Reply to AP Statistics as a 10th grade elective

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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]I teach AP Stats at an IB school.

Yes, AP Stats is frequently taken as an elective before starting the IB sequence (at my school you take IB Analysis 1 followed by IB analysis 2, so keeping those two courses together is ideal). The only prerequisite for the course is algebra 2.

The prior posters have a bit of misinformation in their comments.  There is no calculus, it is taught from a purely algebraic/conceptual standpoint, and honestly the kids who have already taken calculus have a tougher time with stats because they want to spit out straight calculations and stats is more logic/interpretation than calculation.  It is a very conceptual course.  The kids who go back to IB from AP stats tend to write very strong IAs.

The super strong math kids honestly have a hard time with stats because it feels "fluffy" to them.  It's a logic course with an undertone of math, but it's not pure calculations.[/quote]
It "feels" fluffy?? Well, Duh Sherlock, of course it's highly fluffy without calculus, and by extension, without a hint of how any of the formulas are derived! I counter your claim that "they want to spit out straight calculations"; the strong math students actually want to see at least some proofs and derivations, especially if they've taken calculus. So yes, the class IS fluffy, because you can't just handwave stuff and call it "logic" without actually covering some of the math behind it! You see the logic there?[/quote]

No, it feels “fluffy” because there is a whole unit without numbers. We talk about sampling methods, designing experiments, bias. Kids say it’s like a psychology class that gets you a math credit.

It feels “fluffy” because every answer requires a sentence to give context and relevance. It’s not enough to say the standard deviation of the random variable is 2.4. They are required to state, “The number of shots to make a basket typically varies by 2.4 from a mean of 5.1”. Kids say it feels like we spend as much time on vocabulary as calculations.

It feels “fluffy” because during probability the best strategies are to draw pictures (Venn diagrams, tables, trees) vs using formulas. The kids say it feels like they’re cheating.

It feels “fluffy” because there are so many conditions that have to be checked for inference, and conclusions are a whole paragraph. They claim to write more in an average stats class third quarter than they do in an average English class.

It feels “fluffy” because kids are expecting weekly problem sets of wrote calculations, and they end up with only a couple of those over the year.

I’m sorry that the class isn’t calculus based. It is designed that way on purpose to make it accessible to as many kids as possible. I’d say that’s a good thing in a world where we want the general populous to understand where data comes from and what studies are claiming.[/quote]

You misunderstand a bit what the argument is. What makes a great course is building connections between concepts, often through a mathematical derivation to show the logic behind how things work. Starting with the normal distribution, ie half the class, the fundamental ideas are underpinned by calculus, nothing can change that. The skill as a teacher is to condense those principles into accessible information that even the 10th grader can understand so you’d have to introduce some calculus concepts. That doesn’t mean the class is calculus based, or that it needs to take too much class time.

Almost all examples you give are because of compartmentalization of concepts. Experimental design, sampling and bias are introduced because of how they affect ‘numbers’ like the mean, it’s straightforward and more educational to find examples that are more quantitative.

Formulaic sentences like ‘The number of shots to make a basket typically varies by 2.4 from a mean of 5.1’ is what makes the class fluffy, and I’m not sure I even agree, the language is too imprecise, what do you mean by ‘typical’ and ‘varies’. You could literally use the same exact sentence for other measurements of spread like inter quartile range, mean absolute deviation, range etc

Theres nothing fluffy about Venn diagrams and decision trees. Tables are a way to summarize data.

Theres a real teaching deficit in how to write a mathematical exposition, I’ll give you that. Students should know how to write a mathematical argument that involves sentences, equations, logic and make it easy to understand and read, it can be more concise than long paragraphs, but it’s still a skill that’s mostly undeveloped. The conditions for inferences are driven by logic, but that doesn’t come through if they are presented as a check list used to decide what formula to pick.

The calculations are there, but are glossed over, it comes down to choosing the relevant examples and exercises.[/quote]

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