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Just a quick update. We've finally gotten to Cartesian geometry -- after they did linear and quadratic equations (well, "did" in the current "let's mention it then move on to something else" sense), but only barely. The worksheet had a graph with little cartoon bubble labels: slope, x-axis, y-axis, intercept. The slope bubble pointed to the line, which could just as easily be the equation, but perhaps I'm being picky. Below it was a question: If x is 5, what will y be?
It would have been a perfectly reasonable question except that the tics on the axes weren't labeled. Were they 1, 2, 3, ..., or 2, 4, 6, ..., or 5, 10, 15, ... ? That little glitch made it just a tad difficult to answer the question.
That was presented along with set theory, which was your basic Venn diagrams, with unions and intersections.
Then they went back to "probability and statistics" (and yes, those are sneer quotes). I've already said I think it's bizarre to teach either in the 8th grade, but if you're going to teach it, then teach it. There was no new information presented the second time around. "Probability" was nothing more than your standard ball problem ("If there are 8 green balls and 4 red balls in the hat, what is the probability that you will select a red ball?"), which explains embarrassments like this. Worse was the "statistics" component, which was nothing more than median, mean, and mode.
I hate to break it to the math ed folks, but statistics is not "soft," and it is far more than measures of central tendency. Ultimately, even the hard sciences come down to statistics. Carbon-14 dating (and potassium-argon dating) are statistics. DNA testing is statistics. Epidemiology is statistics.
The math ed people I know wouldn't know a frequentist from a Bayesian, or MANOVA from a t-test. Call me cynical, but I can't help but wonder if that doesn't have something to do with this mess of a curriculum. Why revisit the same concepts over and over again? Couldn't they at least introduce -- in concept, if nothing else -- standard deviations or sample v. population?
If you're going to teach it, teach it. That's my outmoded, stale, dinosaurian view, anyway.
We did the "probability" and "statistics" worksheets in fifteen minutes. That's how much substance there was. But there were terms on the worksheet (she'd copied this one from somewhere, you could tell that) they hadn't covered (from the original source). She had told them to ignore anything they didn't understand (what kind of advice is that for a teacher to give a student?) but he wanted to know what they meant. So we talked about the normal distribution, standard error, and standard deviation (the terms from the original source on the handout).
(By the way, there's an interesting video of Peter Donnelly discussing common statistical errors here, if you're interested.)
In more general terms, I'm teaching Ricky formalism, to set up his problems in sequential, logical steps. He finds it anal retentive, and I'm not drilling him a lot because it frustrates him, but some every time I see him. He just doesn't understand why he should write "Let x equal the number of pears" at the top of the problem. I didn't either when I was his age, but I did it because I had no choice (that's the way math was taught back then). Now, I understand why, and that's why I'm passing it on to him. His biggest problem is that he's pretty good at figuring out how to solve a problem, and he doesn't see why he can't skip steps if he knows the intervening ones. I was like that. But there's a reason for it -- so he won't be like these students.
Anway, back to the beef and noodles.
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6 comments:
wouldn't know a frequentist from a Bayesian
Amazingly enough, I actually DO know the difference between a frequentist and a Bayesian!
sort of
He just doesn't understand why he should write "Let x equal the number of pears" at the top of the problem. I didn't either when I was his age, but I did it because I had no choice (that's the way math was taught back then). Now, I understand why, and that's why I'm passing it on to him.
What is the reason?!
It seems like a good thing to do, but that's all I know.
I just have a common sense reason to do it.
wow - great stuff
can't wait to read your post AND watch video!
I am, however, going to revise another couple of pages FIRST.
I've forgotten which textbook Ricky is using - ?
The whole thing is unbelievable.
The reason is you have to define the terms you are using. A variable without a definition is like a pronoun without an antecedent.
Am I right?
The next thing that follows the definition is the "lawyer clause." And it might go something like, "X is an integer, or "X is greater than zero" This keeps some jerk from "lawyering" your solution and telling you it doesn't work because he comes up with a counterexample, "You never said that X couldn't be a purple duck!"
That's my impression anyway. But the point with kids is to make them think very carefully about what they are doing before they jump in. The learn to be precise. They also learn they must justify what they say, not just say it.
He just doesn't understand why he should write "Let x equal the number of pears" at the top of the problem.
I have forgotten 90% of the math I learned after 8th grade, but this phrase has stuck with me. Although before you included it in your post I had not thought of it in years.
Define your terms.
I’ve worked as a petroleum geologist, a financial planner and designing investment products (among other jobs) and somehow this procedure seems to be an appropriate starting point in all types of problem-solving exercises.
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