Poll - Age to start Algebra- Anonymous

[StartingOver]

Just wondering at what age your child started Algebra, the earliest.

[Arcadia]

Formal with books or informal with pen and paper :lol: I am going to vote based on formal.

 

ETA:

Starting formal early has the headache of math credits when kids are in high school, if your child isn't interested in early college. However you can't stop kids from self teaching unless you bar all access to books, internet and YouTube.

Edited February 1, 2017 by Arcadia

[wendyroo]

Do you mean exclusively studied an official algebra course, or began learning and practicing algebraic concepts and problems?

 

DS is 7, and when he does Singapore Challenging Word problems he has completely transitioned from using the visual bar model to solving them algebraically.  He can competently formulate and solve one and two variable systems of equations using substitution or elimination.  I plan to continue slowly introducing algebraic concepts, but he still has some arithmetic to learn before he moves on to AOPS prealgebra and then AOPS algebra.  I expect he will officially start algebra in about 2 years.

 

Wendy

[wapiti]

I have nothing against starting algebra early.  I'd just like to point out, in case this hasn't been considered, that a child so talented in math deserves exposure to more depth and challenge than Saxon and Khan Academy provide.  There are a number of options for how and when to approach that.  Consider adding in some Beast Academy or AoPS Prealgebra, MOEMS problems, etc.  (There are lots of resources for this...wasn't there a quark list?  I can't find it.)  See, e.g., Rusczyk's problem solving talk and/or Rusczyk's shorter article, The Calculus Trap.

[OneStepAtATime]

Do you mean a formal Algebra program geared for High Schoolish level?  Or algebraic concepts?

 

My kids have been exposed to algebraic concepts since lower to mid-elementary.  But they were not ready for Algebra in a formal sense with a Middle School/Highschoolish level program.

[quark]

Is this purely for curiosity? We went by readiness and on the advice of a mentor (mathematician by training). In CA, it was not considered a high school class when DS started it. It was considered a middle school class. He started at 8 years old with Dolciani Structure and Method Book 1. I modeled writing out the problems and step by step solutions side by side until he could do it himself (but I continued to take the course with him for moral support). Finished almost the whole book before he turned 9 and then worked on AoPS Intro to Alg review and challenge problems (one half of book only) till he was 10-ish. Due to the all the feedback I was getting on counting it for high school, I went ahead and gave him 1 high school credit for algebra 1 and because he plans to graduate early, I "grade skipped" him and listed it as a 7th grade class (UCs allow math and FL credits from middle school).

 

I hope this info helps you, OP! Take care.

[Crimson Wife]

My older kids did Hands-on Equations around the same time they did Singapore 3. DS also did that app (Dreambox?) around then too.

 

Singapore splits up algebra over 6, 7, and 8 but my oldest was having difficulty with DM 8 so I switched her to Lial's Basic Algebra.

 

DS did Singapore 6 so he got an introduction to algebra in that. He's now using Elements of Mathematics and should be starting the algebra courses later this spring.

 

I try to have my kids go "deeper" in math rather than faster, so they are only slightly accelerated. My 9th grader is doing Algebra 2 (it's integrated with college-level statistics).

[Alice]

My oldest started in 7th grade, he was 11 and then turned 12 that year. Middle son will likely be 8th or 9th grade. Daughter is only 7 now so who knows. :) 

[Crimson Wife]

I have nothing against starting algebra early.  I'd just like to point out, in case this hasn't been considered, that a child so talented in math deserves exposure to more depth and challenge than Saxon and Khan Academy provide.  There are a number of options for how and when to approach that.  Consider adding in some Beast Academy or AoPS Prealgebra, MOEMS problems, etc.  (There are lots of resources for this...wasn't there a quark list?  I can't find it.)  See, e.g., Rusczyk's problem solving talk and/or Rusczyk's shorter article, The Calculus Trap.

 

:iagree: :iagree: :iagree: :iagree:

 

Just because a school like BASIS has their kids doing Saxon Algebra 1 in 6th grade does NOT mean that's the way to go with a bright child.

 

[Dmmetler]

DD started "Algebra" with Key to Algebra at age 7 along with LOF PA. She was dying to start "algebra", which she saw as real math, and Hands on Equations and the Algebra-ish stuff in SM wasn't doing it for her. She started AoPS Intro Algebra at age 9 (we did AoPS PA at age 8).

 

She plans to double major in math/science education and biology, with a plan of getting a PhD in herpetology, so more math is definitely in her future, but she's not as Math for math's sake as some on this board.

[EKS]

Older one started Jacobs Algebra at just turned 10 and took two years to get through it.

 

Younger one used Larson as a 10yo grade skipped 6th grader at a B&M school. He was in class with mostly 8th graders as well as a few 7th, 9th, and 10th graders. We ended up taking extra time to get through Algebra 2 because his Algebra 1 experience was so bad, not because he was young but because the teacher was horrific (he ended up getting fired).

Edited February 1, 2017 by EKS

[4KookieKids]

Anything else you'd want to do that's fun, first?

Last year (when he was 6) my boy especially liked graph theory (the kind with dots and lines and not bar graphs) and we talked about map colorings and the postman problem and Eulerian circuits and the Koenigberg bridge problem and all of that other fun stuff and he thought it was about the funnest math he'd ever done. :D

Edited February 2, 2017 by deanna1ynne

[StartingOver]

She devours math books, literally. I don't know where this is going, but I am kicking and screaming along the way. She is going to start AOPS this year, she has requested it. She spends her free time on Youtube or math sights searching for new stuff. I am exhausted. Mostly, I wanted to know I wasn't alone. 

[Arcadia]

She spends her free time on Youtube or math sights searching for new stuff. I am exhausted. Mostly, I wanted to know I wasn't alone.

My boys watch every single Numberphile episode on the Numberphile YouTube channel. There was a very young child devouring math books from the adult section of the library. His mom was just the "book retriever" and she was around my height (5'3"/158cm) so the top shelves were tough.

 

Have you look at the free math circles materials from U of Waterloo? It covers varied topics so nice for rabbit trails. http://www.cemc.uwaterloo.ca/events/mathcircle_presentations.html

[wapiti]

She devours math books, literally. I don't know where this is going, but I am kicking and screaming along the way. She is going to start AOPS this year, she has requested it. She spends her free time on Youtube or math sights searching for new stuff. I am exhausted. Mostly, I wanted to know I wasn't alone. 

 

Good for her!  Has she seen Alcumus yet?  I'd get her started with the prealgebra topics in Alcumus (adding in the videos whenever she wants or needs them).  At 8 or 9 y.o., it's worth spending some time either with Alcumus or the AoPS Prealgebra text even after finishing Saxon 8/7 before moving on to AoPS Intro to Algebra.

 

If she's looking for entertaining youtube channels, my dd liked the Vi Hart ones.

Edited February 2, 2017 by wapiti

[quark]

She devours math books, literally. I don't know where this is going, but I am kicking and screaming along the way. She is going to start AOPS this year, she has requested it. She spends her free time on Youtube or math sights searching for new stuff. I am exhausted. Mostly, I wanted to know I wasn't alone. 

 

You could follow her lead for a few years and see where it goes. No need to decide anything now. She could start algebra, take bunny trails galore, double back later, re-do pre-algebra if that helps (mine had to review something in precalc after finishing calc 1, it's all good). Really, it is lovely to see the enthusiasm. We only started getting concerned when he started calculus at 11. My signature links to some of the math resources that mine loved using. He started algebra 1 at 8 but was also working on AoPS C&P and NT so we went deep as well as wide. Homeschooling allows a lot of flexibility in that way.

 

Good luck!

 

Edited February 2, 2017 by quark

[quark]

If she's looking for entertaining youtube channels, my dd liked the Vi Hart ones.

 

Oh yes. And Numberphile! And the Math With Bad Drawings blog.

[booksdelight]

DS(10) started Saxon Algebra 1 at 8 and DS(8) completing PreAlgebra now and starting Algebra 1 in a couple of weeks. These are kids for whom math is fun and they don't consider math as school. On the other hand, language arts is like pulling tooth. My sons and my husband love to attempt ever math challenge ever posted anywhere, while this liberal arts major likes to curl up with novels😃

[4KookieKids]

My boys watch every single Numberphile episode on the Numberphile YouTube channel.

Is there an order to the videos posted, or do you just watch them randomly? I have a kiddo who would be interested in these I think.

[Mike in SA]

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.

Edited February 2, 2017 by Mike in SA

[RoundAbout]

 

 

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.

:iagree:  :iagree: 

 

Add me to the list of people who whole heartedly agree! The difference between algebra programs is huge! My DS started AOPS Algebra I this past September when he was still 9, but it was after maxing out Beast Academy and finishing AOPS Pre-Algebra. Even then we are moving at half-speed because there are so many other topics and interesting mathematics to explore. I have a computer science background so we do a lot of discrete math. We take a break for rabbit trails whenever he has an interesting question, and plan to take a more formal break for the Counting and Probability book next month. I have a kid who is both gifted in math and highly motivated - he constantly works on problems on his own. Having a child in algebra so young is probably not ideal but sometimes you have a kid who can't be slowed down. But there's no point in going through a second rate algebra program when there are so many amazingly rich math resources out there.

[Arcadia]

Is there an order to the videos posted, or do you just watch them randomly? I have a kiddo who would be interested in these I think.

At first my oldest would go for the Numberphile videos on topics he is interested in. Then he watched everything else because we ran out of videos from Vi-Hart as well. Then we watched Crash Course because both Numberphile and Vi-Hart doesn't release new videos daily and we usually watch YouTube after lunch or dinner as an after meal relaxation.

 

My kids love science videos as well, so it is not just math videos that gets watched. In our case, it is more of the science driving the math path.

[quark]

Caveat: son wants to major in math.

 

I admit to wanting to try programs like Saxon and MathuSee because at one time I really did not know how to keep challenging my son. But in the end, we used a big variety of resources from AoPS (supplement not core) to Dover paperbacks written by mathematicians. The difference is that my son sees math in a very different way. It is about as unlike traditional math learning as apples are to oranges. For example, his abstract algebra prof this spring is teaching via the lens of category theory. I am not going to pretend to know what that is but for my son, he immediately sees connections because we took this messy, roundabout, problem solving, deep thinking way vs the rote learning way. He finds it hard but he still probably understands as much as his college sophomore/junior classmates. His mind is so much more willing to probe, try, make mistakes and learn from them.

 

I feel like he has taught me how messy true learning can be. To not always expect linear progressions or to even trust in systems/ traditions. I am so glad I took this leap of faith with him.

Edited February 2, 2017 by quark

[Kerileanne99]

I think there is a HUGE range between starting algebra concepts and problem solving algebra...

 

My sample size is small however😊

 

My dd is radically advanced in math. She was doing Hands on Equations algebra at age 4. There are videos of her on their site. It was extremely intuitive to her.

 

Now, at age just turned 7, she has completed the Key to Algebra series and Life of Fred algebra books. We have 'gone through' Saxon books insomuch as I give her 10-15 of the more challenging problems per day on a dry erase board. (There is zero chance of her looking at a page in the book and completing it without meltdown, primarily due to presentation!)

We have gone slowly though Zacarro's book for real world Algebra.

i tutor several public schooled older kids in algebra...I would MUCH rather Alex spend a lot more time on intuiting/fine tuning/mental math skills than learning to follow a procedure. So no age, but depth of understanding...

Edited February 3, 2017 by Kerileanne99

[Kerileanne99]

Caveat: son wants to major in math.

 

I admit to wanting to try programs like Saxon and MathuSee because at one time I really did not know how to keep challenging my son. But in the end, we used a big variety of resources from AoPS (supplement not core) to Dover paperbacks written by mathematicians. The difference is that my son sees math in a very different way. It is about as unlike traditional math learning as apples are to oranges. For example, his abstract algebra prof this spring is teaching via the lens of category theory. I am not going to pretend to know what that is but for my son, he immediately sees connections because we took this messy, roundabout, problem solving, deep thinking way vs the rote learning way. He finds it hard but he still probably understands as much as his college sophomore/junior classmates. His mind is so much more willing to probe, try, make mistakes and learn from them.

 

I feel like he has taught me how messy true learning can be. To not always expect linear progressions or to even trust in systems/ traditions. I am so glad I took this leap of faith with him.

Oh wow, this is Alex!

Today she told me integers are black or white, whilst rational numbers are 'all wavelengths'.

Oh. Okay😳

[Grover]

If hands on equations counts as started then preschooler - 4 or so.  He loved it!

 

Formal bookwork study of what you guys call "Algebra 1" I dragged my feet on and took him along all sorts of other paths until he was 7.5 and I ran out of other things. He did a number of different programmes at his own pace and interest (Fred, AOPS, Khan, Jacobs, Zaccarro and other stuff we have about the place) and is starting Geometry now (10).  He never has to look at a concept twice, he often intuits methods and concepts based on very little information, it sticks forever and he can apply it all.  I have no idea how his maths brain works, and I have no idea where it will end up.

[StartingOver]

We have Life of Fred, and she does Khan for fun. Saxon appeals to her, for the straight forward way it teaches. She does her own thing and prefers Saxon for her sit down work and explores on her own. I have bookmarked the sights suggested so she can check them out. She has looked at AOPS and we will be purchasing them very soon. I don't know where she is headed, she is leading while I follow. hehe

[SeaConquest]

If Sacha stays on his current trajectory, he would begin AoPS Algebra at age 10. Dragonbox, he did at age 4.

[EndOfOrdinary]

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 spoke 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

[SparklyUnicorn]

I don't remember!

 

 

[SarahW]

What counts as Algebra?

 

Doing a book that has Algebra 1 on the cover? Then I suppose my kid is doing that now at 10.

 

Solving for x and that sort of thing? Umm, I think he was about 8 I guess. It wasn't a formal thing.

 

The problem is that even if their minds are ready for Algebra, the books are usually designed for teens and up. Some kids might be able to handle dense text and have a longer attention span at a young age to use these books as is. Other kids - well, they're still kids.

 

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 spoke 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

 

Wondering if you can give me titles that exemplify what you meant by proof-based but explicit texts.  :001_smile:

 

Crazypants is still driving me crazy. He'll watch math videos, and won't rest till he understand the,how to say..."philosophical underpinnings," the ontological reasoning....for something. Then he'll amuse himself writing down equations which prove the reasoning. But to jump out to something he hasn't carefully reasoned about yet, to solve equations he did not write himself - it's like, I don't quite know how to describe, emotionally terrifying(?). I'm trying to tell him that he can trust himself a little to make reasonable if-then conclusions, even if he hasn't made the full proof yet, but that's a no.  :svengo:  If only he was so careful about his arithmetic!  :glare:

 

I feel so stuck. Like, on the one hand he really likes math, he does it for fun, and I want to support that. But on the other hand I worry that his approach will be ultimately self-defeating. Hmmm.... find a teacher who can explore advanced number theory with him. That's an excellent idea. Now to just find one of those...  ^_^

[TerriM]

Separating it as Sarah W did.

 

We introduced the idea of variables when he was maybe 7 or 8 with some simple solve-for-x worksheets at maybe 8-9.  But formal Algebra I course in 6th grade (age 11).  I'd have considered starting a year earlier, but we had to transfer schools to one that would allow him to work at the appropriate level.  His previous school wasn't going to budge on it.

Edited February 4, 2017 by tiuzzol2

[TerriM]

 Rusczyk's shorter article, The Calculus Trap.

 

That was a great article.  One thing he didn't say, but could've, is that many kids who love math hate Calculus.  It's a lot of memorization and less problem solving, so when they see their future as Calculus, multivariable Calculus, and then Diff EQs they get to college and decide to go into a different field entirely.  

[TerriM]

Changing the direction of this subject a little bit....

 

How do you know when a kid is ready for Algebra?   

[quark]

Have not read all responses, apologies.

 

Apart from The Calculus Trap, I would like to suggest Lockhart's Lament. I admit that although I've started reading it multiple times and have skimmed lots of pages, I don't believe I ever finished reading it. Does not seem to have hurt my kid (so far! :laugh: )

[Runningmom80]

My DS is HG, but hates math.  We started Pre-A at the end of last school year, (with Jousting Armadillos) he was 9, but he floundered.  We finished that book this past fall and then went to LoF decimals and fractions books.  Those were a waste of time so now we are shoring up a few things, and the plan is to start him on AoPS Pre-A with WTMA next fall.  He will be 10 almost 11, which is not incredibly advanced but what's best for him maturity and focus-wise.

 

My younger DS is a math lover and I can see we will probably need it a little sooner. 

 

ETA:  It actually is advanced, he's a November birthday so in public school he would be in 5th grade next year.  Pre-A in 5th grade is advanced and I should probably step away from this board because I have zero idea of "normal" at this point. :lol:

Edited February 4, 2017 by Runningmom80

[Dmmetler]

Changing the direction of this subject a little bit....

 

How do you know when a kid is ready for Algebra?

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.

[chocolate-chip chooky]

I remember when my daughter was 5 she made up a game and called it 'handgebra'.

We would play handball together while giving each other algebra problems.   :001_smile:

 

At that age it started with stuff like 3x = 24  and 20/y = 5. We quickly moved on to things like 4m + 2 = 18.

I realised that I needed to find a way to meet her maths needs if she could do that at age 5 while playing handball. It was clearly intuitive, because she hadn't been taught any techniques.

 

One of the best pieces of advice I've been given from this board is to go with AoPS.

It's the 'why' behind the 'how'.

 

My daughter (now 10) isn't passionate about maths at all, though. She's certainly capable and she finds satisfaction in solving complex problems, but there's no real driving passion at this stage anyway. 

 

 

 

 

ETA: I didn't enter an age in your poll, because I'm not sure what really classifies as 'algebra'.

Edited February 4, 2017 by chocolate-chip chooky

[Runningmom80]

I remember when my daughter was 5 she made up a game and called it 'handgebra'.

We would play handball together while giving each other algebra problems.   :001_smile:

 

At that age it started with stuff like 3x = 24  and 20/y = 5. We quickly moved on to things like 4m + 2 = 18.

I realised that I needed to find a way to meet her maths needs if she could do that at age 5 while playing handball. It was clearly intuitive, because she hadn't been taught any techniques.

 

One of the best pieces of advice I've been given from this board is to go with AoPS.

It's the 'why' behind the 'how'.

 

My daughter (now 10) isn't passionate about maths at all, though. She's certainly capable and she finds satisfaction in solving complex problems, but there's no real driving passion at this stage anyway. 

 

 

 

 

ETA: I didn't enter an age in your poll, because I'm not sure what really classifies as 'algebra'.

 

This is why we floundered.  DS does not have patience for not getting something right away and just needed some more maturity before starting AoPS.  I could have switched him to something else, but I didn't want to start Pre-A unless he can do it the AoPS way.  (I know AoPS isn't for every kid, but I do think it can work for my kid, he just needed some more time.)

[Mike in SA]

That was a great article.  One thing he didn't say, but could've, is that many kids who love math hate Calculus.  It's a lot of memorization and less problem solving, so when they see their future as Calculus, multivariable Calculus, and then Diff EQs they get to college and decide to go into a different field entirely.  

 

In many AP courses, that may be true, but a good calculus course is not run this way.  Mine was theory, theory, and a bit of application.  Not a whole lot of memorization.  Calculus III was the first course I had where I truly fell in love with math as art.

 

I really wish people would stop trying to turn math into arithmetic!

[TerriM]

In many AP courses, that may be true, but a good calculus course is not run this way.  Mine was theory, theory, and a bit of application.  Not a whole lot of memorization.  Calculus III was the first course I had where I truly fell in love with math as art.

 

I really wish people would stop trying to turn math into arithmetic!

Wow!  We are very much the opposite.  I love algebra, series, modular arithmetic, and geometry.  Multivariable Calc was painful (most especially the hand-drawings of curves).  That one killed my interest in going further in math.

[Mike in SA]

Wow!  We are very much the opposite.  I love algebra, series, modular arithmetic, and geometry.  Multivariable Calc was painful (most especially the hand-drawings of curves).  That one killed my interest in going further in math.

 

I don't know that we're opposite - I suspect your multivariate class was taught the wrong way, if it involved any memorization at all.  It was the first one that I took that required no memorization of any sort.

[SKL]

I chose 6-7, 8-9, and 10-11.

 

My kid sister (whom I used to teach long ago) was 7 when she found an antique algebra book and started doing the problems.  She was a natural.

 

My youngest was 9 when the summer math program put her in algebra.

 

My kids are currently 10 in 5th grade, and they are doing an "algebra" unit in Singapore Math 5A.  Still early in the chapter, today's homework included the problem "solve: 5n-9 = 3n+7."  I know this is not fancy algebra, but I guess it counts, and I suppose it will get more real before they are 12.  :)

Edited February 5, 2017 by SKL

[ebunny]

Changing the direction of this subject a little bit....

 

How do you know when a kid is ready for Algebra?

 

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.

Alternatively, when I suspect a child is ready, I introduce the concept of a variable and see where it goes.

 

Integers are introduced in 4th or 5th grade in most schools in India, Algebra 6th grade. Some children are definitely ready much earlier. As early as 1st grade (6 yrs) and as late as 7th grade (12 years).

 

 

 

 

ETA: Typos!

Edited February 5, 2017 by Ebunny

[lewelma]

I knew my ds was ready for Algebra when he found the AoPS Intro Algebra on the shelf and started working on it without me knowing.  :001_smile:

 

Ruth in NZ

[daijobu]

I appreciated calculus for deriving the volume of a sphere. Also I really enjoy drawing 3d graphs. My old exams look like art exercises. I can still whip out a hyperbolic paraboloid (saddle for a 2 humped camel) in 15 seconds. Longer if I'm including the coordinate axes.

 

Sent from my Nexus 5X using Tapatalk

[Grover]

I had to come back to this thread.  DD (7) my NONmath kid was sitting at the table this morning with an algebra two workbook reading the explanations and working her way through the problems.  Erm.  Oops.  My best estimate of Miss I-won't-do-anything-if-you-are-watching was 4th / 5th grade. 

[Kathy in Richmond]

I always loved using Miquon with my kids because it introduced the ideas of algebra early on. And I loved using the ideas in books like The Ideas of Algebra: K - 12 (NCTM yearbook 1988) throughout our homeschooling years. But...I didn't count my kids as being in a formal algebra class till they were 10 or 11 years old. I wanted their fluency and written output to be up to par with their conceptual understanding before I counted that as a credit. No need to rush!

 

As for calculus (& multivariable & diff equations), I loved them all personally. But I took honors versions at Rochester after completing AP calc in high school, and those were wonderful & theoretical courses (we used Apostol :-).

 

Not all mathematicians feel that way, though. Once when I was a grad student, I was following my advisor around the country (after his divorce he traveled a lot, sigh) and we were at the Math Science Research Institute at U Wisconsin. I was working on my plans for teaching calculus the next term at Carnegie Mellon, and I had my calc text opened on my desk when the head of the Institute walked into my office. Yikes, he laid into me for being interested in such a mundane subject as calculus!! I was surprised at the intensity of his reaction & that he didn't think calculus was "real math."

 

 

[Incognito]

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.

 

 

[EndOfOrdinary]

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.