EndOfOrdinary 5,405 Posted February 5, 2017 Report Share Posted February 5, 2017 We started algebra when Ds was writing subtraction problems with negative numbers and then applying regrouping. None of that was taught, he just did it. When directly asked why he was writing it the way that he was, he explained it as "needing two." He did not know how else to explain or write it. He needed formal instruction in order to keep him from developing very bad habits. It was not that his way was wrong. In fact, it was very inventive. It was that he needed to be able to harness and communicate his way into something others could readily understand. So we started with algebra in order to provide him the tools to communicate his way to others. As I said above thread, he grabbed an old PS textbook for Algebra far before that, but I do not count running through problems as Algebra. He could easily do the steps, and even explain the steps, but was not ready for proofs. No proofs, no algebra as far as I am concerned. 2 Quote Link to post Share on other sites

Space station 646 Posted February 5, 2017 Report Share Posted February 5, 2017 I was supposedly a math prodigy and I would have HATED AoPS. Math was my sanctuary space of rigid structure and smooth number crunching. Exploration was on a me-in-control basis. The level of leap of faith learning in AoPS would have caused me a very significant emotional problem and turned me off of math. Thank you for posting this. I think you may have given me a glimpse into my daughter's mind. 1 Quote Link to post Share on other sites

TerriM 236 Posted February 5, 2017 Report Share Posted February 5, 2017 (edited) You need to define "start". Does completing Dragonbox 12+ count as doing algebra? I don't really remember, but a lot of it has to do with opportunity and exposure as well as readiness. Good point. I was asked by a mother at a small B&M school my opinion on acceleration in math for the middle schoolers. She knows I took my kid out of the school because they wouldn't allow mine to work ahead, but to be clear I don't think every kid there is necessarily ready to jump to Algebra in 6th grade. The school is hesitant to allow kids to skip a class, and while I think that's appropriate to be hesitant, there's clearly some kids who should. Ultimately, I told her, the question of feasibility had two parts--scheduling and readiness. Scheduling meaning is it possible for a small school to have the staff, classrooms, and ability to have kids move around to the correct level. Readiness--how does a school know when a kid is ready to jump up a class? So I guess I'm asking that latter question--how does a school (or a parent) judge when a student is ready to skip a year or go into Algebra ahead of schedule? it's a little easier if you're homeschooling, because you can try it out and if it doesn't work, you just do something else. Schools tend to shy away from the stigma of being bumped up then down a class. For me, I figured any kid who could get on achievement roll for the AMC 8 in 4th grade must be just a little advanced.... Maybe that's not a great metric, but if he's scoring 6 points higher than the average 8th grader who takes the contest, there's something a little different. Plus he was bored and would ask us about more advanced math concepts. But for a school, there has to be a more concrete way to determine who to put ahead. Edited February 5, 2017 by tiuzzol2 2 Quote Link to post Share on other sites

Arcadia 23,766 Posted February 5, 2017 Report Share Posted February 5, 2017 (edited) So I guess I'm asking that latter question--how does a school (or a parent) judge when a student is ready to skip a year or go into Algebra ahead of schedule?My oldest did the end of course tests up to 7th grade algebra and then did the algebra 1 test with his public charter teacher proctoring. He didn't get 100% for the algebra 1 end of course tests but he did well enough that the school admin didn't kick a fuss about doing K12 algebra 1 in 4th grade. The school had their own placement tests which were not from K12 even though they use K12 curriculum. Being an online public charter does make it easier for them to allow my oldest to take subjects at whatever level he could cope. He took earth science in 4th grade. ETA: He did the end of course science exams too to subject accelerate. Language Arts we only accelerate a grade because of his writing. When he was in B&M public school, the teachers did a lot of testing too. He entered K doing multi-digit multiplication. Edited February 5, 2017 by Arcadia 2 Quote Link to post Share on other sites

luuknam 15,843 Posted February 5, 2017 Report Share Posted February 5, 2017 When a child starts asking questions like 'does the number line extend both ways' 'are there numbers less than 0?' 'Is zero the smallest ever number?' 'Does infinity extend in all directions?'. Every single child (who I've tutored and taught) who asked questions about numbers beyond natural/counting numbers has been ready for the abstraction in Algebra. My kids have known about negative numbers since they were 3 or 4yo (and asked some questions about them at that age), and have always found them pretty easy. That said, my current plan for my oldest is to try AOPS Pre-Algebra in 5th grade, so, maybe AOPS Algebra in 6th grade? Like, starting it right around the time he turns 11? I didn't vote though, because I don't know how AOPS Pre-Algebra will go. It could go faster or slower than expected, in which case he'd still be in the 10-11 group for this poll (unless we take 2+ calendar years for Pre-Algebra), or we could end up not liking it, in which case I'd still see him doing some sort of Algebra at 11, but I don't see a point in making a prediction. And I'm not even going to try to make a guess about my younger kid. 2 Quote Link to post Share on other sites

Cake and Pi 740 Posted February 5, 2017 Report Share Posted February 5, 2017 If he continues at his present rate, my DS#1 will start AoPS algebra at 10yo-ish. If he takes longer than a year on pre-A or he's not mature enough for a text book presentation (or whatever) then he might not start until 11yo (or later?). Simple, non-official algebra like completing DragonBox 12+ was 7yo. I think there can be a big difference between being ready for algebraic concepts and being ready for a high school level algebra course. My DS#3 did DragonBox 5+ when he was 3yo, but I'll be surprised if he starts an official algebra course younger than 10-11yo. 1 Quote Link to post Share on other sites

Cake and Pi 740 Posted February 5, 2017 Report Share Posted February 5, 2017 Oh, and I didn't vote. 1 Quote Link to post Share on other sites

wendyroo 8,590 Posted February 5, 2017 Report Share Posted February 5, 2017 So I guess I'm asking that latter question--how does a school (or a parent) judge when a student is ready to skip a year or go into Algebra ahead of schedule? When I think of math acceleration, I rarely think of skipping anything. DS is working through 5th grade math and Hands on Equations (among other things) at the age of 7, but that is certainly not because he has skipped anything. I mean, sure, he has skipped lots of practice and review problems when he did not need the practice or review, but it's not like we have ever skipped all or even most of a year of math. If anything, he has done more math than most 5th graders. He has always used two formal math curricula concurrently, plus extra logic and problem solving, plus living math books and math games and math discussions, etc. He's delved deeply into binary, hexadecimal and other number systems. He's read books about fractals. He's "invented" his own method of long division in a never ending quest to convince me that writing out work should never involve more than random chicken scratch. :lol: He would be perfectly capable of tackling a less-rigorous, less-writing intensive algebra 1 course at this time, but that is not the path we will be following. Instead, he will finish Hands On Equations, Beast Academy, enough Math Mammoth to ensure that his arithmetic is rock solid, lots of challenging word problems and logic puzzles and rabbit trails into fascinating topics that are not part of typical elementary math. During that time, I'm sure we will casually cover most algebraic topics, but we still won't dive into Algebra 1 officially. Instead, he will go through AOPS Pre-Algebra and focus on really thinking about problems before diving in and writing his solutions neatly and coherently. Only once those skills are mastered will I consider him ready for a rigorous Algebra 1 that will serve him well as he continues on to higher math. Wendy 5 Quote Link to post Share on other sites

TerriM 236 Posted February 5, 2017 Report Share Posted February 5, 2017 When I think of math acceleration, I rarely think of skipping anything. Totally fair. That said, I've no clue what my son would've done for the next two years if he'd stayed at his old school--I don't feel like he has any gaps, and he did extremely well in the Algebra I class. Maybe his new school lumped Pre-Algebra and Algebra together? 1 Quote Link to post Share on other sites

StartingOver 874 Posted February 6, 2017 Author Report Share Posted February 6, 2017 Depending on whether you wanted "started" or "formal": We started with theory of arithmetic at 6 with younger DS, and that is absolutely a branch of algebra. Formal AoPS algebra was two years later. ETA: echoing what others said, for any child below 10 doing algebra, PLEASE - I implore you - PLEASE do not put them on Saxon! It really is robbing the brightest mathematical minds of the theory which makes the mathematics beautiful. If you do choose to use it, then PLEASE follow it up with a more sound program like AoPS. Two years of quality algebra will not slow their progress down. This is the path I am hoping for, so far she enjoys and has been the one to request Saxon. I have purchased AOPS Pre-Algrebra and Algebra so she can use them too as she wishes. 1 Quote Link to post Share on other sites

StartingOver 874 Posted February 6, 2017 Author Report Share Posted February 6, 2017 Ds did the Hands On Equations/Dreambox stuff early....can't quite remember...but tiny. He started a Scott Foresman discarded PS school Algebra 1 text at 6. The library was getting rid of some giant lot of school discards. After three chapters a week of content (not all the problems, but mastery of content) for a couple weeks I completely discarded it. He was just number crunching. We started AoPS PreA at 8 and there were meltdowns of emotional ridiculousness. AoPS Algebra was added by late 9. Then some C&P. Then he finished PreA after it was shunned for being horrible. Back to Algebra. Geometry made an appearence for a bit. It got all messy. I was supposedly a math prodigy and I would have HATED AoPS. Math was my sanctuary space of rigid structure and smooth number crunching. Exploration was on a me-in-control basis. The level of leap of faith learning in AoPS would have caused me a very significant emotional problem and turned me off of math. I appreciated older math texts that were proof based, but explicit. Then I would play with them. One of my math teachers turned me on to pure math and concepts of advanced number theory. I spent a very long time going down the rabbit hole. If she can find an area of math she enjoys that might greatly help you. Ds likes visual representations like Vi-Hart makes and then wants to see if he can quantify them. It gave him a part of math to hold onto that spokSe to him. From that, I could really give him content that would work for him. Just do not be alarmed if you get a wierd emotional response with AoPS She has not approved of anything else except Life of Fred and Saxon so far so we will see how it goes. I will not assign AOPs it is on the shelf so she can explore as she wishes. ;-) I can see this reaction from her, totally. 1 Quote Link to post Share on other sites

StartingOver 874 Posted February 6, 2017 Author Report Share Posted February 6, 2017 In our case, she was demanding to do Algebra and started printing out and doing placement tests and leaving them on my computer. I figured that was a pretty good sign that she was ready to at least start pre-Algebra :) I figured we could always double back later. And actually we're kind of doing that-DD is taking a college math for teachers class that seems to mostly review high school algebra and geometry, with some logic thrown in. She's finding it ridiculously easy. Emma decided to do this, she tested out of every book I have and started doing placements. I giggled so hard, and decided to just let her go. She has finished test 8 on Saxon 8/7 already, more tomorrow. Quote Link to post Share on other sites

kiana 11,476 Posted February 6, 2017 Report Share Posted February 6, 2017 Totally fair. That said, I've no clue what my son would've done for the next two years if he'd stayed at his old school--I don't feel like he has any gaps, and he did extremely well in the Algebra I class. Maybe his new school lumped Pre-Algebra and Algebra together? For a child in school it's quite different -- if skipped a year or two, a highly gifted child can very frequently fill in holes, because the pace of the new class is still slower than they could go independently. For a child at home I'd prefer to compact curriculum (and to choose one that's amenable to compacting) than to just skip ahead. 3 Quote Link to post Share on other sites

Dmmetler 25,129 Posted February 6, 2017 Report Share Posted February 6, 2017 The nice thing is that she can do Saxon and then do AoPS and, while the concepts are the same, still find new, mind-stretching content to explore. At 8 she has a ton of time to enjoy Math. 2 Quote Link to post Share on other sites

4KookieKids 1,082 Posted February 6, 2017 Report Share Posted February 6, 2017 I was supposedly a math prodigy and I would have HATED AoPS. Math was my sanctuary space of rigid structure and smooth number crunching. Exploration was on a me-in-control basis. The level of leap of faith learning in AoPS would have caused me a very significant emotional problem and turned me off of math. I've been wondering about this, honestly. I was great at math as a kid too, but what drew me to math as a child was very different than what drew me to math as an adult (I ended up with a phd in math). When I was young, I liked math because it was easy, logical, and fixed. I could learn the rules and compute quickly and I enjoyed being "the best." Then I majored in math in undergrad because I needed a major I could complete quickly (limited funding meant I wanted in and out in 3 years and math seemed the easiest way to get that accomplished). Lo and behold, during my second year I come across math that I actually considered fun and interesting and even - dare I say it? - challenging. I enjoyed it so much that I did continue on to my phd and I'm now a very outspoken voice for giving kids more interesting math earlier, since there's so much they *could* actually understand and delve into earlier. But it does make me wonder - would this approach have reached me as a child? Or would I have responded the way you suggest you would have - by getting turned off to math? I'm honestly not sure. But it's interesting to consider. 1 Quote Link to post Share on other sites

Arcadia 23,766 Posted February 6, 2017 Report Share Posted February 6, 2017 When I think of math acceleration, I rarely think of skipping anything. In the context of a public/private school, it is a paper skip not a knowledge skip. My oldest was skipped to 4th grade math in public school at the start of 2nd grade by testing out. His school record is missing 2nd and 3rd grade math. He knew the 2nd and 3rd grade material. For a child in school it's quite different -- if skipped a year or two, a highly gifted child can very frequently fill in holes, because the pace of the new class is still slower than they could go independently. A child could also have self study, attend a afterschool class or be parent taught. For example reading The Number Devil lead to learning Pascal triangle, binomial expansion, way before we read aops prealgebra. Trying out math circles questions again led to acquiring more knowledge. So it is more of a skip on paper. 1 Quote Link to post Share on other sites

slackermom 3,612 Posted February 6, 2017 Report Share Posted February 6, 2017 My dd's second grade public school teacher let her work ahead on her own, using Zaccaro workbooks, etc. She pretty much covered all the elementary math topics that year, but it still just said second grade math on her report card. Her third grade teacher would not let her do anything but what the other kids were doing. When I started homeschooling mid-fourth grade, we chose AOPS Pre-algebra. So, technically she "skipped," but I don't think anything really got missed. When she went back to school for grade 6, she was placed into an accelerated math track based on test scores. It was nearly impossible to find a public school that offered that option. There are just 9 kids in her math class, so the teacher can spot if anyone needs more time on something. 1 Quote Link to post Share on other sites

EndOfOrdinary 5,405 Posted February 6, 2017 Report Share Posted February 6, 2017 I've been wondering about this, honestly. I was great at math as a kid too, but what drew me to math as a child was very different than what drew me to math as an adult (I ended up with a phd in math). When I was young, I liked math because it was easy, logical, and fixed. I could learn the rules and compute quickly and I enjoyed being "the best." Then I majored in math in undergrad because I needed a major I could complete quickly (limited funding meant I wanted in and out in 3 years and math seemed the easiest way to get that accomplished). Lo and behold, during my second year I come across math that I actually considered fun and interesting and even - dare I say it? - challenging. I enjoyed it so much that I did continue on to my phd and I'm now a very outspoken voice for giving kids more interesting math earlier, since there's so much they *could* actually understand and delve into earlier. But it does make me wonder - would this approach have reached me as a child? Or would I have responded the way you suggest you would have - by getting turned off to math? I'm honestly not sure. But it's interesting to consider. My return to college so that everything can get back up to snuff has me getting my middle school math certification. I am excited to bring math like AoPS into the classroom. It obviously cannot be exactly like that, but definitely a far cry from when I grew up. 3 Quote Link to post Share on other sites

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