the A-level syllabus from the same board. As you can see, for stats it includes distributions and hypothesis testing, so much more depth https://www.aqa.org.uk/subjects/mathematics/as-and-a-level/mathematics-7357/specification-at-a-glance https://www.aqa.org.uk/subjects/mathematics/as-and-a-level/m...
- steve_gh 3y agoA level maths is not a necessity for all STEM courses. My daughter is doing AS maths (half way between GCSE and A level, heavily weighted to stats), alongside A levels in Biology and Chemistry (and one non science A level)
- seanhunter 3y agoAah I forgot about AS levels actually. Best of luck to your daughter.
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- hn_throwaway_99 3y agoTo be honest, I'm not that concerned with high schoolers needing "a rigorous and thorough statistical education." I'm more concerned with the populace at-large being able to understand and apply fundamental statistical concepts. For example, another commenter mentioned Bayes Theorem, and how it's a very powerful idea and not that difficult to grok. Related, predictive value positive and negative, and how they are calculated from (but also very different from) sensitivity and specificity, are extremely valuable concepts to understand. To what you point out, I think the concept of "p-hacking" is super important to understand, but I'd be less concerned about a student needing to hand-calculate the steps to run a t-test (that's what a college-level class is for). That said, I decided to look up T-test on Wikipedia while writing this comment, and I found this interesting tidbit. Great example of the applicability of statistics, and something that I think would peak the interest of many high-schoolers: > Gosset had been hired owing to Claude Guinness's policy of recruiting the best graduates from Oxford and Cambridge to apply biochemistry and statistics to Guinness's industrial processes.[13] Gosset devised the t-test as an economical way to monitor the quality of stout.
- sokoloff 3y ago> If they can’t get the statistics right, how can we expect it from teachers with far less education? I’m unconvinced that the incentives pull them towards “better use proper statistical methods” or penalize them when they don’t. This is, IMO, not insufficient education; if it’s not, the premise that math teachers given incentives to get it right couldn’t accomplish it because they have less education than a PhD sociologist is flawed.
- bhelkey 3y agoI imagine that those social scientists would have had a better understanding of statistics if they took stats in highschool.
- Natsu 3y agoI'm thinking we should teach more people do-calculus, to make stats less confusing by breaking the symmetry between observations and interventions.
- alexashka 3y agoNothing in highschool is rigorous or thorough.
- SwedishExpat 3y agoMy wife is an academic and is repeatedly raising the issue of the replication crisis in medical fields too. This is an issue across all of academia and isn't just an issue with flawed statistics but pressures to publish, a lack of replication in the peer review process, a lack of replication by subsequent work building on that original research, using more tools like Machine Learning, etc... Metascience is a growing field at many top universities because of this issue and the belief that modern science may be very flawed right now.
- stillwithit 3y agoLectures are cheaper than actual education. So we ram language constructs into people’s brains, which we started doing centuries ago to preserve knowledge. Yet it comes with none of the warnings by the long dead mathematicians who initially built out statistical tooling[1]. Statistical tools are intentionally crude to help communicate the complexity of stats and yet we build society on crude leaky abstraction. Not out the obvious day to day right in front of our faces. Modern science isn’t flawed. Society is. Boomers and GenX are proper gold star for nothings who lucked into living in the only country that could manufacture anything after WW2. They dismantled the New Deal that propped them up and made us their serfs. They didn’t fight the war or build the economy. They have no muscle memory for doing anything “real”. They went to college (much less rigorous in the 50-70s), memorized the cliff notes and recited the catechisms. Neither generation struggled materially as any generation before them (yes yes distributions, ranges, gradients of truth; relative to material conditions before 1950s). New generation comes along with no awareness of that time and doesn’t feel much obligation to status quo. GenX and Boomers are big mad about it, never mind they walked away from religious life. This time the future will stick to our script. Society wants less to do with their hyper industrialized life due to war time manufacturing habits they had rammed down their throats by a much more imperialist society of decades gone. We keep letting people who cheered on conquest of other countries to stay ahead of them keep running things. Everyone is too apathetic to tell grandpa it’s time for hospice. We let elders implicitly engage in ageism against youth. Everyone is acting shocked the old warlords are looking for idiot soldiers to serve their fiefdoms? All they knew for their formative years was war time …hustle. Embedded deep. Stop with the meta bullshit. Day to day life is just this. The abstract mental models are not helping. They’re distractions apathetic people escape into to avoid reality. Boomers down to apathetic centrists who love their material privilege despite the environmental toll… this culture is a joke [1] Willful Ignorance: The Mismeasure of Uncertainty https://a.co/d/agWe8LT https://a.co/d/agWe8LT