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[quote=pettifogger][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]
Why did you take Math 3 this year after already taking Precalculus last summer?

[/quote]

I thought my child wouldn't be able to handle geometry over the summer, so I didn't sign him up. But he quickly learned geometry over the school year during 8th grade, and learned algebra 2 in the second semester of 8th grade year.

I'm not sure why I didn't sign him up for summer algebra 2 but I didn't, and instead enrolled him in AOPS precalculus during the summer after 8th grade.[/quote]
AoPS precalculus is not  as rigorous as TJ math 4 & 5. Without TJ math 4&5 or tj calc ab, taking on Tj calc bc may be challenging [/quote]
On what basis do you make this claim? I have worked through a large number of problems from the AoPS precalculus book. Many are very difficult, drawing from AIME and other past contests. A select few are from USAMO and/or other olympiads.[/quote]

AoPS has hard problems, but they focus on pure math puzzle problems, not engineering applications. You miss a lot if you only do AoPS. [/quote]
A word problem by definition is an application of mathematical concepts. As long as it highlights the how the math is used, it doesn't matter whether it's about engineering, horses, or flying sheep. I will also dispute your claim about missing a lot. It's far more likely that the opposite is true, where there are many ideas found in AoPS which are not taught in the school classes.[/quote]

AoPS doesn't have many word problems, and the ones that are are silly window dressing. Most of AoPS is abstract expressions and equations.

AoPS is aimed at students on a pure math track. It comes from a contest math pedigree of tricky puzzles and proofs.
TJ and school math in general is aimed at a more general/broad engineering track. 
I've seen very high caliber AoPS students struggle with the sort of engineering type problems (modelling a real world situation mathematically like building a roof for a house) that schools emphasize.

It's a different focus.

Also, AoPS teaches about set theory, where you can learn that it's possible for for two different things to both be missing a lot from each other ;-)[/quote]
I will again dispute your concept of word problems. You seem to be myopically focused on a very stringent definition of a word problem as having to do with "real world application". Speaking of set theory, I will relax your restrictive definition and define a word problem as anything that is an application of mathematical concepts. So yes, your "building a roof for a house" type of problems qualify, but are just a small subset of word problems. It's very important to understand that math is not just about engineering, modeling, or finding a "real world application". It can be about anything as long as it involves applying and connecting mathematical ideas and patterns.

As for your two statements "most of AoPS is abstract expressions and equations" and "AoPS is aimed at students on a pure math track. It comes from a contest math pedigree of tricky puzzles and proofs" -- The first one is meaningless because all math (and even languages) are abstract expressions and equations, which says nothing. The second is completely contradictory because contest problems and pure math are about as different as Earth is from Pluto. Sure, students who enjoy AoPS would likely do very well as pure math majors, but that doesn't mean that is the goal.

Incidentally, the goal of AoPS is to introduce and develop deep problem solving skills in kids, so that they can succeed in whatever path they choose to pursue in college and later in life, no matter how difficult; not to prepare students for a pure math track. Math was chosen as a the mental playground for that because there are many beautiful problems that can immediately expose kids to a rich variety of problem solving techniques. Don't believe me? Here's the transcript of a 2009 speech RR gave at Math Prize for Girls event, where he describes the value of problem solving. At the end he jokingly says that he would have chosen Swahili if it was the best way to teach how to solve problems one has never seen before, but he happened to choose math because he thought it was the best way to teach problem solving. This should be required reading for everyone on this forum:

https://mathprize.atfoundation.org/experience/past-events/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf[/quote]

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