Also, students who are taking pre-calc will be applying much of their algebra and geometry and so will have forgotten less than someone who is taking nothing at all.

Pfft. He's still a twit. I lost someone's assignment this semester and I used the omit function in my gradebook to remove the assignment from calculation completely. But yeah. I'd photograph or scan all future assignments in this class.

The "no purpose to live" is really concerning, over a grade that is not actually that horrible. I would definitely recommend counseling. As far as the class, I would go to the next class and see what the professor says. Sometimes the final will be weighed more heavily if students improve, or sometimes the professor may offer a chance to rewrite for some of the points back. This would be offered to the whole class. I would not ask for "is there any extra credit I can do" though.

Totally. But most people are not very good at self-teaching; it does effectively limit it to those with the gumption to go and find a good self-teaching book and go back through independently, or exchange work of some kind for tutoring. They exist -- I know some of them -- but they're not as common. However, I was originally primarily responding to the "the CC will teach it, " because that is becoming less and less of a possibility. It's more probable that someone who has not been exposed will *have* to find external sources to get themselves up to the end of algebra 1 if they expect to succeed even in CC classes. And unfortunately, they don't even realize that, so they sign up anyway. If your CC still has beginning algebra and intermediate algebra as separate courses, and especially if there's a pre-algebra class, you'll probably be fine. I'm not intending for this to shift into a "let's figure out how these other people could have solved the problem" -- all I'm saying is don't pretend that it's not going to be a problem. Because it is. Edit: I'm also not really talking about kids who by disability are prevented from understanding algebra. I just think it's doing a severe disservice to a child who IS capable to not teach it. So I would say it's a requirement for any capable child.

For Geometry, basic results are usually not taught in college classes and are necessary. Proofs aren't. I mean don't get me wrong, I love proofs and personally I believe that everyone capable should do them, but I don't think it's something that's going to completely mess you up if you don't have it. But knowing things like that to find a perimeter you just add up the lengths of the sides ... that messes with people. They want to try to memorize formulas for perimeters, and they can't find the perimeter of a triangle because they forgot the formula. The area of a rectangle. The volume of a box. They don't need to know the terminology, but I mean, that one is even applicable to real life when you're trying to find cubic feet of things. And more importantly, what does area mean. Why can't you measure area in feet or cubic feet? We don't formally teach similar triangles although I have written a handout dealing with them because I have found so many of my underprepared students do not know them, but it's still a "do this on your own". We don't teach vertical angles or transversals (although a handout on that is forthcoming too) but they're used all the time in trig/calculus word problems. The Pythagorean Theorem is also something they should know. We do teach supplementary and complementary but it requires some time to actually understand what they mean. What words like parallel and perpendicular mean. Or even what a right angle is, and what an angle is. What does an acute angle mean? Why can't you find the complement of an obtuse angle? Most of what I've listed shows up in pre-algebra (or at least in my pre-algebra book from 1989, lol) and the rest shows up in even a basic geometry course. A half credit would probably be plenty to be able to function in a developmental math class. But all of the above are things that I've had people have serious trouble trying to understand. In case it isn't obvious, we're in the middle of a developmental math semi-major redesign (fixing stuff following a major redesign) and I've been doing a lot a lot a lot of thinking about these types of things.

Financial aid won't pay for that. Cost is prohibitive for many in the population I'm working with.

More depressing than anything else. I've seen the rhetoric in the radical forums where they insist that if your kid really wants to learn, they'll be able to pick up the knowledge. I've seen some extremely far-fetched stories. In reality, there's a limit to how much can be learned in a year by even the brightest and most motivated students. Edit: I can take someone who can understand a variable and is ready to begin to understand the concept of a function and get them through our streamlined track. But for a lot of students, there is a time gap between when they're ready to understand variables and when they're ready to understand the more abstract concepts, and they'll do okay in the beginning parts because they're ready to understand variables, but they're NOT ready to move to functions. And this is why algebra 1 is an absolute requirement, in my mind, for a student who is at all capable. It will often be required, even at the CC associate's in applied science courses, and it closes doors that someone may never be able to open again.

It is because overall, the statistics (correctly) say that students who enroll in accelerated tracks are more likely to complete their college credit classes. Fewer of them pass each semester, but because fewer semesters are required more will complete it. The majority of students are more successful in this track; most of the students who are not successful would not have been successful in any track, because they are not passing due to not doing the work (whether it is due to personal negligence or external issues, it does not matter -- both are very common). But it sure does suck for the students who would have been much more successful in the old track, and for the students where it is genuinely new information and they have never, ever learned it before.

I think stats is sufficiently different from algebra that it would be completely reasonable to include a couple of stats units every year as well. Here, while I think doing MEP completely might not pair well with the US curriculum, adding some of the units from GCSE level that are specifically probability/data (5, 8, 9) and then the year after unit 20 (which is aimed at GCSE statistics) would be completely reasonable. Because of personal interest, they would probably work well as summer courses too. After that, if desired, there is sufficient material on statistics/discrete math in the A level curriculum to easily make a credit.

I want to comment on this specifically: The college world is leaning more and more towards "corequisite remediation". In many states, colleges are being pushed or even legally forced to streamline or eliminate developmental mathematics in favor of placing students into college-level classes with the developmental material needed taught using "just-in-time remediation". This has a reasonable chance of working for people who took four years of HS math and just forgot it, but someone who has never learned it in the first place has virtually zero chance of success in this system. I have pretty strong personal opinions about this, but none of that is going to change the way the climate in *general* is moving. I'm in a "streamlined" state right now, and I had several students last semester/this semester saying "Why does it have to be so FAST? Why can't we take this over two semesters?" All I could tell them is to write their state legislators and tell them how pissed off they were that there can't even be an OPTIONAL slow track. p.s. I have absolutely no problem with mandating that there has to be a "fast track" and I don't even have a problem with making it the default. I just have a major problem with not providing even a single section of a slower track. At my last job, we had one, three-credit developmental course before students got into college algebra. It got into algebra in the first week and ended with quadratic equations. I had several bright, articulate, intelligent, and quite lovely students who were all from the same unschooling group and had literally never seen a variable before. They did fine in all of their humanities courses and struggled in their science classes, and many of them ended up dropping out before graduation because the math requirement was insurmountable. One of them was in my developmental math class two semesters in a row and then finally scraped a C in the third semester with someone else, only to then not pass college algebra on the first attempt. He was unusually persistent ... because he wanted to go to medical school. I feel so bad for him, because F, D, C in developmental math and then F, D, C in college algebra is never going to get him there 😞

BC, dual enrollment, or alternatively something outside the mainstream that will show him whether he likes pure math or applied math in time to pick a college major -- something a bit proofier and more in the discrete math realm, or maybe group theory.

Okay. One of the newer books in the college math market is called "developmental mathematics" -- designed for accelerated and combination developmental mathematics courses, it is called "developmental mathematics: basic mathematics and algebra". It is basically a combination text for carrying you from pre-algebra up through intermediate algebra. I think it would be great for someone in your situation. The disadvantage is that it's going to be slightly more expensive because it's a newer format -- but I think the all-in-one approach would be right for you. I'd use it in a diagnostic-prescriptive manner -- test yourself, then work problems. If you have trouble finding one of those, beginning + intermediate algebra or introductory + intermediate algebra is an old version of similar combo texts that won't have quite as much pre-algebra, but should be totally workable. Lial has a version of the above, but so do many others. You don't need to restrict yourself -- pretty much any major publisher's will work. Martin-Gay is one of the ones a lot of my friends like to teach out of, though I haven't used it. I would buy the student solutions manual FIRST, then the text. People often list the wrong edition, especially for the solutions manual, and you want them to match. That way if someone accidentally sends the wrong edition, you can get the matching text. If you need to check a solution for a computational problem and you don't have the solutions manual, Wolfram Alpha is really nice. In a more electronic approach, Khan Academy is good for brushing up.

Yes, I mean do you know what they use for placement? Is it accuplacer? The reason I was asking was that accuplacer has a preparation app that explains things as well, if it's a "brush up" you need rather than intensive teaching.

Are you solid on pre-algebra as well? A lot of errors my students make in algebra are traced to pre-algebra. What test are you preparing for?

I wouldn't stop taking math too early and plan on counting the middle school classes. But I would put them on the transcript -- I've heard of people denied admission because "geometry" did not specifically appear on the high school transcript after having been taken in middle school. It's a lot easier to ignore information you deem irrelevant than to conjure up information you find relevant.

Going around the unit circle, starting at (1, 0). The angles are marked every 30 degrees (every pi/6) and every 45 degrees (every pi/4). I think of drawing pizza when I draw this. A friend calls it his pizza pi(e) when counting radians. The coordinates are all 1/2 of the square root of one of {0, 1, 2, 3, 4}. You start at y=0, so as you move around, y increases until 90 degrees -- the values are 1/2 sqrt 0 (starting point), 1/2 sqrt 1, 1/2 sqrt 2, 1/2 sqrt 3, 1/2 sqrt 4 -- then you've reached 1, so y starts to decrease, hitting the same points in the opposite order. You start at x=1, so as you move around, x decreases -- 1/2 sqrt 4, 1/2 sqrt 3, 1/2 sqrt 2, 1/2 sqrt 1, 1/2 sqrt 0 ... then moves negative, because x-values are negative left of the y-axis. Using this strategy, you can fill one out whenever you need it.

Exactly what regentrude said. The chair of our department answers a lot of those questions.

Understanding that the point (2, 1) means that the distance from the x-axis is 1 and the distance from the y-axis is 2. I mean really understanding, beyond a formulaic "count two right and one up". Understanding that the distance formula IS the pythagorean theorem. When I transition to the unit circle (which is after only one chapter), we still draw triangles inside it for some time, and that seems to help with that. I forgot to mention that allowing me to use non-fractional values for sidelengths is another reason.

Ask someone at the college. This is too specific. Both of them feed into calculus 1, so there's not an obvious pathway difference. Some colleges really want college algebra to include a chapter of trig so that they can use trig in classes without requiring another major. Some prefer to teach trig in one class. It looks like they're trying to cater to both.

I've found that when I start with the unit circle, they seem to forget about triangles and forget that it's supposed to actually mean something in a physical context. They just look at it as a magical black box (which they're prone to anyway). It also lets me throw in the word problems sooner, and give problems designed to set up for the inverse trig triangles later on, e.g. draw three triangles where cos theta = 2/3. I can do this with the x/r definition as well, of course, but it doesn't seem to click as well. I think some weakness in analytic geometry is going on here as well. I also like the derivation of the 30-45-60 values better, and giving the triangles as a mnemonic works for me.

I personally prefer starting with right triangles, so I would do the geometry chapter first. But this is a subject of debate, not one where people tend to agree. He won't need to do the intermediate algebra text -- the algebra prereq for trig is more to really understand functions. My trig students tend to not really "get" the difference between f(1/2) and f(x) = 1/2, and even if they will write it carefully, it's just to humor their meanypants teacher. I doubt this will be an issue.

That's the only one I remember it in as well, but I missed a couple of his. And I'm not sure trisexual aliens would really count. Timothy Zahn's written a prequel series in David Weber's Honorverse and I've been really enjoying it. I've also gotten his prequel to his Star Wars trilogy and had a blast.

I disagree about the sex scenes. I mean, yes, terms for body parts aren't explicitly mentioned, but the vein of nonconsensuality is pretty strong. I read them at twelve and didn't notice the sex; I read them again at seventeen and was gobsmacked to see all that had gone over my head. Don't get me wrong, I loved these books and I still go back and reread them sometimes, but it was there. The first two harper hall books are just fine, and there's a brief interlude in dragondrums but I still think it's fine -- it's very non-explicit and between two characters that are already somewhat romantically inclined. But for someone who specifically wants to avoid sex scenes, I definitely wouldn't go beyond that.

It may work better to split up the time (and she may be able to get more done) -- two 30-45 minute sessions seem so much easier and fatigue the brain less than one 1-1.5 hour session. I also think that it's better to work on more days than extend the time -- if she can fit in a single 30 minute session on weekends, it will help keep her "in the groove" while not overwhelming. You may be able to find an expat who can work with her on math, american style. I'd give it a shot anyway. You might also be able to find a tutor who can skype with her from the US.

For a homeschooled student, I would worry less about him going slowly. If algebra goes slowly, he can finish it in 9th grade and personally I'd just give him the credits then. As a mathematician, if I'd been asked to learn from Saxon ... I'd have majored in something else. It would have totally killed the fun that I found in math. I'm not sure I'd have even taken calculus. If possible, I would lay your hands on a few programs before picking one. Jacobs might be one to consider -- he includes a lot of pre-algebra, and the instruction is very solid. College beginning algebra texts are totally usable (college beginning algebra corresponds to high school algebra 1) and very cheap used. Lial's is an okay brand, and I like Martin-Gay. Blitzer has great word problems although the explanations aren't my favorite. Alternatively, if you want to expose him to a different perspective, consider the jousting armadillos series. The first book will be material that he has already covered, but for a slow methodical worker who finds no interest in what he's doing I think it would be worth doing. There are some samples on their website.