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Kathy in Richmond

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Everything posted by Kathy in Richmond

  1. Have you seen their Assessment in the Online school article? It explains the difference between short answer problems and proofs and how they're evaluated. It sounds like you and your son are doing wonderfully right now! You're doing just what I'd recommend to self-learners: doing Alcumus for fluency, going back through the text later to tackle the challenger problems, and doing MathCounts type problems on the side for mixed review and a fun challenge. I was a long time AoPS mom when my kids homeschooled, starting when the school first opened. We did the original texts (Vol1 & 2) on our own at home, and we took several classes online: most of the contest math offerings, but also number theory, intermediate algebra, precalculus, WOOT, and olympiad geometry. Some thoughts: You don't have to do all or nothing. You could let him do intro level classes at home, and do the online school when he hits the intermediate level. Or you could do the main courses at home, and let him do the extra classes (number theory, C&P, AMCs) online. My daughter enjoyed the group experience very much, and made some lasting friendships in her classes. Participating in the forums also led directly to math team (incl ARML) invitations when she hit high school age. Now she even works for AoPS, so I'm super happy in retrospect that she had those opportunities...I'm a mathematician & could easily have done it all at home... Proofs are nothing more than well reasoned and well written answers to problems requiring more than a calculation. There are plenty in the textbooks - they just don't appear in the two-column format that we all learned in school in geometry class. If your son is studying the solution book and comparing his written answers to theirs, he is learning how to write a proof. You know him best! For kids who tend to skip that step, for those who don't like to admit what they don't understand fully, or for those who tend to skip steps when it involves writing more than a line or two, then having an AoPS mathematician grade their proofs can be very helpful. They hold the kids to high standards, both in accuracy and style. As for class speed, take a look at the syllabi online to get an idea. The Intro Alg book is covered in two 16 week sessions (A and B), so approximately one school year in length. The book is very meaty, though, and many kids do better having more than a year to get through it. In an online class, you'll be doing a problem set a week. These are not the textbook problems, but special sets made for the classes. For some kids, it keeps them "marching along" and not getting bogged down. Some do better on their own pace at home, and some benefit from that "push." My kids were average typists when they took the classes online, but not super speedy. Anyone who wants can submit answers to the teacher's questions, and the teacher selects a subset of those answers to display. There is a bit of a speed issue if you want to have your answer be correct & displayed, but we found it was as much about fast thinking as fast typing. One thing that helps is to read the chapter in the text before class. You want to grasp the basic ideas before wrestling with the in-class problems. And it helps to realize that a lot of the AoPS students are after-schoolers and may already have taken the basic course in their schools. So it's hard to be the top of the class, and that bothers some students more than others. Again, you know your kid best...
  2. She was a beauty! So sorry for your loss. ~from a fellow kitty lover
  3. In the AoPS Academy ad, she's wearing a floral top & makes a few quick appearances, and in the Online school ad, she appears briefly in an office scene starting at 1:38. No speaking roles, though! ❤️
  4. My daughter showed me this the other day, and I picked Sacha out right away! So cute!! Dd is in there, too! She's the teacher in the floral top. Do you know that there are 3 separate ads? I saw Sacha in the BA ad, too, and he has a speaking role there 🙂 BA ad: AoPS Online School ad: (dd is in this one, too 🙂
  5. Algebra 2 always should cover rational functions and their graphs. As for limits, I tutor a lot, and the alg 2 kids learn all of these limits if they take the honors level class. They do struggle with them for sure. Not sure how it works elsewhere though!
  6. I’m traveling this week & can’t look through my bookshelf, but my first thought would be to grab any good calc text. The first chapter usually treats rational limits. You’d want to study the behavior of rational functions in these cases: (1) End behavior as x tends to +/- infinity. This is pretty straightforward. You just look at the highest degree term in the numerator & the denominator & take the limit of that easier expression. So for the end behavior of f(x) = (2x^3 - x)/(5x^3 + x^2 -3), you’d look at the expression 2x^3/5x^3 = 2/5. That would be the value as x tends to +/- infinity for this example. (2) as x tends to a value where the function has a vertical asymptote, like f(x) = 2/(x-3) which has a vertical asymptote at x=3. Here you have to be careful to specify whether you’re talking about right or left hand limits. As x approaches 3 from the right, f(x) goes toward positive infinity, and as x approaches 3 from the left, f(x) goes toward negative infinity. (3) as x tends to a value where f(x) has a “hole.” An example would be the limit of f(x) = (x-1)/(x^2 -1) as x approaches 1. The function is undefined there (since denominator = 0), but it simplifies to f(x)= 1/(x+1) for all other x values. So the limit as x tends to 1 is 1/2, even though the graph of the original function has a hole there. It would be super helpful to spend some time reviewing graphing rational functions by hand, too. All these limits seem easier when you can picture the graphs.
  7. Thanks Laura, lol!! Would have loved to have more time to get together, but we’re only here till Saturday. With dd in San Diego & ds up here, we always feel like we’re not spending enough time with either one on these trips! I really miss the days when both kids lived in the same area... Arcadia, that’s neat that you live near ds! He’s been here near Levi stadium for a few years now. Happy Thanksgiving!! 🦃
  8. Thank you for the updates! We are driving up 101 now to spend Thanksgiving in Santa Clara, and we were a little worried about the air quality.
  9. We put up our artificial tree for our sweet kitty's first Christmas, & we got as far as the lights when she decided to claim it all as her own. Since then we haven't attempted any ornaments. She leaves the wrapped gifts alone and just scoots up and sits in the tree.
  10. Sure, you could try it then, since linear algebra doesn't require any calculus background. It's usually taught later in the curriculum because it does require more mathematical maturity; i.e, comfort with more abstract thought and familiarity with proofs.
  11. Aw, I'm so sorry that your girl has to face scoliosis. Sending prayers her way that surgery goes well and solves her problems! Glad she can transfer into another AoPS section post-surgery, though.
  12. Quick thoughts: For the trig, I'd suggest Gelfand's Trigonometry, which has much the same flavor as AoPS. For the linear algebra, look at Gilbert Strang's class on MIT OCW. Another thought is Pre-Calculus Mathematics by Shanks, Brumfiel, et al. .It's an older text from the 1960s, so you should be able to get it for a few bucks. It covers most of the AoPS precalc material at a more challenging level than modern texts.
  13. Oh, Colleen, I am so thrilled to hear your news! Happy and excited for both you and your daughter!! (where's the balloon emoji when you need it??) You guys are often in my thoughts ?
  14. Awful, horrendous news. I can't even imagine... I'm not Jewish, but I lived in Squirrel Hill for several years during grad school, and it's one of my favorite places ever. Such a nice, welcoming community.
  15. Honestly? I've never heard of Mu Eta Sigma. I took a look at their website. All they require is a standardized test score (SAT math 600 or equivalent), 10 hours of community service per year, and an *annual* membership fee. I think that while it can't hurt your son to apply, I doubt that it would be of any significant help in college apps.
  16. My husband went gluten free a few months ago for other reasons, but he's found that his joint pain is much reduced as a bonus.
  17. I used to follow GA homeschool admissions because I wanted my kids to have a shot at Georgia Tech, where I used to teach and where I met my husband. Back when my son graduated (2006), it was a definite NO for us, though. The GA schools wanted something like 7 or 8 SAT subject tests from homeschoolers (not kidding!)...basically substantiating every single academic area (multiple for history and science). There were stories of kids at the time who jumped those hurdles, but we chose to look elsewhere in spite of our love for Tech. By the time my daughter graduated (2010), they wanted a few specific tests. Not as many as earlier, but more than most schools were requiring of homeschoolers. She chose to apply elsewhere. From what I've read, though, they've changed a LOT in recent years for the better, as Good Grief relates above.
  18. I'm so sorry, Quill. Hugs and prayers. Stay positive and surround yourself with positive thinking friends and family... Three years ago I was in your shoes and remember the shock of life turning upside down suddenly. But I'm still here and doing well! You will be, too!! Go out and beat it!!
  19. Yep, I've found this to be true for most kids. The chapters on roots of unity and the geometry of complex numbers were the most challenging for the kids I've taught.
  20. Hugs on your loss! It's just so sad and heartbreaking when we have to let go of our pets. They really do become our little friends and family members. Your tribute to Ursula was absolutely beautiful to read.
  21. Scary for sure! I live in Midlothian off Rt 360 not far from where the tornadoes touched down. We're out and about on that stretch of road all the time. A couple of the destroyed businesses were places we've patronized. My tutoring kids were sheltered in place in their high schools for hours after school yesterday. I had one parent texting me pictures of the black clouds from the parking lot where she was waiting for her daughter to be released. Never want to go through that again... Glad you made it through safely!!
  22. Any interest in math competitions? Even if they're not interested in the competitive aspect, it's a great way to meet other kids with similar interests and to find out what's going on in the area. Here's a list of tournaments available in Alabama. Looks like it's only been partially updated for this academic year, but they could poke around and ask questions. Here's another listing I found on the AoPS site. Vestavia Hills has traditionally had a strong math team/culture. Maybe reach out to someone in their math dept?
  23. I can't help with finding a video, but maybe I can explain why it works. Draw segment AC in the figure. Look at triangle ABC, and notice that EF bisects two sides of this triangle (AB and BC) By the Triangle Midsegment Theorem (most geometry courses include this, though it may have a different name in yours), EF must be parallel to the 3rd side, namely AC. You can do the same thing with triangle ACD to show that HG is parallel to AC. Since EF and HG are both parallel to AC, they must also be parallel to each other. You can also draw segment BD and go through a similar argument to show EH and FG are both parallel to BD, and thus are parallel to each other. Since both pairs of opposite sides are parallel, EFGH must be a parallelogram.
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