I haven't done as much coding since I switched from CS to math several years ago, but I used to use a combination of using well-chosen sample values, as a previous poster mentioned, to see if I could determine whether each block of code was doing what I wanted it to do, and commenting out all but one block at a time to test each block independently. Once I knew each block worked independently, I could start un-commenting one more block at a time, and testing to see whether each block worked with what had already been tested.

My DD8 has been working through it alongside and while waiting between books for BA4, just doing the sections she finds interesting. I sat down with it and the early AoPS books and marked all the sections in M:AHE that were unique to it, to be given special consideration when she was deciding what to do next. My DS10 also uses it occasionally when he's AoPS'd out. It works best for us as a "tapas" approach.

He's getting confused by the ordinal number ''first'', because there isn't one for zero. ''Ordinal'' has the same root as ''order'', and there isn't a zero-th place in order--as in, something that comes before the first thing--because then that thing would itself be the first thing, contradicting the premise that it comes before the first thing.

Thanks so much! I decided to put The Feelings Book on hold at the library so he and I can look at it and decide whether it'll work for him, and I have Understanding Myself in my Amazon cart in case it doesn't. I'll have to look out for the film zoobie mentioned.

American Girl's The Feelings Book gets great reviews, but I'm wondering about the degree to which it speaks specifically to girls, because I need something for my son. He wouldn't be put off by reading something with girls in it and so on, but I imagine it might feel alienating after a while to read something that clearly isn't including you, ifykim. I'm seeing books for boys that are specifically about anxiety and other issues, but he just needs ''I'm feeling very ten right now, which is like *this*, and it's totally normal and fine,'' which is the vibe I'm getting from the American Girl one. Is this some kind of holdover, and girls are allowed to acknowledge their emotions, but boys aren't? We have It's Perfectly Normal and he found that helpful, but he could do with a more in-depth discussion, and not just from his mother. I'd love to hear if the AG one isn't as ''special secret girl time'' as it looks like it might be, or if there's a gender-neutral or boy-specific option I'm not finding. Thanks!

That's not quite what the article you linked to says. It says the VA Supreme Court sent the case back to the lower court after addressing an error, but the fate of the college is still up in the air. The article also answers your question about the finances: ''“With the trust issue now resolved by the Virginia Supreme Court, we will move to seek the appointment of a special fiduciary to assess the college’s true finances and determine what is needed to close the current funding gap to ensure the College can remain open,†Clement said.''

It would depend on what other options there were for the language and forest stuff. If you can do language immersion at home, send him to the forest school. If you can't do the language, send him to the language school and get a pass for your state parks. The academics of the early years are easy enough to pick up along the way, but the language and the forest school are unique opportunities.

Certainly set theory is worthwhile and much-used, just generally not in the context of roots of polynomials, at least not in anything beyond basic algebra. So since the term is actually terminal in its usefulness in that context, why not just use the zeros/roots from the beginning?

Actually, solving an equation and finding its zeros/roots aren't the same thing, so the same instruction couldn't be used. I think they used the term they did because zeros/roots are the much more common terminology for the purpose than "solution set." If a math professor told students to find the solution set of a polynomial, the students would blink and then say "Do you mean to find the zeros/roots?" If we call them by their proper names from the beginning, surely it saves confusion?

I'm not convinced that the term was coined to help weak students. For my entire university education, the terms "zero" and "root" have been interchangeably, even by professors of very "mature" years with Ivy PhD's, who are extremely disdainful of anything they perceive to be a "dumbing-down" of math. My father is a physicist who has never set foot in a modern--or American, for that matter-- K12 math classroom, and uses the terms interchangeably as well.

The ''zeros'' of a polynomial are the solutions when you set it equal to zero. They occur where the graph of the polynomial crosses the x-axis, and thus the y-coordinate is zero (which is why setting the polynomial equal to zero makes sense). They're the x-intercepts of the polynomial. ETA: of course, you can set x to zero and find the y-intercepts, too. The x-intercepts just provide more useful information, and in calculus and beyond, the y-intercept just isn't interesting as often. It's the language used in every math class I've taken since algebra (math grad student here), and used in course lectures I've watched from a variety of universities, most of the which are not local to me (so it's not just my region).

My husband started with a blade brand I don't recall the name of, and moved on to Feather. He agrees with both the endorsement of and warning for these blades. He has a Merkur razor, and a good brush. A ceramic mug to keep the water hot makes for the best lather, he says. It's an investment up front for everything, but it's cheaper by a very large margin within the first year, compared to disposables, and since the only part that needs repurchasing is the incredibly cheap blades, the savings mount year after year. After lots of trials, he settled on Proraso pre-shave cream and aftershave, and Cella shave soap.

My husband and I have many years of coding between us, and neither of us can think of a reason to make algebra a pre or co-requisite for Java, unless his Pre-A didn't do any work with variables.

This is what I was going to say. AoPS covers topics not covered in all Pre-A programs, and covers typical topics in much greater depth, so it wouldn't be a waste of time. He would get quite a bit of long division in the third chapter, and rock-solid fractions in the fourth.

For our library's, it's the one they're going into.

Google says: http://www.learndc.org/sites/default/files/resources/ELA%20Text%20exemplars.pdf I tried to copy and paste the text, but it was full of inserted special characters. Anyway, my interpretation of what it says on the linked page is that Euclid is something the teachers themselves are supposed to use as one of their guiding texts, but students don't necessarily read it themselves. If students were to read any of it, I would guess it would just be the main Euclidean axioms used in geometry.

Graduating high school at 12 or 13 would generally mean a student would still be at university at 15 or 16, so if courses with mature themes were absolutely unavoidable (which I truly doubt), they could be delayed until the last year or two. If a student were to major in mature content, well, that's the choice of the student and parents, and shouldn't affect the institution or instructors. If there have been litigious issues regarding minors on campus, that's ridiculous. I suppose it's not too surprising, considering America these days.

The age of consent in the Western world averages 14-16, with a few outliers in both directions. But you're saying American teenagers should be kept from even discussing academically what they'd legally be allowed to do in most similar cultures? I did DE starting at 15, and took a human sexuality course in the sociology department. The only part of the course that was censored for me was an optional field trip to a sex shop, which I couldn't enter. If a particular student is too immature for a class (and there were a few who fit that description in my class, all over the age of 18), then they should choose not to take it. If a student is a lit major, they can choose which classes to take. I've taken many English classes and my sister is an English professor, and I can say with reasonable confidence that it's possible to choose appropriate classes within the major. If a student wants to take a class on Greek sex poetry but needs a few more years to mature first, they can save it for grad school. This concern is really absurd.

For the same reason CA graduates sit in the sun baking away in medieval European scholar garb every summer: it's what's always been done. The transplants (who designed and bought the houses) brought it with them.

The FAQ says 128 plugs/tray. And you're probably right about the boysenberries and the nuclear attack: we had raspberries when I was growing up, and my mother had them removed three times before it finally worked. They were never watered, but they flourished.

Marijuana and same-sex marriage have been legalized because of the mountains of evidence that they cause no societal harm. I've yet to hear of a jurisdiction in which prostitution was legal and not basically still a living nightmare. I think it could be possible, in theory, but it's never actually happened as far as I know. ETA: others have mentioned prostitution ''legalized'' for the prostitutes themselves, but remaining illegal for the johns. There's a fine but distinct difference between something being ''legalized'' and ''decriminalized'', with the latter being the appropriate term for this situation.

You piqued my curiosity so I Googled, and found their FAQ (money trigger alert--it includes pricing ;)):http://ucverdebuffalograss.com/faq/ It sounds much better than traditional turf, but it also says UC Verde goes dormant in winter and turns brown. So I'm not sure it's a solution for people motivated by greenness, since it just trades brown in summer for brown in winter.

There's a strong precedent for ''We're okay, but these other people are just taking it too far''. The transgender community has felt marginalized by the gay/lesbian community for a long time, as has the asexual community. You also see this in marriage equality discussions when the question of polyamory comes up. I'm not surprised that the transgender community isn't necessarily thrilled to be associated with the transabled. My first thought was ''Okay, as long as transabled people are somehow prevented from making use of society's provisions for the disabled, since they're actively choosing this,'' but then, the same could be said of women who have babies they can't afford and then make use of welfare. I think in the end, the number of transabled people will be so small as to not have much of a fiscal or other logistical impact, and it would probably be more complicated (and quite possibly more expensive) to discriminate against them. I imagine that ''ability-reassignment'' surgery would carry the same psychological exams and prerequisites that gender-reassignment currently does, if it were legitimized.

My son started AoPS Pre-A after 4B, having also done some of MM Blue series on decimals and integers (both now covered by 4C and 4D). My daughter will start after finishing 4D. If your son needs more time and practice, I'd be more inclined to use the Key To... books or MEP than to try to align a complete program like SM to his needs. We also used Khan Academy weekly for basic skill practice like long division, because procedures ''rust'' quickly in the brains in this house. If you're certain he'll end up in AoPS Pre-A, you could just buy it and try it, and decide in real time whether he needs to back off for a bit.