Oddbean new post about login | logout The subtext is that statistics is somehow "easier" than calculus since it's more connected to the "real world" -- But, nothing about real world problems is easy. Real world problems are harder, require more experience, more analysis, are less susceptible to canned techniques and strategies. And more importantly it's hard to really understand much about statistics without knowing some calculus. Not a popular opinion. I know. 2/
But there is an even more fundamental danger in trying to quickly pull away from calculus to some other math subject as the "capstone" of most programs. I don't think many of the people considering the change understand the magnitude of what they are trying to do. Calculus has been refined and developed as subject for math education for decades and decades. From theory to problem sets huge sets of material have been refined by thousands of people-- stats isn't so well developed. 3/
If the argument is that stats ought to be that well developed I agree. I also think that working with data sets, and reading data presentations should be a bigger part of social sciences education, and science education. But it's not like there is a fully formed educational version of statistics that exists that could be dropped in to replace all the things that calculus is trying to do... at the moment. 4/4
Cue the Texas Board of Education banning calculus as woke and a yuge downer to their own peculiar style of grade inflation. @134318c2
@97401183 Calculus is basically "banned" at the schools most working class kids attend. It's why colleges must absolutely NOT assume that a high school grad ought to know it already. And I get pretty mad when they do.
@134318c2 Why isit banned? What is the consequence if a child learns it and violates the ban? @97401183
@b05df304 @134318c2 @97401183 I think that "banned" is the wrong term to uses in most school districts. They simply lack the capacity to teach advanced math, including Calculus, even if they thought it was important and wanted to do so. Starting with early grades, they think of math as a series of drills to be memorized. Who would teach the needed abstract reasoning concepts? It is the lefty liberal districts, that do have some math capable teachers who do actually ban access to higher level math. They do so because they are worried about "gaps", the early sorting of students into high and low math tracks, a practice that disproportionately disadvantaged Black and Latino students and made it harder for them to access advanced courses down the line. If you prohibit Algebra until 9th grade, some students are either getting outside supplementation, or they are being slowed down. Opportunities to burst forward are also not accessible. https://www.edweek.org/teaching-learning/san-francisco-insisted-on-algebra-in-9th-grade-did-it-improve-equity/2023/03 Of course the issue isn't just school sorting, it is social and educational privilege that enables some families to provide their offspring with enriched environments, starting at the preschool level. It is hard to create catch up opportunities in public schools, especially when so many elementary school teachers have week abstract learning/math skills themselves. And we are a far cry from being a society where most adults understand at least the basic concepts of rate of change or approaching a limit. People don't understand that Calculus might actually have some relevance.
@97401183 (Also I don't know if all teens are developmentally ready to learn calculus... especially if they aren't naturally "in to" math. By the time a person is in their early 20s they probably have the executive function skills to manage the subject ... but it's unreasonable to think every teen will be ready and silly. )
@134318c2 @97401183 wait what. Thought most colleges assumed you were going to start with calculus if anything
@134318c2 Well put. I also wonder if there's room for linear algebra. I don't think linear algebra is any "harder" than calculus, and it seems to gain more relevance all the time in our digital world. For me at least, linear algebra introduced an element of "beauty" to math which I hadn't appreciated before. It's abstract in a way that taught me, at least, why abstractions are important: because they help you generalize, for example from 3 dimensions to 100 dimensions.
@134318c2 I really don't like the framing of "replacement" or treating stats as somehow "easier" at all. Like I've seen people who have masters degrees in other disciplines trip over themselves with even basic probability and stats. I'd love to see greater literacy here (I could see an entire class based around Utts's "What Educated Citizens Should Know" paper https://ics.uci.edu/~jutts/AmerStat2003.pdf )… but it isn't a capstone, a replacement for calc, etc… and as you point out we don't have the buildup.
@134318c2 I feel the same with the way physics is usually taught without calculus. It simply doesn't make sense that way, you need a rudimentary understanding of integrals and derivatives to actually know why all the formulas are the way they are.
@134318c2 I'm confused by these reasons. 1) in what sense is calculus required for understanding statistics? Isn't the core concept probability? 2) probability is massively important in daily life and poorly understood (eg the lottery, "hundred year storms", risk pooling, etc.) What's the analogue for calculus? 3) you think that simple, engaging concepts for teaching calculus are common? Hoo boy, not my take (and I was an A student in math and calculus.)