Ah, this is the other one I reference sometimes. It's also about reading skill, plus (down a few posts) has a list of classic lit. http://forums.welltrainedmind.com/topic/509936-so-how-to-work-through-progressively-more-challenging-works/

I had this one bookmarked, is this what you were thinking of for scientific reading skill? http://forums.welltrainedmind.com/topic/467812-developing-advanced-reading-skills/ I think I have the other bookmarked too (hope I didn't just print it)...hang on.

Two lectures. One when the thread was first posted 18 months ago, and the other when it was bumped a couple of weeks ago. Like the OP, when it comes right down to it we've gone with school because my kids' other parent is most comfortable with the status quo. I've made my peace with that. If I felt strongly enough that homeschool would be a significant benefit for my kids, I'd argue in its favor. But there are honestly pros and cons. My kids have friends at public school, and I'm able to use my time and skills to benefit my whole community (volunteering in class, serving on the PTA board) instead of just my own kids. I will admit I crave the flexibility of being able to shuck off the public school schedule and the constraints of the curriculum -- but I am also attached to the freedom of having safe, reliable, free childcare during the day that lets me balance my home duties and personal time with my parenting and other responsibilities. The chance is growing that we're going to hit our breaking point with public school. My kids are outliers and last year was kind of egregious with respect to how little their needs were met. I'm going to keep closer tabs on them and be ready to make a change this year. But if that happens, I won't regret their public school years at all. In fact, I'd almost say that PS elementary and HS middle school (and hybrid high school?) could represent the best of all worlds, for *my* family.

I'm trying to put my kids in Jules Verne and Jack London and Mark Twain. But their interest flags quickly with that material. Lord of the Rings holds them a little better. But it's summer...they're reading for 3-4 or more hours a day, and if a lot of it is low-level (DD8 is on a weird Big Nate kick) I just let that go for now. So on that vein, some material that they've enjoyed around that age but that's well below 10-12th grade in level would include the Chronicles of Prydain, the Enchanted Forest series, and anything/everything Rick Riordan. ;) Oh, and Alcatraz and the Evil Librarians.

How sensitive is sensitive? My daughter still has nightmares about Medusa in the film version of "The Lightning Thief" -- but the first 2-3 in the Harry Potter series were no problem for her, nor were any of Riordan's books, or the Dealing with Dragons series, or the Chronicles of Prydain. She and another second grade friend both went through a Ramona phase *and* a Roald Dahl phase right at the beginning of this year, which I thought was an interesting coincidence. :) I think a couple of her classmates also had a Series of Unfortunate Events phase (DD is currently re-reading the first few). Sometimes I think finding good books for a specific child's reading level is mostly a matter of throwing everything at them and seeing what sticks. We go to the library a lot and DD gets a ton of picture books and Smurf graphic novels, but I can usually toss 3-4 "good" books into her pile and sometimes one will catch on like wildfire. (I still can't believe she won't even try anything by Marguerite Henry though. I LOVED those books as a kid.)

I think a lot depends on the kind of learner you have. My son is a "don't teach me, let me dive in" kind of guy. He'd probably thrive on a meandering multi-stream path like what quark has described through the years: http://forums.welltrainedmind.com/topic/320275-designing-a-non-traditional-math-course-for-a-math-loving-structure-hating-child/?p=3272174 My daughter prefers structure (as far as I can tell) and would probably do well just working straight through BA. I think if I kept her home I'd consider doing math M-Th and taking Fridays to be a "mess around with different topics and approaches" kind of day, which would be a time for pulling out the competition math and such, or programming, exploring in Khan, whatever. For now though, all those "extra" resources have basically just served as stopgaps to keep my public schooled kids from imploding on a steady diet of school math. ;) We use them on occasional weekends and breaks to make sure the kids know that there's a beautiful science of mathematics out there, quite apart from the drudgery of school workbooks. :lol: It's sort of a "slow them down" concept, but also kind of a "feed their need while we figure out where we're going with all this" concept.

If your student doesn't have the stamina for these yet, then maybe you don't want to push their interest level by insisting on multiple problems like this every day. Pace yourselves. But these examples have all been chosen to demonstrate how, as humans, we can work SMARTER than a calculator and reduce the calculation required and the memory space needed. They aren't difficult at all to someone who's had any practice looking for the clever way. A student who's come all the way up through Singapore, for example, shouldn't have any problem at all seeing a thousand in 997 + 605 and near-instantly seeing the outcome of the addition problem. If they haven't had a lot of practice composing and decomposing units of higher value (eg. making tens) then that's the skill level you need to be working more on, not just brute-force chugging through these problems without the benefit of paper. My DD is working on third grade math but we haven't built those skills and she would be very intimidated by these problems. Our summer plans will include games to build her subitizing skills.

Did you not get answers you liked in your previous thread about this? http://forums.welltrainedmind.com/topic/639389-is-mental-math-a-necessity-in-the-primarily-years/ I think working memory is a muscle that can be built up, one that weakens if left unused. I think that manipulating numbers abstractly requires a greater depth of understanding and number sense than just going through a rote algorithm to perform an operation. And I find that my kids get a great sense of accomplishment if they can come up with a strategy to tackle a large calculation and hold multiple steps in their head. So yes, I do think there's value in working on this skill. "Training" the skill as a separate thing? Not really, not so much. I mean, the goal of getting educated in mathematics is to train the mind to work with patterns and abstractions. If all we needed from math was the ability to calculate, the marvels of this technological age mean that we are almost never more than an arms reach from some type of electronic calculator. Human calculations are largely redundant.

We do karate year-round, plus one sport per kid per season (fall, winter, spring.) We re-evaluate the karate schedule each season once we know about practices (we always have very late notice on that too.) Sometimes we re-evaluate each week. Anyway, I'd schedule a meeting with the principal to discuss homework expectations in 6th grade. What have you got to lose?

Just looking at the table of contents, I'm not seeing redundancy. One introduces the bare outline of an idea, the other fleshes it out with mathematical rigor. I wouldn't go into those Intermediate chapters without the understanding you'd surely get from the Intro chapters.

Maybe a librarian who's engaged with him about areas of interest?

My kids like Reflex Math, IF they are intrinsically invested in improving automaticity after they already have good number sense. Just for building familiarity through repetition I like some of the pages in Beast Academy, like the jumbled times table. It works the brain from a slightly different angle, you know? Still...you don't need fluent math facts to do logic and set theory. And as I'm learning from my 10yo, if they're clamoring for the deep end, sometimes you just gotta toss 'em in. I've spent like two years insisting that if he really wants algebra and beyond, he needs to have solid arithmetic especially on fractions and decimals. Finally I threw up my hands and said, "Fine, do Alcumus on topics you've never seen." He's in heaven and learning like a sponge. Who knew?!

This makes me recommend the Brief Lessons all the more. :) I was a physics major who rolled my eyes at my freshman year professor's attempt to connect the concepts we learned to historical figures in science. I just wanted to do the equations and get the right answer. Now that I'm listening to these expositions on how wildly divergent and beautiful Einstein's epiphany was; how eclectic were the variously conceived bases of quantum mechanics -- to the point that early contributors could be completely flummoxed by the developments of later contributors who built on their ideas; how iterative was the development of our modern view of the cosmos...it's incredible to see the human touch in everything. :)

The Euclidean Algorithm is introduced on page 44, immediately after the page in question. LOL. This stuff is absolutely intended as a thought experiment to introduce the EA. IMO, and take this with a grain of salt because I'm using it as a supplement only, plus my kiddo who's ready for BA5 is 10 years old with great frustration tolerance...but instead of jumping in to teach, I'd jump in to learn alongside. Talk these concepts out. What I like about Beast and AOPS is the mathematical thinking. Why does this work? How? What tools do we have and how can we apply them? I wish like anything that my children had a math circle available, but failing that, they have Beast, and the little monsters' conversations in the Guide, and my interested engagement. (My kids HATE. IT. if they think I'm doing that faux-Socratic thing where I fish for the right answer by pretending not to know it. But they appreciate it if I offer *just* as they're getting frustrated, "I think I see a thing. I have NO idea if it's the right approach, but I want to see where it goes. Mind if I share?")

Just for a literally 15-20 minute blitz that teases some of the relevant sub-topics and invites inspiration, your kiddo might enjoy the second of the "Seven Brief Lessons". We've been listening to it on audiobook, my DS10 loves it. http://www.sevenbrieflessons.com/the-quanta

M2b, the book writes it in symbols as well: GCF(a,b)=GCF(a,a-b) for integers a and b. It then asks the student to determine whether or not GCF(a,b)=GCF(a+b,a-b), giving a counterexample if it's false or a proof/explanation if it's true. Fun stuff!

Michael Clay Thompson's Classics in the Classroom is a great reference. https://www.amazon.com/Classics-Classroom-Michael-Thompson/dp/0880922206 It explains beautifully the kinds of questions that readers can ask and discuss with peers, in order to delve deeply and encourage a book to open itself to them, without artificially imposing an external analysis on the work. It's based on Bloom's Taxonomy, and encourages gifted students particularly to focus their work at a higher level. It also has a list of 1300 suggested works, taken from lists like Harvard Classics, Great Books of the Western World, AP recommendations, etc. I'd love to use it as the base for teaching literature to an interested high schooler (or better yet, a book club of interested high schoolers?) Oh! And I'd also love to see an interested high schooler use Mortimer Adler's How to Read a Book. I found it so inspirational as a guide to a growth mindset in literature, increasing your ability to delve for meaning from more and more complicated works as you challenge yourself to read at a higher level. https://www.amazon.com/How-Read-Book-Intelligent-Touchstone/dp/0671212095

We got scores back last week and DS did horribly. :laugh: I wasn't expecting much else, but he kind of had his hopes up. I was super proud that after just a few moments of shock and disappointment, he dove in to the problems and figured out how he was meant to solve all the ones he got wrong. It turned out to be a great boost for his math interest and I'm glad we did it! I don't think we'll be doing the February round though -- we'll play with some more math, especially discrete, before we do anything like that again.

DS10 did the second round yesterday. He didn't finish. I think it was a great experience for him. He got frustrated, but persevered, and came away still pondering the one he almost finished. Definitely a good exposure to more interesting, and more discrete, math than he gets in school. :)

Just got the email…DS made it to round two. :) We are supposed to enlist someone unrelated to proctor the test.

The auto-response to our submission went to junk mail. I don't expect my DS qualified, because he got frustrated and rushed on a few questions, but I haven't heard anything about Round 2.

All I can say is that when my peers and I took the sophomore course in Discrete Mathematics as required for our physics major, it crushed most of us. Utterly left us staggered and confused. We would turn to each other and whimper, "COUNTING? How is COUNTING the most difficult thing we've encountered after 13 years of math? I thought I knew how to COUNT." So. I personally enjoy introducing a bit of counting and combinatorics and probability to my 9yo. And I get excited when he spends his own time, sitting in the car, figuring out things like how many individual symbols can be represented in Morse code by a maximum of five dots or dashes. (Ah, Benedict Society, thanks for putting that in his head, LOL.) But anyway, I found the book (and the MOOC) Introduction to Mathematical Thinking several years ago, about the same time I read Knowing and Teaching Elementary Mathematics, and I guess between them they've really shaped my thoughts about mathematical education. I believe there's a place for school math, but there shouldn't be the abrupt distinction between "math as a way to calculate" and "math as a way of thinking and a science in its own right" that currently exists in the transition from school to university. IMO, we need to ease this transition for those who will make it -- and presumably our very precocious young math learners *will* someday encounter *some* sort of math at a college level, as taught by a mathematician -- by introducing mathematical thinking right from the beginning, even if it's just one strand among many, even if it has to ebb and flow with their maturity and frustration tolerance. And I also really like this quote by Keith Devlin: "Education is not solely about the acquisition of specific tools to use in a subsequent career. As one of the greatest creations of human civilization, mathematics should be taught alongside science, literature, history, and art in order to pass on the jewels of our culture from one generation to the next."

You keep coming back to this idea that the only problem solving being done at the elementary level is effectively a "gotcha", forcing kids to do problems with one hand tied behind their backs. It's just not true. Just because a problem can be solved with both a bar model AND an algebraic equation, doesn't mean that the only value of the problem is in re-inventing the wheel of algebra. Conversely, it doesn't mean that having an algebraic skillset negates the need for a bar model or other strategy that is based more on an understanding of the numbers than of the procedures. I think you're not using the right books, to be honest. I have an idea of what you're talking about, as I've also seen "challenge math" that's just silly. But I find that Beast starred problems and Borac competitive math are much more worthwhile. Where are you getting your "competition" math?

So, here's the thing. I was a gifted child, and I LOVED number stuff. I got a workbook and did multiplication problems on my own, pages of them. I thrilled to the structure of setting up a complicated long division. It tickled me pink when my dad showed me how to set up an algebra problem to solve third grade math. Hearing about your son and the area of a cone takes me right back to my own childhood mindset. ;) And that stuff is great, and loads of fun! But what I was missing as a kid is that it's not MATH. Mathematics IS mathematical thinking -- and using that process to solve problems. Any calculator can plug and chug, but it takes a human being to make connections and draw conclusions. So as I came up through the system I just kept getting heaped more and more praise for quickly understanding more and more advanced algorithmic solving approaches, and getting told I was so good at math because of it. Algebra…Trig…Calculus…all setting up the right equation and then solving it the right way. It took me until sophomore level college math and physics before I hit a point where my gifted-kid skill of matching patterns was no longer enough to get the right answer. Instead I was looking at problems that *had* no one right answer, where there *was* no algorithm in the text book to apply. This blew my mind -- and in the end, crushed my ability to succeed in my chosen field. I limped through and got my bachelor's in physics, but have never returned to math or science. I don't want that for my kids. I want them to have the joys of trying and failing while they're still young enough to appreciate it. But they're public schooled and "math time" for them means just doing lots of plug and chug. So I distinguish very clearly between "school math" (learn the right algorithm for the right problem,) and "real math." They work at school math and often enjoy it, but if sometimes they get bored with the repetition I can say, "It's okay. It's just for school. That's not real math anyway. You have to learn it for school, but don't worry, we can make time for real math too." So at home we can practice discrete math, logic, computations with more than one approach, etc. I highly recommend that you go to Amazon and look up one of the Borac competitive math books. Here's one. https://www.amazon.com/dp/0692244905/ Then use the "Look Inside" feature to read the Foreword. They say it better than I ever could. :) I drive my kids' educations with a mantra I got from the Boracs, "Mathematics is not meant to be easy. It is meant to be interesting." Of course it's okay for your son to just explore around and make his pattern-matching mind feel soothed with mathematical structures. But for the long term, it's really probably good for him to get some frustration tolerance built up, and to find some work that stretches and builds his ability to tackle real math. I bet he'll rock at it. :)

The book Doodling Dragons covers all the sounds of each letter in the alphabet. That could be a good resource to start associating the "name" of the letter with its sounds. My son knew the letter names, but not the alphabetical order, as he was entering kindergarten. We drilled him and taught the alphabet to him in one day, the day before he went to school. That's the nice thing about accelerated learners, they usually catch on fairly quickly.