Another "early" question- Algebra in 3rd grade??

[Dmmetler]

I think the best comparison is to something like gymnastics. Some kids start at X age, and move along sequentially, about 1 level a year. Some kids start out a little later and move through multiple levels, often developing skills in what seems like only days, and then get to a higher level and stay there awhile. Some kids are future potential Olympians. Some are college scholarship candidates. And some will never go beyond a local club team or school team and are very happy there.

 

My daughter is a recreational gymnast who makes consistent, slow progress. But when it comes to math, she's the kid who suddenly "got it", seemingly overnight. For her, that came at about age 7-suddenly, something clicked and she was able to apply the arithmetic skills she'd already learned (through SM 4 or so at the time) to problems of kinds she'd never done (things like being able to figure volume by looking at a diagram). We spent the last year and a half, or so, on pre-algebra, doing LoF Decimals and Percents, both Pre-Algebra books, and Key to Algebra, plus LOTS of math enrichment and math competition resources. Math went from another school subject to something that I leave for the end of her school day because she'll happily spend hours and hours on it. She's good. I don't think she's "potential olympian" good-in large part because I don't think she really wants to be a mathematician, physicist or an engineer (I think zoology or wildlife conservation are more likely to be in her future), and I think math, right now, to her is more of a fun, new puzzle as opposed to her deep, abiding passion.

 

 

But I did nothing to get her there except provide a solid math curriculum, a household where math is valued and discussed over the dinner table, and lots of math enrichment, and a willingness to compact and work at her speed. In other words-I did exactly what many parents who have a child who is on or slightly over grade level in math do.

[Crimson Wife]

FWIW, this is what happened to me in PS. They wanted me to do page after page of single-digit addition problems and it was so damn boring. I had no motivation whatsoever. Then they wanted me medicated for ADD because I spent all my time staring out the window instead of doing math. They also wanted to keep me back a year because I was young for grade and 'failing math'. Yeah.

 

 

There are materials that are intellectually challenging without going faster through the sequence- Singapore IP, MEP, Beast Academy, etc. I don't think kids are done any favors by racing through an easy math curriculum just to get ahead.

[lewelma]

I think this is where "the where" the classes are taken and how they are approached really matters. For kids that love math and want that mathematician proof-driven/theory-oriented experience, your typical university is probably not going to meet those needs. Whereas schools like Stanford/MIT, etc those are going to offer theory-oriented classes starting at the freshman level and those classes are going to be filled with great math students that love that sort of challenge.

 

 

This is eye opening and really disheartening. I've been thinking that all I need to do is get him to University, and all will be well. sigh.

[8filltheheart]

 

 

This is eye opening and really disheartening. I've been thinking that all I need to do is get him to University, and all will be well. sigh.

 

Ruth, if I thought my ds had any interest in being a mathematician, I would be 2nd guessing our decisions every single day. These math classes are serving the purpose of providing him with the math skills he needs for the physics he wants to do. But as far as stirring his mathematical interest or developing mathematical analytical skills, no.

 

Perhaps the universities near you are different?

 

 

[Momof3littles]

My DS1 is a 9 yo 3rd grader (young 9). We are finishing up SM5B (we've done the IP and CWP with each level). He's messed around with the Zaccaro Primary Grade Challenge Math book, Penrose, he is playing around a bit in LoF Decimals and Percents and Pre Algebra. I picked up BA recently, and he's revisited some topics in there for fun.

 

My Kindy aged DD is working on Singapore 2A right now, and has done some work in BA level A like area, perimeter, etc.

 

Next year with DS1 (4th) we'll be trying the first few chapters of Jacob's Algebra as a prealgebra course, and AOPS pre-algebra.

[LucyStoner]

I have a gifted son. I vote wide and deep rather than racing through basic curriculums. This is not about algebra but about calculus but it is why I opted not to start my son with AOPS pre-A until this summer. He will be 10 in June:

 

http://www.artofprob...ge=calculustrap

 

We have done a lot with arithmetic, which naturally includes some algebraic thinking, but I layered in more and more challenge type math, intensive practice and courses designed for gifted young math students (one on Infinity, another on Perfect Squares) rather than jump up grade levels. While some kids certainly need to go faster than him, I am leery of teaching watered down accelerated topics versus having him gain fluency and explore a love of the subject. He's pre-read a few of the AOPS Pre-A chapters and is excited.

[Alira]

So if they complete Algebra in 3rd or 4th grade, that would put them on track to potentially finish your run of the mill high school math courses by the time they complete middle school, right? So in high school, what would they do? Are those of you doing things this way planning on enrolling them in college early?

Yes, Ds13 finished "high school" math last year in 7th grade. His goals for math were a little different than some I've seen mentioned here. He does not want to be a mathematician, and has never shown any interest in math competitions. From the time he was 6 or 7, his interest in math has been driven by his love for chemistry and physics. For this reason, we focused on algebra, geometry, trigonometry and calculus, and only dabbled in other areas of math. He did start taking college classes last year (through dual enrollment), but that was based more on science than math. There are online options available for the first few college math courses that we likely would have used if he hadn't been so desperate to get inside a chemistry lab.

[boscopup]

My son will be doing prealgebra in 4th (at just turned 9), using AoPS. We did get through elementary math quickly (starting in first grade when I pulled him from school). A lot of it is repetitive. Once he learned place value, he understood big numbers. He didn't need to learn one new place per year. Likewise, once he could do the 4 operations with 2 digits, he could do it with any number of digits. I didn't skip grades, though I did skip half of 2nd grade MM because it was mostly 3 digit addition and subtraction. At the same time, we were using Singapore IP and CWP, and he was doing 3 digit addition and subtraction in those, so I gave him the end of semester test, he passed with flying colors, and I moved him on to the 3rd grade book. From there, we only had occasional sections to skip or breeze through. In grades 4 and 5, I've not really skipped things. We've often done multiple lessons in a day if the material is easy though.

 

The thing about a kid gifted in math is that they often figure math out before you teach it. My oldest figured out addition and subtraction before K, and shortly after starting K, he figured out multiplication. Soon after, we had an impromptu negative number lesson on a napkin, and from them on, he could add and subtract negative numbers, having never practiced them in a math curriculum. He just gets math. Once we found where he really was in math, I was able to slow him down a bit.

 

I have no intention of graduating my son early (I see no benefit in our situation right now). He will most likely need DE for math, but our local uni doesn't take kids until senior year. If he hits calculus before 11th grade, I have to beg and plead and hope they'll make an exception, and I don't know if they would. So... I have an AoPS path laid out that would get him to calculus in 11th at the earliest, assuming he does one level per year (except number theory and counting & probability, which are semester books, I believe). In reality, we may need to go slower, and I'm cool with that. We'll spend as much time on prealgebra and algebra as we need in order for that foundation to be rock solid. I just don't want him hitting calculus super early, given our DE options (CC takes 11 graders, but I don't think those courses would be a good fit).

 

My second son started K math at 4, so he's doing first grade Singapore for K and 2 grade for first. I haven't accelerated him beyond that yet, and we've not even done math every day (otherwise he'd already be using the grade 2 book). Like his brother, he gets math. As he starts to get bored at his level, I'll accelerate him. Until then, my priority is reading.

 

Youngest will start K math this summer at 4. He is more language oriented at the moment, so I don't know if he'll need as much acceleration or not. He did learn the other day that 1-2=-1. :lol: Concepts aren't there with him yet. He just memorizes well. ;)

[kiana]

 

There are materials that are intellectually challenging without going faster through the sequence- Singapore IP, MEP, Beast Academy, etc. I don't think kids are done any favors by racing through an easy math curriculum just to get ahead.

 

I do not think I said anything that even implied that students should race through an easy curriculum. As a matter of fact, I have repeatedly recommended the opposite. Now, none of these curricula were available when I was a child, and my parents did the best that they could with the materials they had available. I have said (in this thread, even), that if AOPS had been out I think I would have been far better served by working through those materials instead.

 

I will really disagree with the bolded. If the child has sufficient mathematical talent, even these intellectually engaging curricula (and I like all of these curricula very much) may not be enough without acceleration.

[kiana]

 

This is eye opening and really disheartening. I've been thinking that all I need to do is get him to University, and all will be well. sigh.

 

I don't know as much about the NZ system of higher education, but isn't it more similar to the UK system where students enter with a declared major and take courses only towards that? I believe that the mathematics courses in such a system usually are significantly more theoretical and proof-oriented than the ones in the US, where at most universities (especially community colleges and smaller state colleges) students with multiple goals (med school, engineering, physics, geology, math) all take the same calculus I class.

 

If I'm wrong, ignore me :)

[beaners]

 

I will really disagree with the bolded. If the child has sufficient mathematical talent, even these intellectually engaging curricula (and I like all of these curricula very much) may not be enough without acceleration.

 

I strongly agree with this.

[Crimson Wife]

 

I do not think I said anything that even implied that students should race through an easy curriculum. As a matter of fact, I have repeatedly recommended the opposite. Now, none of these curricula were available when I was a child, and my parents did the best that they could with the materials they had available. I have said (in this thread, even), that if AOPS had been out I think I would have been far better served by working through those materials instead.

 

I will really disagree with the bolded. If the child has sufficient mathematical talent, even these intellectually engaging curricula (and I like all of these curricula very much) may not be enough without acceleration.

 

 

Agreed that bright kids might still need acceleration even through a more rigorous curriculum (my oldest is in Singapore DM 7 this year) but what I'm cautioning against is using acceleration through an easy program just to knock out arithmetic. I've seen posters bragging about how fast their child raced through [insert name of easy program] and then start algebra at some young age. But then said child needs multiple years to get through algebra 1. I'm skeptical that this is the wisest course.

[LMD]

Exactly!

 

There's some stuff I don't mention on these boards just to safeguard DS's privacy as much as I can. It's not just that DS can't do the mundane stuff. There was another reason that forced our hand to accelerate him. It was heart-breaking to watch DS when he wasn't being sufficiently challenged. Acceleration for us was not really an option for that reason...he needed it. I agree with everyone who says it has to come from the child. It's just not the same if it is planned and structured by the parent.

 

I totally agree with this. My kids aren't gifted, but they do 'get' maths with little instruction. We use Singapore (amongst other things) and my oldest was literally in tears over having to do another page of the same type of problems. I was making her do them all because of mistakes, but she was so very bored she just kept making them. So we agreed that if she aced the review she'd move on. She aced it, we moved on, her eyes lit up again. We speed up and slow down depending on her.

[quark]

This is eye opening and really disheartening. I've been thinking that all I need to do is get him to University, and all will be well. sigh.

 

That was my wish as well. Me thinks (and hopes) my DS will continue to "homeschool" himself on the side (fingers crossed). That's the good thing about keeping the love of learning burning bright ya?

 

If the child has sufficient mathematical talent, even these intellectually engaging curricula (and I like all of these curricula very much) may not be enough without acceleration.

 

Thank you for saying it, kiana. I wanted to say this too but you've said it much better than I could. Very true in our case. And with SM, although the CWPs were challenging DS at one point, I found that allowing the acceleration while also working on CWP was a much better fit for the boy. But that works because we have always, since the beginning of our homeschooling journey, dedicated several periods of the day to math, sometimes on purpose to help him break through a wall of frustration, but usually, it just works out that way because that's what he has wanted to do.

 

I totally agree with this. My kids aren't gifted, but they do 'get' maths with little instruction. We use Singapore (amongst other things) and my oldest was literally in tears over having to do another page of the same type of problems. I was making her do them all because of mistakes, but she was so very bored she just kept making them. So we agreed that if she aced the review she'd move on. She aced it, we moved on, her eyes lit up again. We speed up and slow down depending on her.

 

Awesome! The bolded is what I'm always looking for in our day to day homeschooling. It is very important to me that there is joy in his eyes. I know I learn better when I feel all "lit up" myself. ETA: Because we outsource so much of his homeschooling now, I purposely choose to work on some math or something else alongside him during one of our co-learning sessions together just so we can joke around a bit together. Learning together is such an awesome, awesome experience...sometimes when you are accelerating and challenging your kid, it can become frustrating when they do the age-wise things instead of the "more mature" expectations that sometimes, inadvertently creep in because they are learning at a level expected of an older child. So when we have these co-learning sessions, it takes the pressure off, lets us be ourselves and we realize that it doesn't have to be all serious and bookish. It feels to me like a meeting of peers, not a parent handing down info to a child (nothing wrong with it, I like taking a break from it though) so we loosen up a lot and it helps keep that light shining in his eyes. Darn it, I love homeschooling. It feels so good to be able to challenge your child at his level and also watch him laugh while learning, be respectful of each other's questions without having to feel like you are asking silly ones and hope to goodness that these are the memories your child will have--of the two of you learning together, that learning can be fun at any age and should be enjoyable--when he is facing a tough period later in his academic life.

[Χά�ων]

Finding a good math curriculum is hard! My DS gets math. I hate most math curriculums I find most underwhelming or I felt I was getting ripped off because I would be tossing half the curriculum because it was all review for DS even though it was expected to be new concepts. I found a wonderful curriculum written and designed by a math teacher at a local private school. It fits with how he learns math. The grades are a bit different from standard and from comparing it to Singapore DS (3rd) is learning concepts taught in 4th along side his multiplication tables. I am a bit sad because the curriculum only goes through 5th grade and the kids pick up algebra in 6th. I am a bit concerned about finding just as awesome of an algebra curriculum.

[wapiti]

I found a wonderful curriculum written and designed by a math teacher at a local private school. It fits with how he learns math. The grades are a bit different from standard and from comparing it to Singapore DS (3rd) is learning concepts taught in 4th along side his multiplication tables. I am a bit sad because the curriculum only goes through 5th grade and the kids pick up algebra in 6th. I am a bit concerned about finding just as awesome of an algebra curriculum.

 

Can you share the name of this wonderful curriculum? Is it available on-line?

[SKL]

My kid sister found algebra very intuitive and started doing it for fun at age 7 or 8. (Her IQ is not particularly high, nor was she accelerated in school.) I think a lot depends on how the kid is wired.

[serendipitous journey]

There are materials that are intellectually challenging without going faster through the sequence- Singapore IP, MEP, Beast Academy, etc. I don't think kids are done any favors by racing through an easy math curriculum just to get ahead.

I do not think I said anything that even implied that students should race through an easy curriculum. As a matter of fact, I have repeatedly recommended the opposite. Now, none of these curricula were available when I was a child, and my parents did the best that they could with the materials they had available. I have said (in this thread, even), that if AOPS had been out I think I would have been far better served by working through those materials instead. I will really disagree with the bolded. If the child has sufficient mathematical talent, even these intellectually engaging curricula (and I like all of these curricula very much) may not be enough without acceleration.

 

I was thinking that both of these seem true. There are challenging materials available, and perhaps not everyone uses them -- it does seem likely that some parents wish to move "forward" as quickly as possible in order to reach algebra and/or calculus at earlier ages than usual, and such parents bypass these richer resources as pointed out in a PP.

 

On the other hand those more rigorous materials are not necessarily optimal and/or sufficient for all children through their elementary years, and the "less rigorous" materials may fit a need particularly well. I myself did compact dramatically with MathUSee until that no longer worked well for us, but do not think that was a mistake for this child, and do know people who use MUS with accelerated children in the upper levels, to good effect.

[Five More Minutes]

I was thinking that both of these seem true. There are challenging materials available, and perhaps not everyone uses them -- it does seem likely that some parents wish to move "forward" as quickly as possible in order to reach algebra and/or calculus at earlier ages than usual, and such parents bypass these richer resources as pointed out in a PP.

 

On the other hand those more rigorous materials are not necessarily optimal and/or sufficient for all children through their elementary years, and the "less rigorous" materials may fit a need particularly well. I myself did compact dramatically with MathUSee until that no longer worked well for us, but do not think that was a mistake for this child, and do know people who use MUS with accelerated children in the upper levels, to good effect.

 

 

I agree. As I've been reading through the posts on this fantastic thread, I've been thinking that there are different flavours of acceleration, and they can't really be compared to each other for method and materials.

 

One kind of acceleration is the "get 'er done" acceleration, and in my experience it's primarily parent-driven when we're dealing with young children. Motivation could be bragging rights, or the ability to access a class, or how it looks on a transcript, or whatever. But it's not driven by the student's passion. This is when students may quickly complete the different grade levels in a comparatively easy curriculum, without a lot of intentionality on the part of the parent as to how that compression happens. It's about completing levels and "finishing" math.

 

Another kind of acceleration is used by the parent of a bright / accelerated / mildly gifted child in response to that child's ability. She gets the math; she's bored by the topics; she can move through at a faster pace. The parent chooses a strong program, moves at the student's (accelerated) pace, and supplements widely, to keep her engaged and challenged and to develop a strong understanding of the material. This is not just about getting to the next level; it's about really learning the material and building critical skills in the area. Finishing math doesn't factor into it, because there's a whole lot of math out there beyond the traditional programs.

 

And then there's that wild acceleration that is driven by, or in response to, a student's ability and passion. This can look like a lot of different things: thoughtfully compressing an "easy" math program to pave the way for challenging material; accelerating through a known rigorous program; supplementing with lots of materials to go deep and wide; bringing in tutors; early college courses. In this kind of acceleration, the students are the main drivers because they will visibly wither under a traditional program and pace. And it strikes me that parents enabling this kind of acceleration also put a lot of effort into tuning into their child's passions (and deep need to fuel that passion), and then finding the right mix of materials and supports that give these students the chance to fly. It's a whole other animal, this kind of acceleration, and seems to become more intensely individualized the further it progresses.

 

And it doesn't make sense for a parent whose underlying motivation is to have their student "finish math" to look at the wild kind of acceleration as a blueprint for success. They're two different animals.

[Χά�ων]

Can you share the name of this wonderful curriculum? Is it available on-line?

Sorry. :( The books were donated to another organization and I happened to be the lucky one who got to look through the stuff first. What I have is workbook format with two workbooks per grade; they complement each other well and provide some review without overkill. It covers each topic, has a few practice problems and moves on. She might have more worksheets in the classroom but the main books she created are perfect as is for DS so I am thrilled with them.

 

If I didn’t have this program I would probably print off a checklist of math skills and just work through each concept or check off each concept that he has already mastered. That way I can make sure nothing is skipped and am not spending money on a curriculum that covers topics he mastered 3 years ago.

http://coachingchron...hecklist[1].pdf

[jujsky]

I'm not reading the whole thread, so sorry if I'm repeating anything, but I just started using Hands on Equations with my 8 year-old DD and it is awesome! If you want to introduce the concept of algebra to a child early-on, that's the way to go. Sometimes Homeschool Buyer's Co-op has it at a decent price. That's where we got our set.

[Crimson Wife]

 

Not saying you are directing this at me, but we also did IP, CWP, MEP, AoPS pre A, Life of Fred, Zaccaro, and some other things on top of the regular math program and my son started algebra when he was at the end of 10. Just saying it's not fair to assume it's about rushing a kid through.

 

Nope, I wasn't thinking of you at all. There have been at least a couple posters on one of the previous threads on the AL board about going faster vs. "deeper" who feel that arithmetic is "boring" and higher level math is just so much more fun that kids should be allowed to race through [insert name of easy curriculum] to get into algebra as soon as possible. But then said child has to do multiple algebra 1 courses, which suggests to me that he/she didn't actually have all that solid a foundation in arithmetic.

[Hedgehogs4]

Not by 9, but my current 11th grader finished through Horizons 6 around 10 1/2. By the end of 8th grade, he had completed alg 1, 2, 3, geo, and counting and probability.

 

FWIW, **I** didn't **do** anything. He just absorbs math. By the end of 7th grade, I rarely understood anything he was saying in regards to math. :p

 

ETA: Now I don't understand 1/2 of what he talks about in general. ;)

 

This. I think that there are kids who have brains that do math. Everyone else is equipped with regular brains that grasp math at certain developmental points along the way. I think there are concepts that "click" just like some kids can struggle with reading one day and be reading chapter books the next with virtually no logical progression of learning. Everyone seems to be on slightly different timelines, and I think it is risky to try to push beyond a child's ability in order to have an accelerated learner. I believe these children self-identify and a parent will not be in the dark as to whether their child could handle a faster pace or more complex material.

[Pamela H in Texas]

Just wanted to say thanks for the DragonBox mention! I saw it an hour or so ago. Since then, my just turned 6yo has stolen my iPad and has no intention on returning it. 3 chapters down....

[quark]

I don't know why I feel the need to defend what I'm doing, but I just think you aren't considering why some people have their kids do an algebra program for three years. Being ready for a certain thing is not always about not understanding the concept. There are other factors.

 

I feel as if Wendy is responding about my child too here. I don't need to defend myself because I know and see for myself that what we did is working. It may seem like we rushed through arithmetic and truth be told, I felt it too...why on earth was I skipping levels like this? What's going on...I thought MEP Year 1B was working last week, why is it so easy this week? We went through MEP like water that way and I was second guessing every single day of it. Was I shortchanging him in some way? Was it for my own ego? But you know, I know now that my gut instinct had been right. Sometimes, it's not just the academics. It's meeting the child on as many levels as you can and that includes mental and emotional well-being.

 

So what if you do algebra 1 over and over again? We are not talking about school kids here right? We are talking about customizing the approach for each child. Some kids need to do it again and again -- either for the fun of it, or because they need the variety or they just need something harder the year after to cement what they had learned a year earlier. I am of the opinion that bragging is harmful and dislike it when I think I have accidentally bragged and go back and edit or even delete some posts when I think I have said too much. But it's my truth. It's what I am facing. Some days I bring the algebra books out again because I have so many doubts that we spent enough time on it. But like someone else said somewhere, can't remember if it was this or another thread, algebra is algebra. It's not a mystical, magical stage indicating mathematical genius. It's another way of thinking and solving math and gaining tools. Because it is a gateway to higher math so many people think it's impressive and yes, I do think it's impressive for a youngish child to get it but let's not forget, how many people master algebra in one year anyway? Perhaps my definition of mastery is different?

 

I also sometimes wonder if it's a boy thing to need to do it again and again. I have no experience parenting girls, maybe that's for another thread.

 

Nope, I wasn't thinking of you at all. There have been at least a couple posters on one of the previous threads on the AL board about going faster vs. "deeper" who feel that arithmetic is "boring" and higher level math is just so much more fun that kids should be allowed to race through [insert name of easy curriculum] to get into algebra as soon as possible. But then said child has to do multiple algebra 1 courses, which suggests to me that he/she didn't actually have all that solid a foundation in arithmetic.

 

Perhaps if I tell you what we are doing for writing it would make better sense. Writing is a skill too right? And it doesn't come easily to my son at all. In fact CW, I was so incredibly impressed by your daughter's Shakespeare-themed story some time ago and I felt like wow, this girl has so much promise and talent! It was a really nice piece of work for one so young. My son could not have written that despite being the same age as your DD. He might be able to think like that but he couldn't actually put it down on paper even if I asked him to type it or gave him a few days to do it.

 

Still, we are not using grade level writing programs. Why? Most are written to be too cutesy and too simple for him. When I teach him writing, I still can't approach it like he is a 5th grader because he doesn't think like a 5th grader (actually my personal feel is that most 5th graders in ps can do so much more, at a higher challenge level, than the cr*p thrown at them). So I have to buy something written for higher grade levels and tweak, tweak, tweak, then leave it out altogether for a few months, then try again, tweaking as I go. It's tiring. It's frustrating. I want to outsource writing too but I just can't afford outsourcing anymore. We are already outsourcing 4 subjects. There's only so much I can balance.

 

It's just so tiring to have to read and process judgmental posts sometimes. Please let's be more forgiving and accepting of everyone's approach? We are all (or at least most of us) are just trying our best with our kids, each one is unique and precious and so deserving of the best education we can give them.

[Five More Minutes]

I feel as if Wendy is responding about my child too here. I don't need to defend myself because I know and see for myself that what we did is working. It may seem like we rushed through arithmetic and truth be told, I felt it too...why on earth was I skipping levels like this? What's going on...I thought MEP Year 1B was working last week, why is it so easy this week? We went through MEP like water that way and I was second guessing every single day of it. Was I shortchanging him in some way? Was it for my own ego? But you know, I know now that my gut instinct had been right. Sometimes, it's not just the academics. It's meeting the child on as many levels as you can and that includes mental and emotional well-being.

 

....

 

It's just so tiring to have to read and process judgmental posts sometimes. Please let's be more forgiving and accepting of everyone's approach? We are all (or at least most of us) are just trying our best with our kids, each one is unique and precious and so deserving of the best education we can give them.

 

I can't respond on Crimson Wife's behalf, but when I read her posts I think she has an entirely different kind of parent and an entirely different mode of acceleration in mind when she critiques using "easy" programs to "race ahead." I believe she's putting her finger on a phenomenon that happens: some parents may choose to use an easy curriculum so that their students can complete levels faster. It is a race to finish levels.

 

But Quark and Wendy, it's obvious that you're not seeing this as a race. Acceleration isn't about getting it done faster; it's about meeting your child's needs and supporting them. You're making considered, intentional choices with your student's learning in mind. It's completely different from that other kind of acceleration.

 

Confession: I recognize myself in the first type of acceleration. :leaving: When we started homeschooling, I was very tempted to use programs that didn't necessarily challenge or meet my student's needs because they could complete them faster ... and then when people asked me questions about the quality of education I could provide, I could say, "Well, she's in Gr. 3 math and she's only 6!" Completing Gr. 3 Kumon-style workbooks just so I can say that she's at that level isn't the same as thoughtfully accelerating. I'm pretty sure that's the type of situation that CW is pointing out, and as one of those parents, I needed to encounter that critique early on.

 

I am now, I hope, someone who is really thinking about the programs that will best enable my students' learning and am trying my hardest to ignore levels. (Although with my dh as a ps teacher, sometimes the questions come fast and furious, and it is SO tempting to hand the kids a quick workbook and ask them to finish it so I can say, "See? Gr. 4 math at 6 years old!" :001_rolleyes: )

 

When I read about what you all are doing for your students, I'm inspired. It's hard, hard work to fit materials and programs to students who aren't following a typical learning curve.

[quark]

 

I can't respond on Crimson Wife's behalf, but when I read her posts I think she has an entirely different kind of parent and an entirely different mode of acceleration in mind when she critiques using "easy" programs to "race ahead." I believe she's putting her finger on a phenomenon that happens: some parents may choose to use an easy curriculum so that their students can complete levels faster. It is a race to finish levels.

 

But Quark and Wendy, it's obvious that you're not seeing this as a race. Acceleration isn't about getting it done faster; it's about meeting your child's needs and supporting them. You're making considered, intentional choices with your student's learning in mind. It's completely different from that other kind of acceleration.

 

Confession: I recognize myself in the first type of acceleration. :leaving: When we started homeschooling, I was very tempted to use programs that didn't necessarily challenge or meet my student's needs because they could complete them faster ... and then when people asked me questions about the quality of education I could provide, I could say, "Well, she's in Gr. 3 math and she's only 6!" Completing Gr. 3 Kumon-style workbooks just so I can say that she's at that level isn't the same as thoughtfully accelerating. I'm pretty sure that's the type of situation that CW is pointing out, and as one of those parents, I needed to encounter that critique early on.

 

I am now, I hope, someone who is really thinking about the programs that will best enable my students' learning and am trying my hardest to ignore levels. (Although with my dh as a ps teacher, sometimes the questions come fast and furious, and it is SO tempting to hand the kids a quick workbook and ask them to finish it so I can say, "See? Gr. 4 math at 6 years old!" :001_rolleyes: )

 

When I read about what you all are doing for your students, I'm inspired. It's hard, hard work to fit materials and programs to students who aren't following a typical learning curve.

 

 

I've really enjoyed your very insightful posts, Five. Thank you! Yes, you bring up a valid point and I had not looked at it that way at all. We have used Kumon too you know and I know CW has brought it up many times before about "those" Jr. Kumon parents lol. And I can understand her objections. I have seen "those" parents myself. I have used Kumon too, and goodness me, I actually drove my son to their centers and had him do worksheets for 3 years lol! Yikes, should I find that "creeping away" smiley? :)

 

But I have only used their materials as a tool, not as the be-all and end-all like some parents do. And once it stopped being a tool and became a source of frustration and dislike for my child (although it was easier for me to use it), I dropped it. There's really nothing wrong with using Kumon in my book. It's the "way" it's used that I feel needs to be examined. One could decide to use BA and AoPS, SM, MEP, the most challenging and well-written curriculum in ways that are wrong for the child too right? I too am learning all the time. I am not without fault and without bad judgements and I hope I don't represent myself as one who can do no wrong.

 

My request was to not judge every parent the same way. CW mentioned the AL board, and I felt that some people will fear to post and ask questions there because goodness knows, you are already second guessing whether you should post there at all sometimes right? I hope I have not caused any hurt to CW.

[Spy Car]

 

 

This. I think that there are kids who have brains that do math. Everyone else is equipped with regular brains that grasp math at certain developmental points along the way. I think there are concepts that "click" just like some kids can struggle with reading one day and be reading chapter books the next with virtually no logical progression of learning. Everyone seems to be on slightly different timelines, and I think it is risky to try to push beyond a child's ability in order to have an accelerated learner. I believe these children self-identify and a parent will not be in the dark as to whether their child could handle a faster pace or more complex material.

 

I believe there is a 3rd sort of way between having children who are born with the gift of a "math brain" and those who eventually get math when they are "ready." This involves teaching for a depth of understanding using means that meet the child's state of development, and making concepts easy for them to understand.

 

If that 3rd approach is followed, and one teaches for understanding and depth, I think one should expect to have a child who is somewhat accelerated, and that rather than being "risky" it is an approach that is higly likely to result in them being fond of math. Which leads to using fun and challenging materials, which compounds the depth and understanding and sense of fun, and leads to a virtuous cycle.

 

This is different than having a child who is so brilliant they don't need teaching, or having a "regular" kid who will catch onto the standard curiculmn when he or she is ready.

 

I know we are in no rush to race through easy curriculum, but by working the most challenging programs I can find to allow us to go wide and deep, we are still "ahead." And it think it is because we started out seeking a depth of understanding—something that was not "inate"— and did so respecting my child's intellectual development at each stage of learning.

 

Bill

[Five More Minutes]

 

I've really enjoyed your very insightful posts, Five. Thank you! Yes, you bring up a valid point and I had not looked at it that way at all. We have used Kumon too you know and I know CW has brought it up many times before about "those" Jr. Kumon parents lol. And I can understand her objections. I have seen "those" parents myself. I have used Kumon too, and goodness me, I actually drove my son to their centers and had him do worksheets for 3 years lol! Yikes, should I find that "creeping away" smiley? :)

 

But I have only used their materials as a tool, not as the be-all and end-all like some parents do. And once it stopped being a tool and became a source of frustration and dislike for my child (although it was easier for me to use it), I dropped it. There's really nothing wrong with using Kumon in my book. It's the "way" it's used that I feel needs to be examined. One could decide to use BA and AoPS, SM, MEP, the most challenging and well-written curriculum in ways that are wrong for the child too right? I too am learning all the time. I am not without fault and without bad judgements and I hope I don't represent myself as one who can do no wrong.

 

My request was to not judge every parent the same way. CW mentioned the AL board, and I felt that some people will fear to post and ask questions there because goodness knows, you are already second guessing whether you should post there at all sometimes right? I hope I have not caused any hurt to CW.

 

:iagree: :iagree: :iagree: It's the goal and the way that the materials are used that matter. There's nothing wrong with Kumon books when they are working as a tool to encourage learning the material. They were just the first thing that came to mind from my experience as something that can easily become an end in themselves rather than a tool. It was just so darn tempting to complete them and chalk up the levels ... :lol: Thankfully I didn't stop there and early on found these boards, where I've encountered so many ideas that have made me carefully consider what I'm really trying to achieve. I've found it to be hugely challenging, but rewarding, to find programs that enable my dds to really learn.

 

(Thanks for the kind words, too.)

[Arcadia]

We have used Kumon too you know and I know CW has brought it up many times before about "those" Jr. Kumon parents lol. And I can understand her objections. I have seen "those" parents myself.

........

My request was to not judge every parent the same way. CW mentioned the AL board, and I felt that some people will fear to post and ask questions there because goodness knows, you are already second guessing whether you should post there at all sometimes right? I hope I have not caused any hurt to CW.

I'm wondering whether the Kumon "syndrome" is regional. Even the public school teachers here are talking about Kumon centers and they actually verbally recommend them. A few public school teachers have asked me about whether my kids use Kumon, your post kind of put their questions in perspective.

 

Besides the AL board, there is also the SN board. My kids are probably mild 2E, I just have to be thick-skinned and ask when I need opinions/advice :)

I'll leave the post so that other people in similar situation can have ideas, and know of the Assouline resource.

 

Which Susan Assouline resource are you referring too? My boys think faster than they write and we are using typing on the ipad to accomodate for the moment.

[jennynd]

I understand the frustration. It took a while for me to sort things out and get #1 son to where he could be intellectually happy while his handwriting was developing and his vision problems were worked out. I don't wish years of misery on any student.

 

 

I am having same problem now with my younger DD. As the school years end, the skip grade conversation started again. Two seperate screening from a private and public school both suggested to have my DD skip a grade. But when I look at her hand writing and the speed of her hand writing. I just have a hard time to agree with that. She is nowhere to what my DS can write at the same age

[Dmmetler]

I also think that sometimes it's a chicken and the egg situation. I know two parents with very accelerated kids using math curricula that are considered on the lighter side. In both cases, the kids are grades ahead of their age level. But it's not because the parents are trying to use easy curricula to "just get 'er done" or for bragging rights. It's because the PARENT is weak in math, and needs something that holds their hand more than, say, Singapore or MEP. It took taking two teacher training courses on Singapore Math for me to feel comfortable teaching it, because it was so different from what I'd done in school. And I admit, some of the SM IP and CWP problems, some of the contest math problems, and some of the stuff on AOPS's web site scares me, because it's taken me serious brain effort to solve problems that are designed for kids as young as 2nd grade. I can see why a parent who isn't comfortable with math, but has a mathematically focused child, would feel uncomfortable supplementing, or even in deciding which supplements are a good fit.

[quark]

If that 3rd approach is followed, and one teaches for understanding and depth, I think one should expect to have a child who is somewhat accelerated, and that rather than being "risky" it is an approach that is higly likely to result in them being fond of math. Which leads to using fun and challenging materials, which compounds the depth and understanding and sense of fun, and leads to a virtuous cycle. [...]

 

I know we are in no rush to race through easy curriculum, but by working the most challenging programs I can find to allow us to go wide and deep, we are still "ahead." And it think it is because we started out seeking a depth of understanding—something that was not "inate"— and did so respecting my child's intellectual development at each stage of learning.

 

That is so spot on. Especially the bolded. I realize now that we didn't need to do 6+ years of math and could progress to the next levels faster because we (and my DH really needs to take most of the credit for this because he saw it for what it was sooner than I did) chose problems carefully for our whiteboard teaching activities and did co-teaching (we teach DS, DS teaches us something back) in such a way that it became so obvious there was understanding. We took a bit longer through fractions and decimals and percents because DS hit some pretty solid walls there but when the breakthrough happened, when he saw the patterns for himself, it was so smooth sailing after that. That spark, that moment when he truly sees it...that has always been the priority for us and I think I haven't made that clear enough in most of my previous posts. And because he could see it and was so clearly understanding it, we just didn't see a need to repeat a concept to death. And my DS is quite expressive you see...it is very clear when he is excited and when he is not so it was easy too for us to catch on that we were boring him instead of helping him.

 

I'm wondering whether the Kumon "syndrome" is regional. Even the public school teachers here are talking about Kumon centers and they actually verbally recommend them. A few public school teachers have asked me about whether my kids use Kumon, your post kind of put their questions in perspective.

Im in the NE. Kumon is recommended as an option here for children who are behind but don't qualify for special education, basically for parents who don't have the ability to move their child up. I'm sure other tutoring centers would be recommended if they were in driving distance.

 

Yes to Arcadia about the Kumon syndrome being regional (my humble opinion). I just wasn't aware that in NE it is recommended as an option for kids who are behind. That is very interesting!

 

We were lucky because the head instructor in the center we chose was open to accommodating for DS (yes, accommodating a highly drill-and-kill, worksheet-based curriculum like Kumon, isn't that funny? I find it quite hilarious now actually but am really grateful she agreed). After a few weeks, I could see the disconnect between his ability to understand and his inability to do it quickly so I stopped timing him at home and told her so for her to understand why it was taking him 30 minutes when every other kid on their computer database was taking 10 minutes or maybe 15 at most lol. I also asked that she reduce the number of worksheets. I told her clearly that we were homeschooling and only needed the worksheets for practice and were enrolling him in the center for the class experience too (we felt at the time it was important, maybe it was not, another example of learning as I go on this journey). Even with fewer worksheets, he was going up the levels fast (and not because I planned for him to, I was trying to make it slower for him by cutting down the work!) and I'm really thankful she was open minded enough to see that we were working with the child and not against him or doing it to hurry him along. We still paid her the usual monthly fee, we didn't request a discount for taking home fewer worksheets.

 

After a while, the work became just too repetitive and DS was no longer liking the class experience either. The tool stopped being a good tool, and we stopped using Kumon classes.

 

Did the experience benefit DS? I don't know for sure. It gave him a lot of practice so that at home I could just focus on the more living math style books, puzzle like books, codes and ciphers style books and so on. And spend about 10-15 minutes a day using the whiteboard with problems from MEP, sometimes SM. It was a good tool while it lasted, but possibly, mostly for me. On hindsight, maybe we could have saved the money and used it on more books. :)

[Dmmetler]

 

Oh this is definitely my problem. I used SM and some of MEP and I had no trouble with that. But now I'm getting nervous and I don't know where to go. So hence the MUS. Which is not a terrible program. It's light on challenge problems, but the concepts are there.

 

But I decided to get over myself and order the damn AoPS algebra book and just stop being a wuss.

 

So if you hear any loud screams from NY, that's me.

 

:lol: I just ordered AOPS Pre-Algebra and Algebra ;). I don't regret giving DD a year of lighter pre-Algebra (especially not at age 7) and I don't plan to drop Fred since she loves him so much, but I've decided that I need to jump in and just do it-so we'll try Fred beginning Algebra with AOPS Pre-Algebra in the fall, and see what happens. Of course, I'm tempting fate-DD has this annoying tendency to take new books as a challenge.

[Five More Minutes]

 

Oh this is definitely my problem. I used SM and some of MEP and I had no trouble with that. But now I'm getting nervous and I don't know where to go. So hence the MUS. Which is not a terrible program. It's light on challenge problems, but the concepts are there.

 

But I decided to get over myself and order the damn AoPS algebra book and just stop being a wuss.

 

So if you hear any loud screams from NY, that's me.

 

:lol:

[8filltheheart]

I believe there is a 3rd sort of way between having children who are born with the gift of a "math brain" and those who eventually get math when they are "ready." This involves teaching for a depth of understanding using means that meet the child's state of development, and making concepts easy for them to understand.

 

If that 3rd approach is followed, and one teaches for understanding and depth, I think one should expect to have a child who is somewhat accelerated, and that rather than being "risky" it is an approach that is higly likely to result in them being fond of math. Which leads to using fun and challenging materials, which compounds the depth and understanding and sense of fun, and leads to a virtuous cycle.

 

This is different than having a child who is so brilliant they don't need teaching, or having a "regular" kid who will catch onto the standard curiculmn when he or she is ready.

 

I know we are in no rush to race through easy curriculum, but by working the most challenging programs I can find to allow us to go wide and deep, we are still "ahead." And it think it is because we started out seeking a depth of understanding—something that was not "inate"— and did so respecting my child's intellectual development at each stage of learning.

 

Bill

 

I'm not sure if I agree or not. If this is speaking in terms of generalities and general advancement, then I do agree.

 

However, if you are speaking in terms of exposure in general meaning that large numbers of children will be able to do algebra in 3rd grade (not HoE or SM bar method alg. I mean standard high school alg), then I disagree. (and achieving alg in 3rd grade is what the OP was asking about. It is a very unusual child that is doing full blown alg in 3rd grade.)

 

This goes back to the thread that this spun off from (college at age 12). No, exposure is not going to make the avg student able to do highly advanced materials at really young ages. Teaching "more" or even in a specific manner is not going to enable the avg 12 yr old to succeed at "good" normal college level expectations.

[kiwik]

 

 

This is eye opening and really disheartening. I've been thinking that all I need to do is get him to University, and all will be well. sigh.

 

Were you thinking of him going to Victoria? Or somewhere else in NZ? Or out of NZ? If the first you could look at him sitting in on some stuff now and maybe getting to know a bit about the professors. That may allow him to skip some early stuff (he will probably be ready for 3rd year). Otherwise he may have to go through first year which will be repeats for him with A+ grades and then they will talk to him.

[Arcadia]

Im in the NE. Kumon is recommended as an option here for children who are behind but don't qualify for special education, basically for parents who don't have the ability to move their child up.

 

Here Kumon is actually recommended for acceleration. Some parents use it as affordable child care if their in-laws are helping to look after their kids after school, to give their in-laws a rest and gossip time outside the centers. The public schools here are relatively well funded for remedial math by title one and other funding.

But I decided to get over myself and order the damn AoPS algebra book and just stop being a wuss.

 

I'm going to get the solutions manual when I order the algebra book. That way hubby can help check without taking up too much of his after-work time. He checks and works out the AoPS Pre Algebra challenge problems when I am not in the mood to.

[regentrude]

That said, I showed my husband the book and he said, oh this looks like stuff we did in 4th grade. People think these concepts are too difficult for younger kids, but there are younger kids in other parts of the world who are in fact working on these concepts. So is it that most can't do it, or that it's not generally taught here at that age? I wonder. I don't think DS is some sort of math genius. Sure he is smart, but again, no genius.

 

I see two aspects:

 

1. In other parts of the world, math teachers are competent in math. They understand more math than they teach and thus have a deeper insight into the concepts. IMO, a thorough mastery of math above the level you are teaching is essential for a good teacher.

 

2. Elsewhere, math is not packaged into neatly wrapped parcels labeled "prealgebra" or "algebra". Math is math. Thus, there is no need to wait with teaching the simpler algebra concepts (expressions, linear equations) until the kids are mature enough to grasp the more advanced algebra concepts (factoring quadratics), because those are not taught at the same age. In German schools, the geometry of the triangle, congruency theorems and proofs are taught in 6th grade; linear equations in 7th, quadratic equations in 9th.

Teaching math as an integrated subject, not as individual parcels, with geometry interspersed throughout the years instead of compressed into a single school year, is a much better approach.

 

We pulled DD out of school when we found out that, at the beginning of 6th grade, her US school was a full year behind in math compared to the German school she'd have to attend in the spring semester. (Showing the math department the German 6th grade curriculum just got the answer "oh, we won't teach any of this until Junior High- get a tutor").

It is the combination of bad teaching and low expectations that keeps US students behind students from, say Russia, or Singapore, in math, not intrinsic ability.

[quark]

If that 3rd approach is followed, and one teaches for understanding and depth, I think one should expect to have a child who is somewhat accelerated, and that rather than being "risky" it is an approach that is higly likely to result in them being fond of math. Which leads to using fun and challenging materials, which compounds the depth and understanding and sense of fun, and leads to a virtuous cycle.

 

How could I have forgotten to bold being risky? :) Being risky becomes quite fun after a bit. It's thrilling actually. :) But it's not really extremely risky either if you are homeschooling and customizing heavily because you can dial it back a bit if it is too much for the kiddo.

 

Apart from leading to a fondness of math here, being risky has also led to being more hardworking and responsible. That's what fondness for a subject does to you I guess. It wasn't all that obvious to me at first. I was only aiming at making math a subject he wouldn't fear. Then it became obvious that a child who is being respected for his intellectual development can also rise up in other areas, especially those executive functioning areas. I realize that we actually used the love of math to teach some executive functioning skills, instead of waiting for those executive functioning skills to come first.

[Pamela H in Texas]

allow us to go wide and deep, we are still "ahead."

 

This is what we did with my oldest and are following to an appropriate for them degree with my littles.

It also meshes the "do it a few times" and acceleration nicely. Of course, that balance has to be found for each child.

I think it is perfectly reasonable for some kids to be doing Algebra before they are double digit ages.

I also think it is perfectly reasonable to enjoy various aspects of maths, explore them in different manners, etc.

I also think it is good for a child to learn what he can in a subject even if he has other things to learn

(for example, my kindergartener really liked that app this morning; but he has plenty of k-6 math to learn still).

[Spy Car]

 

 

I'm not sure if I agree or not. If this is speaking in terms of generalities and general advancement, then I do agree.

 

However, if you are speaking in terms of exposure in general meaning that large numbers of children will be able to do algebra in 3rd grade (not HoE or SM bar method alg. I mean standard high school alg), then I disagree. (and achieving alg in 3rd grade is what the OP was asking about. It is a very unusual child that is doing full blown alg in 3rd grade.)

 

This goes back to the thread that this spun off from (college at age 12). No, exposure is not going to make the avg student able to do highly advanced materials. Teaching "more" or even in a specific manner is not going to enable the avg 12 yr old to succeed at "good" normal college level expectations.

 

You may have missed my previous posts, in which I expressed similar sentiments about "algebra."

 

I said many children are likely "developmentally ready" for algebraic thinking in modified form (PGCM, HOE, Beast Academy 3D, DragonBox, and things of that sort). And this was different than starting AoPS algebra at 9, or 10, or 8.

 

The latter is something very few are likely to be prepared for (even if there are a few who are). I agree on this point. This doesn't change my feeling (and one I expect we have in common) that there are elements of algebraic thinking that can be incorporated to good effect with younger children.

 

I am personally in no rush. But I still think mathematical understanding can be cultivated by using developmentally appropriate (but challenging) means in younger kids, rather than simply waiting for them to mature to the point where they can (hopefully) use challenging courses designed for older kids. It seems to me this is exactly were the AoPS folks are coming from with Beast Academy.

 

I assume we are of like mind here.

 

Bill

[8filltheheart]

 

I assume we are of like mind here.

 

Bill

 

Ok, yes, then we are on the same page. Exposure and enrichment definitely develop and enhance skills.

[Spy Car]

 

 

Ok, yes, then we are on the same page. Exposure and enrichment definitely develop and enhance skills.

 

My beef, and excuse me for expanding on it, is I often feel we get locked into seeing a false dichotomy when it comes to math education.

 

One choice is to "push," by using methods that are intellectually inappropriate.

 

The other is to "wait," so the children will (hopefully) grow into the materials that were formerly inappropriate.

 

What I'm saying is that it's possible to use challenging materials that are intellectually appropriate if you teach for deep understanding from the outset. That this approach is not "risky," but one that is likely to be successful if parent/teachers can help make math fun, in part because it is understood and in part because the materials challenge a child's thinking skills.

 

Not exactly controversial opinions on my part, but I think this third way is too often overlooked.

 

Bill

[lewelma]

I don't know why I feel the need to defend what I'm doing, but I just think you aren't considering why some people have their kids do an algebra program for three years. Being ready for a certain thing is not always about not understanding the concept. There are other factors.

Wendy, I totally understand you. My ds took almost 3 years to get through AoPS Intro Algebra (ages 9, 10, and 11). Now, I know it includes a lot of Algebra 2, and I know he did it independently, but really, 3 years? That's a lot of time. But it was exactly what *he* needed -- he needed to work at his own pace and absorb at his own level. Now, at age 12 he is flying, really flying. He will finish AoPS geometry, number theory, and counting at age 12 and is working through a university level proof based book. He just really needed that secure foundation, and only time and effort could provide it.

 

Second guessing is the bane of the homeschool parent, but for *this* child, if I had waited until 10 or 11 to do AoPS algebra, he would have withered on the vine. He just *had* to do something *impossibly* hard. In fact, for the first 3 months of AoPS, he would cry every day over the challengers while he struggled on his own for a couple of hours. He would NOT let me help him. Finally, worried and uncertain, I hid the book and would not give it back to him until we came to an arrangement about taking breaks, allowing help, etc. My point is the *right* path is rarely obvious, and anyone looking in might judge. Anyone could have judged me. Why *let* him do something that clearly was too difficult? But in the end we have to stand firm that we *know* our child and what is best for him, but we must also be very vigilant that we have our child's interest at heart and are not caught up in the societal competition.

 

Ruth in NZ

[kiana]

I see two aspects:

 

1. In other parts of the world, math teachers are competent in math. They understand more math than they teach and thus have a deeper insight into the concepts. IMO, a thorough mastery of math above the level you are teaching is essential for a good teacher.

 

2. Elsewhere, math is not packaged into neatly wrapped parcels labeled "prealgebra" or "algebra". Math is math. Thus, there is no need to wait with teaching the simpler algebra concepts (expressions, linear equations) until the kids are mature enough to grasp the more advanced algebra concepts (factoring quadratics), because those are not taught at the same age. In German schools, the geometry of the triangle, congruency theorems and proofs are taught in 6th grade; linear equations in 7th, quadratic equations in 9th.

Teaching math as an integrated subject, not as individual parcels, with geometry interspersed throughout the years instead of compressed into a single school year, is a much better approach.

 

I agree with BOTH of these a lot.

 

The number of prospective elementary school teachers who will vigorously resist learning arithmetic and how it works because "I'm just going to teach kindergarden and you don't need fractions there" is both astonishing and sad. We are not talking requiring them to learn calculus, we are talking requiring them to learn to do fractions, long division, multi-digit multiplication and addition, and explain why it works (as if they were teaching children).

 

I also totally agree with introducing simpler concepts earlier instead of holding back on algebra until they're ready for advanced concepts. As a matter of fact I think we should introduce linear equations very early (in a simple form) and continue working on them (introducing slope close to when we do triangles and doing lots of work on them) throughout several years. I think a lot of issues really boil down to not understanding why linear equations work.

[LMD]

In threads like these, I feel like I'm just soaking up the wisdom...

 

I just googled 'linear equations' - think I'll need to beef up on that before we get there! *flashbacks of studying for hours in high school without knowing what I'm really doing*

[4KookieKids]

Wow! There's so much content on this thread!! :) I won't try to respond to everything, but I'll give my experience as a mathy person (not in a braggy way, but I was just always gifted in the area) and also as an instructor who has taught math at a variety of levels (including graduate level courses, and courses for math teachers).

 

As far as the "how it's done", I strongly agree with other people that you shouldn't just skip large chunks. Instead, just let them go at their own pace, however quick that is. If they feel like they get it after just a few practice problems (choose the later/harder ones to make sure it's not just the easy ones they can do with ease), certainly let them move on without all the drill (because that'll just kill them!). Just take periodic quizzes or tests to make sure you really are getting it and not missing things.

 

I know that I was able to teach myself the concepts just by doing a few of the problems. I would review the section as I did the problems, and it was usually easy enough for me to do each lesson in just a fraction of the time that it was supposed to take.

 

On some of the other things that have been discussed:

 

He didn't really learn much new in that course that challenged him and told his professor that he was disappointed that they didn't spend more time on proofs.

 

This semester he is studying diffEQ. He hasn't stated that it is review (like last semester), but it certainly has not been a challenging class.

 

I think this is where "the where" the classes are taken and how they are approached really matters. For kids that love math and want that mathematician proof-driven/theory-oriented experience, your typical university is probably not going to meet those needs. Whereas schools like Stanford/MIT, etc those are going to offer theory-oriented classes starting at the freshman level and those classes are going to be filled with great math students that love that sort of challenge.

 

 

I'm not sure I agree that this is true. Our uni gets to proofs and theories pretty quick, but doesn't require them of students until later years (closer to Junior). However, if you test out of calculus, you can jump right into the theory classes. At the uni I attended as an undergrad (fairly small state school, truth be told, and it probably worked in my favor), I was able to get "special permission" to jump into the theory classes as soon as I'd tested out of calculus, and was taking graduate level classes by my second year. My guess is that a school like Stanford/MIT wouldn't make these sort of "allowances". Now, maybe they're not necessary at those schools, but I just thought I'd throw out there that there may be pros to some of the non-super-technical schools, too.

 

For kids that want to be mathematicians, sending them to the local CC would be imo a disaster. Sending them to a typical university will be jumping back into traditional textbook problem-solving with students that are being taught how to solve problems and then solving the problems, etc and all that goes with that approach.

 

 

I think this just depends on what level the kid is at. I've seen people become mathematicians without being the super talented/gifted student that we're talking about, and in that case, I think a CC can be a great option for getting the basics (Calculus, diff Eq, etc.) done. Those are courses that you'd be taking under a grad student (who may or may not have any experience teaching) or with a faculty phd but in a class of 100-200 (and see the grad student for half the week anyway) at a uni, whereas at a CC you get a someone with at least a masters, if not a phd, who definitely wants to teach (as opposed to the possibility of having someone teaching when what they really want to be doing is research...), and you have smaller classes.

 

Now, I don't think all big uni's are bad, but I figured I'd paint a picture of it that may not generally be considered.

 

He can't exactly type all of his math. That's not very practical.

 

 

Just so you know, later math is almost always typed. :) I was doing it in half my classes halfway through undergrad, and in all my classes in grad school. There's actually a pretty cool program called LaTeX that you can look into. It's pretty easy to learn and really helps later in math, when you realize you forgot one line in a proof but you don't want to re-write the entire proof... You just open the document, insert the missing line, and typeset it again.

 

That said, I showed my husband the book and he said, oh this looks like stuff we did in 4th grade. People think these concepts are too difficult for younger kids, but there are younger kids in other parts of the world who are in fact working on these concepts. So is it that most can't do it, or that it's not generally taught here at that age? I wonder. I don't think DS is some sort of math genius. Sure he is smart, but again, no genius.

 

 

I agree with this. We were doing algebra in grade school, but not calling it algebra. It was in the form of word problems that you had to set up with variables and then solve. I moved a lot in middle school, and kept getting put pre-alg or alg at that point, and it was terribly boring for me because I'd done it already. :p

 

 

Most children are not developmentally ready to do Algebra at 9 or 10, and even less ready to do calculus in middle school. Even if developmentally ready for the texts, they simply might not be ready to complete such a thick text each year.

 

 

I don't know of any research concerning this particular comment, but I can say that I know that there is research showing that really complex abstraction doesn't usually start until the early 20's, which is beyond when we usually push the really abstract stuff. So it'd make sense to me if, in general, we are asking students for too much abstraction at earlier ages as well.

 

On the other hand, I wonder if the research is skewed, because we don't start teaching kids to abstract well-enough and early enough. Most of the high school math I've seen (not just my own, but from teaching hs math teachers) is very procedure oriented, rather than focusing on concepts, so I also wonder if people would learn to abstract earlier than 20's if they were taught how to do it well earlier. I don't know which way I lean, but it's an interesting topic to consider, especially when you consider other cultures where more abstract topics are usually taught earlier.

 

 

So if they complete Algebra in 3rd or 4th grade, that would put them on track to potentially finish your run of the mill high school math courses by the time they complete middle school, right? So in high school, what would they do? Are those of you doing things this way planning on enrolling them in college early?

 

With a young, gifted child there's no reason to head straight for the run of the mill high school math program. There are many electives that can be done after only algebra 1. AOPS does a counting and probability course and a number theory course, and there are other courses that could be done early if the parent, tutor, or mentor is capable. IMACS has books in mathematical logic and set theory that could be completed even prior to algebra and definitely after algebra 1. Once geometry is completed there are more advanced courses in geometry which could be completed. After algebra 2 some more advanced courses in counting and probability (aops), number theory (many elementary textbooks would now be accessible to someone who completed the AOPS introductory course and a solid algebra 2 course), statistics, graph theory, etc. After precalculus it opens still more and after calculus still more. Specific courses chosen could depend on the child's interests -- for example, a kid primarily interested in biology could, after algebra 2, self-study some matrix algebra and then do a basic course on game theory w/evolutionary/ecological applications (I find this fascinating myself), while a kid interested in physics would want to head more towards calculus and then afterwards look at subjects like differential equations, linear algebra, mathematical statistics.

 

I would also recommend reading The Calculus Trap (an online article) about why you shouldn't just rush a gifted kid through the standard curriculum on the way to calculus.

 

 

 

I really agree with this.

 

There's actually a ton of interesting math that's accessible to kids that's not on the standard "calculus track". This is actually a big beef of mine in normal schools, especially for kids who are *not* math-inclined, actually. Get into combinatorics and other discrete math, like graph theory, coding theory, number theory, probability, or higher level algebra like group/ring theory, etc. and the *majority* of these (with the exception of the higher level algebra, which relies on some of the earlier fields mentioned) require no special or technical knowledge beyond solid algebra and the willingness to think about things in new ways. Moreover, they're really INTERESTING (but maybe this is my own bias towards non analytical type math :D), to math people like me, but even (and maybe especially) to people who think they don't like math because all they've ever known of math is algebra/pre-calc based. (Aside: I had a student in a graph theory class like this who had failed every math class she'd ever taken and had been diagnosed with some catch-all disorder claiming she just couldn't do math. Turned out she aced my course, because it was just completely different and allowed her to use her abstracting skills in a way that didn't rely so heavily on pre-calc type math. She was *elated* and I felt great to be able to offer her that experience.)

[lewelma]

And I admit, some of the SM IP and CWP problems, some of the contest math problems, and some of the stuff on AOPS's web site scares me, ....I can see why a parent who isn't comfortable with math, but has a mathematically focused child, would feel uncomfortable supplementing, or even in deciding which supplements are a good fit.

 

Oh this is definitely my problem. ..... But now I'm getting nervous and I don't know where to go. ......

 

But I decided to get over myself and order the damn AoPS algebra book and just stop being a wuss.

 

So if you hear any loud screams from NY, that's me.

 

 

 

I know what it is to not understand the math your child is doing, and I can totally see why it could be so hard for a parent. But I would love to support anyone who is trying to learn the material so as to help their child. We as homeschoolers often outsource what we don't know/can't teach, but I wanted to share with you how learning the material *with* your child can be incredibly beneficial. Here is a x-post that I'm sure some of you have read, but hopefully others will find useful. The bolded is the most useful part to this conversation, but I think you need the background to understand what I am saying:

 

X-post

 

yes, that is the book. My son is 12. We are currently able to understand only 30% of it. It is a University math majors textbook. The author states that you should read each chapter until you don't understand, then move to the next chapter. When you finish the first pass of the book, you start again. This approach allows you to work at your personal level in each topic, and allows your ability in all topics and problem solving to be increased concurrently.

 

There is NO way that my son could work with this book independently. We work on each problem together and then read through the proofs together. If the problem is easier, we each separately investigate it and write up a formal proof and then compare. My goal is to find ideas in each problem that will be generalizable to other problems. We keep a list, and I quiz him every day about the different generalizable skills we have learned. For example, what kinds of problems are would likely be helped by the extreme principal? or what kind of problems suggest a proof by induction? How can you recognize parity in geometry problems? These types of questions are not directly answered in the text -- they are more of a way for us to really internalize what we are reading and categorize all the ideas. Plus, it helps us review esoteric ideas by recalling specific problems that reflect them. We've decided that if there are 20 different tactics that are possible, and we can recognize that 4 are good candidates for a certain problem, we can try those four. If one works, great, if none work, then at least we have gotten our hands dirty and have a much better understanding of the problem and can go from there.

 

To help in proof writing, I drill him on specific phrases like "This specific case is generalizable because the only special feature of 11 that we used is that it is odd." (yes, I am memorizing all this too, so that just popped out of my brain). This drill has really helped him not only with the language of math, but also helped him realize different approaches he could use to prove a conjecture. For example, the above case showed us that you can use an example as your proof in many cases of parity. This is very important to know, because most proofs do not allow this. Our overall goal is to get as many tools in our tool box as we can, and then remember what tools we have in there!

 

All this is really working. I cannot believe how far we have come in 2 months.

 

I told someone last week that I could only go through this process once because what I am giving my son is not a knowledgeable tutor, but rather a skilled learner who is at his exact level in math. If I ever go through this material again with a student, I would be much much more knowledgeable and I would loose the confusion that has been so critical in helping him battle through this material. What I am finding is that because I don't know the answers and I cannot teach him how to do it, I am instead teaching him how to learn problem solving -- what questions to ask, what answer to hunt for, how to compare problems, how to really interact with this material. No tutor who knows the material well could do this as well as I can, because once you have the knowledge, it would be virtually impossible to relive the confusion.

[8filltheheart]

 

 

I'm not sure I agree that this is true. Our uni gets to proofs and theories pretty quick, but doesn't require them of students until later years (closer to Junior). However, if you test out of calculus, you can jump right into the theory classes. At the uni I attended as an undergrad (fairly small state school, truth be told, and it probably worked in my favor), I was able to get "special permission" to jump into the theory classes as soon as I'd tested out of calculus, and was taking graduate level classes by my second year. My guess is that a school like Stanford/MIT wouldn't make these sort of "allowances". Now, maybe they're not necessary at those schools, but I just thought I'd throw out there that there may be pros to some of the non-super-technical schools, too.

 

 

 

I think this just depends on what level the kid is at. I've seen people become mathematicians without being the super talented/gifted student that we're talking about, and in that case, I think a CC can be a great option for getting the basics (Calculus, diff Eq, etc.) done. Those are courses that you'd be taking under a grad student (who may or may not have any experience teaching) or with a faculty phd but in a class of 100-200 (and see the grad student for half the week anyway) at a uni, whereas at a CC you get a someone with at least a masters, if not a phd, who definitely wants to teach (as opposed to the possibility of having someone teaching when what they really want to be doing is research...), and you have smaller classes.

 

Now, I don't think all big uni's are bad, but I figured I'd paint a picture of it that may not generally be considered.

 

 

 

I'm sure that some of the unis out there do offer higher levels of theory in their classes than what our ds has experienced. His access has been limited to 2 different local universities in 2 different states. One was the largest public university in the state and the other is about 1/3 its size. He is taking the math classes required for a physics degree, so opting out of them would not be an option. That said, the classes have been very much "problem-solving" based vs. theory based. That is not a negative in general b/c most of the other students are engineering majors, so that is what they need. It is really going to depend on what is available locally.

 

As far as the CC----our experience with multiple CCs over the yrs is that the classes are not taught on a very challenging level and the students in the classes have not been engaged in serious learning or have needed a lot of repetition of explanations. Not that all students fit that description, but enough that my kids complain a lot about it.....far more than in their university classes.