Proposal: replace Algebra II and Calculus with "Statistics for Citizenship"

You can’t just look at number of patients in a month. If you add up the time spent actually working with those patients, a doula spends much more time with the 10 patients than the OB does with the 30-50. It’s not wrong that someone with many more years of education and training makes more, obviously, it’s just disingenuous to claim that doctors are seeing 3-5 times as many patients as a way to bemoan the salary of a foot soldier.

Sure, the OB’s I know acknowledge this. They generally want to spend more time with their patients, but can’t.

It probably is a better system for mothers. But it was sold as a way to save the government money, it doesn’t definitely do that. Not only do they pay the doula’s more than the OB’s, some babies end up getting charged to both since mothers often start with a doula but end up getting delivered by an OB for a variety of reasons.

The thing they really complain about is that the doula’s are taking the “easy” patients. So whereas before they could deliver 50 babies a month, a mix of easy and hard deliveries, they are now seeing 30 babies a month, mostly difficult deliveries. The difficult deliveries pay slightly more than the easy ones, but not enough more to compensate, so they’ve seen their take home pay go down considerably.

How wonderful, though, that doulas there have regular employment with an annual salary. What country is this?

The doula’s are on fee-for-service, just like the doctor. That 80K is if they’re doing 10/month. I believe that’s the maximum they’re allowed to do per month.

The government is Ontario, Canada. I didn’t mention it before because everything I’ve said is secondhand heresay. So take it all with a huge grain of salt.

Oohhh: when you say “doula”, you mean what we call a midwife! In the U.S., a doula is a helper – trained, but still a layperson, not medical – who stays with the woman from the first contractions until the baby is born. Some are trained to help with initial nursing too. But they don’t do anything medical. They don’t deliver the babies!

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I’d say offer a choice, because while most folks will have more use for statistics in their adult life, being shown calc and trig at an early age will also identify the kids who are interested in higher math and will go to MIT and win the Fields Medal.

You know, like some loser kid from South Boston who falls in love with a Harvard student.

Having a math and science requirement to graduate does not even remotely mean they have to take calc. Even art schools like CalArts have math requirements to be accredited but let me tell you the classes they offer are a joke.

Do you or do you not actually know of any school that requires art students to take calc, not just a math requirement, not pre-calc, but actual calculus?

First, it should be broader than stats. It should be data management, which should include qualitative methods. It should also include an understanding of criteria for evidence and “proof”. So many of my grad students believe that proof arises on the basis of some anecdotes or one study, etc. Even in the granite-like lawful science of physics, proof is provisional–laws are regarded as being inductive and therefore subject to refutation. In fact, it is the possibility of refutation in principle that makes scientific inquiry scientific and distinguishes the scientific notion of theory from belief systems. So, understanding of the nature of scientific evidence, the limits of inductive knowledge, as well as the mathematics of statistics are all valuable and useful.

But what about algebra? Statistics without algebra? OMG! Who can predict when algebra might be useful? I took Latin in high school and when I was doing a Master’s degree at the University of Waterloo, I was studying the algebraic theory (a la Chomsky) of language syntax. My Latin clicked in. But, even if that hadn’t happened, did studying a dead and useless language become a drag on studying truly useful stuff, i.e. to get a job? Studying Latin made me more aware of language, grammar, Caesar, and approach to learning other romance languages. Studying Shakespeare did not help me get a job. It has not been “useful” in my life. Except that the cultural references, which abound in our society, made me feel like an educated person and gave me a richer sense of language and culture. Maybe that’s why Shakespeare has been translated all over the world and students all over the world study Hamlet or Macbeth, among other plays and various sonnets.

Getting back to algebra. I argue that those who have no contact with it, who don’t see its power as a structural, deeply cognitive way to view symbols — which allow us humans to model aspects of reality and to see beyond our limited senses when algebra is applied to chemistry, astronomy, cosmology, and many, many other aspects of the universe — don’t have contact with the profundity of human cognition. It doesn’t matter whether they apply algebra in their lives or not. What does matter is that they become informed and that they are able to understand discourses when algebraic topics come up in newspapers and magazines. It’s almost as if they are illiterate, and that clings to our psyches like a bad odor.

Finally, algebra is not the problem; the approach to teaching and learning is. There is a marvellous power associated with being able to formulate an equation which represents something that we know about. It’s amazing that by pushing around a few symbols and reorganizing the structure of a polynomial allows us to reveal information. I don’t know how string theory works at the detail level, but I do understand that it is algebra that allows such a powerful view of a deeply difficult aspect of reality. I marvel at the way elliptical functions can be connected to number theory to prove Fermat’s Last Theorem. That’s worth learning and teaching. Yes to algebra, no to bad teaching.

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The next time you ask me how far away something is, I’m going to tell you how many miles per gallon my car gets.

That’s nice.

Again, the point is just to get my hands on a very large photo when I need one from a photographer. If they want me to specify a specific size, I’m happy to, but it’s a waste of their time and mine. No math needed. Send me what it was shot at, high res. It’s my job to crop, size, and rotate it to what the client’s needs are.

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Instead of calling it “algebra,” which means “complicated irrelevant fiddly stuff” to most people, let’s call it “50 Weird Tricks They Don’t Want You to Know About.”

Understanding numbers can help you win bar bets, if nothing else. How many seconds are there in six weeks? 10!

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Statistics and lottery have nothing to do with each other. People gamble for the chance to win. There is no calculation of probability, not because they are illiterate in statistics but because that’s not the point. There IS a chance and nobody can deny it. As my granpappy used to say: You can’t catch a fish if you don’t throw your hook in the water.

Complete false dichotomy. People die because they don’t feel comfortable with their doctors.

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If they’re three for forty, they’re gonna charge you at least fifteen bucks if you only want one, algebra be damned.

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Speaking as someone who teaches math for a living, there is plenty of room for updating the way mathematics is taught at the K-12 level. However, Hacker’s suggestion of replacing has a number of problems.

Let’s look at these:

The A.P. syllabus is practically a research seminar for dissertation candidates. Some typical assignments: binomial random variables, least-square regression lines, pooled sample standard errors.

The Carnegie and A.P. courses were designed by research professors, who seem to take the view that statistics must be done at their level or not at all.

First, that’s obviously hyperbole The AP courses and exams are nothing like research level stats. What part of stats is going to be left if you remove things like linear regression? Possibly probability? That requires a bunch of algebra though.

And this:

Even with small classes and extra support, almost half of the students got D’s or F’s or dropped the class.

There is a significant proportion of college students who do not understand what a variable is. How is making those variables random going to help?

And this:

For example, there’s probably nothing more cumbersome than how we measure time: How quickly can you compute 17 percent of a week, calibrated in hours (or minutes, or seconds)? So our class undertook to decimalize time.

Imagine if we had a 10-day week, each day consisting of 10 hours each. The class debated whether to adopt a three-day weekend, or to locate an “off-day” in midweek. Since a decimal week would have 100 hours, 17 percent is a flat 17 hours — no calculator required.

So I guess he wants us to teach arithmetic … but in seminar discussion form.

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Arithmatic is alegbra without letters.

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Half thats the same as nearly everyone.

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Didn’t the french already consider and reject decimal time?

That may be true, and the two things are certainly not mutually exclusive, but for me, the ability of my doctor to understand/use statistics to focus diagnosis and treatment would give me the necessary comfort.

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Number Theory (advanced arithmetic) often involves letters.

Hacker is not a professor of mathematics at CUNY.

Keith Devlin has written a pretty compelling dissection of Hacker’s book, here:

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I both agree and disagree. Don’t get me wrong, for most citizens, a good grasp of stats is definitely a good thing. My university doesn’t let you graduate without it (or you can choose calculus- but most people don’t). That being said, most math classes get highly theoretical about the applying the most mundane operations. I still get mad when I thought about the kid who lost points on an assignment for realizing that multiplication is commutative. It remains un-fucking-fathomable to me that you would start a kid off in grade school with every intention of teaching then cross products and matrix multiplication years later. Changing the topics you teach in math isn’t going to fix anything if you don’t change how math is taught. So much of it is teaching you to perform computational operations and then penalizing you for making inevitable mistakes because you’re learning a skill. Teach stats that way and it won’t matter that you’re teaching stats.

Math is more than just a set of computations or even puzzles, it’s a playground for the mind, and it can be incredibly rewarding when viewed through that lens. It’s also where math becomes valuable, because learning to think mathematically is not something that happens when you’ve found x for the billionth time. Learning to think mathematically ranges from things as simple as understanding that 60 mph is a mile a minute and therefore 30 mph is a mile in two minutes and estimating your arrival time the easy way to things as complex as figuring out just how exactly the NSA fucked you over. Not because you were taught to do these things explicitly, but because you were taught that these things can be figured out and understood by normal humans with a little research. Instead of inspiring confidence, most math classes in high school inspire fear and loathing.

That’s before you even get to the real beauty of it, where you learn about surfaces of infinite length and surface area, or the infinite possibilities of cellular automata. So yeah, teach kids stats, but teach it right. (Although teaching stats without a little algebra is like teaching people to wear shoes without shoelaces.)

From Hacker through the link you cite:

“Along with phenomena like earthquakes and cyclones, nature also has some numbers that control or explain how the world works. One of them is pi, whose 3.14159 goes on indefinitely, at least as far as we know.”

Oh pee-yew, that’s a real stinker.

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Proposal: if you even think you might possibly want to be a STEM major, regard this article as total bullshit or you’ll be so far behind you’ll never catch up.

If I, as a scientist, were to make the same argument regarding Shakespeare as related to STEM majors, I’d be laughed out of the room.

Same damn point.

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