BA had not been published when we started homeschooling, so we started off with Singapore for elementary math. We did Singapore 4 days a week, and on Wednesdays I had my students complete a MOEMS contest at home. Since the AoPS problem sets often contain contest problems, this was a good way to prepare in elementary.

It is a challenging class, but taking calculus prior won't prepare you for NT. They are completely different topics.

I agree, it was a super-hard class. It was made more difficult by the fact that there is no textbook. I was despairing that I was learning very little each week, but now I find, a couple years later, that I'm reaching for those skills with my current problems. It's funny how you don't really think you are learning, when in fact you are.

3blue1brown has a series of excellent videos about vectors and matrices that I have my AoPS precalculus students watch.

I question whether taking calculus in your senior year is really "accelerated" or if we aren't just underestimating generations of students. Again, I argue we should be "front-loading" our education, making students work a fair bit in their 13 years before graduation. Sure, keep music and sports, but not at the expense of learning virtually nothing in K-12. Otherwise, you have kids who become proficient baseball players, and then need to spend their young adulthood going to CC to get their education. Why not reverse this sequence? Education first, piano lessons later.

Paper used to be such an important tool in teaching, when my DH was TAing CS classes, he and the other TAs spent the bulk of their time just photocopying handouts. A running joke was that his nickname was "Handout Boy." As in, the lead instructor would call to DH in a sing-songy voice, "Oh Handout Boy!!!"

Exactly. We should be using that precious time when they are under 16 to be studying. Instead they are learning a sport or playing an instrument. Even high school these poor students get jobs. Why not use that time to learn those academic skills before life gets in the way?

See, my eyes glaze over when I see text blocks on screen. There seems to be an inverse relationship between how critical information is and how well I can parse it on screen. I use an online calendar, but really I make so many calendar data entry errors the advantages aren't so great. I just wonder if students aren't in the habit of printing things, or maybe they don't even have access to a printer?

No, these AP classes are pretty much NOT college level classes, IMO. I believe all students should take these classes in order to graduate high school. My kids did not take AP classes to finish college early. They took them to show they took reasonably difficult high school classes, and have the EF skills to complete them. I've been hearing a bit lately about free community college for underserved students. It's tough because they are often working or have families and they don't have a lot of money for tuition. Or time. When do underserved students have time? When they are too young to work, elementary, middle, high school. Why not use some of that time to actually study and learn these high school level classes. They can graduate and perhaps get a meaningful job (since a high school diploma could actually mean something), without struggling to learn these basic skills while earning a living.

I'm curious whether this information is on paper or on screen? We are coming up on the MathCounts Chapter Competition (tomorrow!) and I've been receiving LONG emails from MathCounts HQ about all manner of rules and schedules and timing and everything. I can't parse these long detailed emails unless I first print it out and get my red pen and start underlining and making notes to myself. I wonder if students these days aren't in the habit of printing out critical documents? Also, I've been in situations where information is scattered in emails, on drives, in random documents with undescriptive names. (I'm looking at you, Math Kangaroo.) Weeks later I'll need some information and I have no idea where to start. So I email HQ and as them to resend. When I receive physical paper, I (again) underline in red pen important points, jot things in the margin, make a to do list, and THEN I will file in a hanging folder or punch into a 3 ring binder. I didn't do that with the Math Kangaroo stuff, and now I'm ...in a bit of a bind. My course syllabi was typically 1-2 pages long, hole punched and placed at the front of my binder. I received a physical book that served as the university directory. I wonder if in our zeal to go paperless, we've lost a lot of information transmission?

Generally the problem sets are shorter, but more challenging. You may start with some basic problems, but then they are throwing stuff at the student from left field, and they must solve using the material from the chapter, but in a novel situation. Many of the problems are lifted directly from math contests.

Unwritten Rules of Friendship

I think all the work she's done sound like community service, especially if she isn't being paid for her work.

To keep his skills fresh I might supplement with some math contests either for real if he enjoys that sort of thing, or just at home just for practice. He might enjoy doing old MathCounts, AMC and Math Kangaroo. You can find old exams for free on the AoPS website, or for sale at the contest websites.

Standard Sequence: Prealgebra Intro Algebra Intro Geometry Intermediate Algebra Precalculus Calculus Extra bonus classes, optional but highly recommended: Intro Counting and Probability Intro Number Theory Intermediate Counting and Probability Here's more info from AoPS about their recommended sequence.

One thing you can try is if you have a frustrating session as you described, shut your book and rest a couple of days. When you have some idle time like during boring housework, think about the kings, castles, and princesses. Think about 3 times as many kings as castles. (Why would there be more kings than castles? Wouldn't one expect to have more castles than kings?) Think about 7 times as many princesses as kings. (Big families back then.) Really ruminate on this. Think about how many princesses are running around if 2 kings got together with their families. How many princesses would there be? Think about how much food you would need for 3 kings and their families. What if every king had 5 princes? What if every king had 3 dogs? Don't stress about getting the numbers right, but just think about it when you are otherwise idle. After a couple of days return to the same problems and try them again, slowly. Maybe just try attempt one single problem. If you get it right, read the second problem, close your book and think about that one for a day or two. I really believe in the power of active meditation and sleep to help difficult topics sink in. Learning is uncomfortable. Ed: Misspelled "princesses"

Stanford Online High School. It was an excellent course.

My student took AP chem freshman year followed by AP bio.

I think it sounds amazing to do a math history course with your students. I had never heard of Cardano, and came across this article. But I wish I had assembled a math history course as you describe! We never did this, just Singapore for elementary followed by AoPS in prealgebra and beyond, and lots of math contests. My younger dd AIME qualified every year starting in 8th grade. (My older dd never got her AIME, but did respectably well on math contests.) I myself like to look up random things on wikipedia like the origin or the equals sign https://en.wikipedia.org/wiki/Equals_sign or different methods to round numbers: https://en.wikipedia.org/wiki/Rounding . We take so much for granted about math including popular algorithms or notation.

I'm on a private FB group for tutors. I can probably find someone for you, but I could not personally vouch for them. PM if you are interested.

You are wise to check on this. My dd took the SAT in middle school through a talent search. They wouldn't let me into the building so I dropped her off and drove home. Turns out they weren't going to let her test because.--I forget now--reasons? Fortunately there was a small crew of middle school students there to test and it escalated and was finally resolved that the students could actually test there. I was furious! SAT talent search has been around since at least the 1980s, and these ppl were unaware? Anyway, my advice is if your student does not currently have a cell phone, get them a burner phone for the day so they can contact you if there are any issues. Don't leave the parking lot. Coach your student, and print out stuff that shows that yes, middle school students can take the SAT. Ask other parents where they've successfully tested their middle school students. Insult to injury: that school's HVAC was turned off during the weekend, so it was bitterly cold inside. The other students were aware and brough coats and hot tea. We did not return to that school, and had a much better experience elsewhere.

I outsourced my first class (writing/English) in middle school, and it was still my busiest time in homeschooling. I had NO TIME for anything. Most of my extra time was spent prepping for science which was a step up in complexity and required me to demo projects in advance so I could run them with success for my kids. Because I was outsourcing even more (especially science), high school was much easier.

Chiming in also to say I thought penny candy was a head scratcher. After listening to Freaknomics and Planet Money for years, it was weird to have a children's book devoted 100% to money supply. I mean, I get money supply is important, but isn't there so much more to economics?

...and just as @Not_a_Number predicted, students are relying on lies and exaggerations in their essays for admissions. https://nypost.com/2022/01/13/how-college-applicants-embellish-admission-essays/ https://nypost.com/2022/01/11/rhodes-scholar-denied-honor-after-dishonesty-about-life-story/ https://www.chronicle.com/article/the-dredging "Multiple college consultants told The Post that the college application process now features more questions about overcoming obstacles. The 2021-2022 essay prompts from Common App, the organization that oversees undergrad applications for more than 900 schools, include “Recount a time when you faced a challenge, setback, or failure.” "an anonymous accuser sent an email to Penn and the Rhodes Trust, claiming Fierceton’s story was “blatantly dishonest.” The email reportedly alleged that Fierceton grew up in St. Louis, Mo., with her mother, an educated radiologist; that her family was upper-middle class; and that she had attended a fancy private high school and enjoyed such high-end hobbies as horseback riding." "Fierceton lived with her mother, Carrie Morrison — a divorcée and director of breast imaging and mammography at a local hospital — “on a [suburban] tree-lined cul-de-sac with large houses and well-groomed lawns.” "According to Winkelstein’s subsequent report, Fierceton was raised in an upper-middle-class household; it also notes her mother is a radiologist and that her grandfather had graduated from college." “If ‘first generation’ means the first in one’s family to attend college — the widely used, common-sense meaning — Fierceton’s answer would be plainly false.” However, according to the school’s website, this definition can also include students who are the first in their families to “pursue higher education at an elite institution.” Fierceton’s mother did not attend an Ivy League university" "The committee concluded that this was “inconsistent with the hospital records,” adding, “Either [Fierceton] has fabricated this abuse by her mother, or her mother has lied about the terrible abuse…”" “On the economic side, there are so many applications to schools that it is impossible for schools to fact check everything.” "Some kids will claim in their essays that they “published” a novel or memoir, when in fact their parents have hired a self-publishing outfit to produce what looks like a legitimate book. Other teens will write about their “meaningful” volunteer work in developing countries, when their moms and dads have funded the trips abroad just so they can have college essay fodder. Now, some students are even going so far as to register their own patents for research they have never completed." “Basically, these schools are pushing kids to have a trauma in their life before they’re 17,'” said one Manhattan-based tutor, adding that they have worked with deserving students who have never had huge obstacles in life, and as a result cannot compete for the top schools, such as Yale, Princeton or Harvard. “The irony of going ‘test optional’ is that it opens the door to more shenanigans,” he told The Post. In 2016, one parent took to social media to complain about a friend of her son who created a charity in her name dedicated to the deaf. “She registered it, made a website, logo, the works, but hasn’t done ANYTHING with it,” the unidentified parent posted on an online forum set up by College Confidential, an education consulting company for users asking questions about college admissions. The parent went on to say that the student put the charity on her list of extracurricular activities and was accepted to Stanford that year. Meanwhile, some legitimately underprivileged students resist dwelling on their personal hardships and insist upon being accepted on their merits. One college essay tutor told The Post how she urged a high school student to play up her background to win points. “I worked with a student in the fall who actually had hardships — she immigrated to the US as a child and has seen and lived in real poverty,” the essay coach said. “But she was reluctant to capitalize on that because she didn’t want it to define her.”

I'm not an expert on these classes but my sense is that AP Lang and Comp is more about your ability write on topics that are presented during the exam. AP Lit tests that plus you need to bring some prior knowledge of texts to the exam. That is, you will write about material (classic novels?) you read before taking the exam. I'm sure there are many students who take both classes, but I think more often students take one or the other, with future English majors (or those who have read the classics widely) opting for AP Lit. If you are taking both, I'd recommend starting with AP Lang/Comp. Some colleges offer some credit for a high score on either AP Lang/Comp or AP Lit but not both. Check with the colleges your student is interested in. It may not be worthwhile to take both exams. I think it isn't worth taking both classes unless, again, you have a future English major who really wants to.