What happens in the future if math is accelerated?

[ack25]

My ds, age 7, is ahead in math. If we continue accelerating the math, what happens eventually? Where does it go? Is there a conceptual wall that is hit at some point that forces him to slow down? What happens if he doesn't hit a wall and is accelerated beyond a year or two at high school age? I am just not sure what the long-term plan is, and I cannot see how it plays out.

[Spetzi]

Good question! Have you read this??

 

http://www.artofproblemsolving.com/Resources/AoPS_R_A_Calculus.php

 

 

You are right to be concerned. I believe that there are going to be topics in math that my ds may not be devlopmentally ready to tackle such as proofs in geometry or calculus itself.

 

This year we spent some time working on problem solving, statistics & probability, as well as reinforcing basic manipulation of fractions and decimals. I felt that we should slow down. However, while ds enjoyed the work he did, he was eager to get started with algebra and is tearing through that curric as well.

 

There may be a plateau year or season when things don't proceed as quickly, but now I'm just feeding him. He's really enjoying the challenge and appears to have a full understanding of the concepts.

 

I believe as long as we continue to consider the child's interest, ability and well being, we can proceed either forward or outward (it's a bit harder to find engaging materials outward, but it's possible.)

 

Enjoy the article!

[JeanM]

Good question! Have you read this??

 

http://www.artofproblemsolving.com/Resources/AoPS_R_A_Calculus.php

 

 

:iagree:

 

That is a great article.

 

My oldest is now 10, and rapidly approaching algebra. I'm just taking it one step at a time and if we hit stuff that he isn't ready for then we'll do something else for a while. There is lots of math to learn. I'm planning to throw in a year of statistics and probability at some point, and maybe more geometry.

 

I don't know if this helps or makes it scarier. I don't think holding him back and having him do lots of repetitive practice is the answer. If he isn't ready for the more abstract stuff when you get to algebra, there are other options. Some people here have talked about doing Russian math for a year, or working on problem solving books.

[KAR120C]

It depends on the kid, and probably on the curriculum too. Some kids will find the transition to algebra difficult at some ages or with some approaches... I don't know if DS's ability with math is entirely his own propensity for the subject, or if the way it's taught or both... but I can say that not all kids will hit a wall at algebra.

 

My strategy has been to let arithmetic go as fast as the kid wants to, and then flesh out more at algebra. Either you can transition to algebra when you're done with arithmetic, or you can't -- either way there's more to do then. You can do a year of problem solving before algebra (Mathcounts, for instance), or delve more deeply into the connections among different math topics... Having all the tools of arithmetic at hand makes those more interesting.

 

But once you've done basic algebra the options open up tremendously -- more problem solving, more connections, mathematical logic, number theory, statistics/counting/probability, financial math... You'll never run out of topics, but algebra is prerequisite for many of them.

 

The way DS and I are doing it now is to alternate years between "regular" math (Algebra, Geometry, More Algebra) and "extra" math (Statistics, Number Theory, Financial Math). I'm not in a hurry to get to calculus in particular, especially if he's going into engineering (his current interest...), because a lot of colleges are going to want him to take THEIR calculus anyway. Not that I'm keeping him away from it in particular, but that I'd like to save formal study until he's almost ready to graduate. Plans could change of course, but I like knowing that even though we started high school math ridiculously early we have options that will keep us busy (and engaged!) until he's fully 18 if we need them.

[ack25]

Thank you for the replies and the article. Sometimes I panic. :chillpill:

[joannqn]

Honestly I think in part our thinking comes from what we have been told for years. That certain concepts in math can't be learned by kids who aren't yet a certain age. I'm learning that isn't totally true. Some people think it isn't possible to teach an average 5 year old multiplication, or basic algebraic concepts to a kid not yet in middle school. I say, hogwash. It CAN be done. I have no idea if my son has any special propensity towards math, but I have seen that he has learned things easily that I didn't realize a young person could learn so easily. There is nothing special about me with regards to my knowledge of math (that is for sure).

 

I'm finding the same thing to be true. My son hasn't had any trouble learning anything. He's 7 and basically taught himself his multiplication facts, multiple digit multiplication, and long division simply be paying attention to his sister's math. The only practice he got was setting up some problems himself on the white board. He also has a very basic understanding of algebra even though we haven't officially covered it. (We've done a couple of rabbit trails.)

 

I don't know if this helps or makes it scarier. I don't think holding him back and having him do lots of repetitive practice is the answer. If he isn't ready for the more abstract stuff when you get to algebra, there are other options. Some people here have talked about doing Russian math for a year, or working on problem solving books.

 

I agree. Actually, I finally came to that position late this year. Before then, I was trying to slow my son down by making him do every problem on every page...he still finished two years of math in one. I finally realized that it was silly to continue making him do pages and pages of things that he taught himself last year and almost never gets wrong.

 

I don't have a plan yet for our future. I'm taking it one year at a time. Next year, my son hopes to finish MUS Epsilon and Delta. I'll also be adding in either Singapore's Challenging Word problems or MEP for extra practice on different types of problems. If he finishes (which I fully expect he will), he'll be doing pre-algebra at 8 years old and will do algebra at either 8 or 9 years old. I've decided not to worry about what's next until after algebra. That's the point where we might start branching off into other things.

[KristenS]

My plan, if my kid hits a wall or goes faster than *I* am comfortable with, LOL, is to expand outward. Do the fun stuff. Raymond Blum is the king of math (and other) puzzle books ... start with some of his stuff. Try Vicki Cobb's "Bet You Can't" and "Bet You Can" for some science and math variety in thinking. Do logic puzzles, and then do lateral thinking puzzles. There are all sorts of ways to broaden the horizons of math till a child is ready to get past any wall they might hit.

 

My experience with math is that I could do the work all the way up through college Linear Algebra (thankfully the last course I had to take) but that I didn't 'get' most of it. It's possible to make A's and be totally clueless, apparently. LOL. This baffles my dh, who lives and breathes math the way I speed-read my way through libraries. We're an interesting marriage.

 

Ted seems to be taking after dh, so far, so at some point dh is gonna have to be the primary math teacher. I can pass it, but I doubt I can teach some of the higher stuff. I know my limits!

 

There's a cute series, which appears to still be in print, called "___ the Easy Way." Most of the series are dry boring books, but the Algebra, Trig, and Calculus books are story oriented ... a fantasy kingdom explores math as they find problems they can't solve using the methods they already know. I found the Trig one very helpful in high school, and part of the Calc one too. I need to get the Algebra one for just in case. :) Though that wasn't a struggle for me.

[AndyJoy]

Not everyone hits a conceptual wall. My dh was accelerated in math (fighting the public school tooth and nail to do so!) and never hit a wall in his studies. By 16 1/2 he had completed college calculus I-III, differential equations, linear algebra, and a couple of math electives.

 

At 14, he was ready for calculus and somehow managed to convince the school to let him take it at the university rather than the high school. After that, the school had no more courses to meet his needs, so he continued with the university math courses. He even (deviously) scheduled his math courses to interfere with his high school English courses so he could take those there too!:D

[Storm Bay]

Individuals vary. However, since my 11 yo is no more ready for long problems than my 14 yo was when she was 11, she (the current 11 yo ;)) is doing Russian Math from Perpendicular Press along with CSMP now that she's finished Singapore Math 6. ie, we're going deeper. CSMP is simply fun for her, and she just does the sheets on her own, little knowing how it's helping her. Russian Math is harder in some areas than Singapore Math 6 was, and is forcing her to thing about math in new ways, even though some of it is review.

 

When she's done Russian Math, she'll do Japanese Math 7 along with Life of Fred Algebra. I think she'll find LoF fun, which is what I want, and then she'll do a rigourous Algebra when she's about 13 (maybe starting at 12, but I don't know.) I have to say that even though this particular dd is accellerated in math and is mathy, history is her "thing" along with art (although she hates to study art, but is very artistic--was drawing animals in motion when she was in K, thinks & sees the world differently, etc). If she were driven in math, we might have handled it differently.

 

One of what I call my math "gurus" on the highschool forum did all kinds of cool math with her dd when she was in high school that most highschool kids never get too see, and I'm including homeschooled highschoolers in that group. Her dd is now studying math in college. I can't remember if it was Lori or Jann in TX who did that (the other current hs math guru for me is Jane in NC, as Charon & Myrtle haven't been posting there). Others may have done this, but I'm thinking of a fabulous post I read on some thread there once where she described it.

[joannqn]

I've just got to say that I'm so excited that I read this thread and that Spetzi posted that link to the art of problem solving website!

 

The art of problem solving has online classes and textbooks designed for the top math student that are based on problem solving, not just basic math. It looks like it could be interesting!

 

Not only that, but I followed a link from there to http://www.themathleague.com/ which has math contests. One of the things that they offer is books of previous tests that look like they could be an interesting supplement. There are sample tests. My kids and I went through the 4th grade sample test today. I think my son could do well in these contests with some problem solving experience, especially since he still has 2 years to go and half of the problems were easy. I'm excited about these new possibilities!

[kpupg]

... expand outward. Do the fun stuff.

 

I recommend the Murderous Maths series of books.

 

Karen

[KristenS]

Ooh, haven't heard of those. Author?

[Storm Bay]

I recommend the Murderous Maths series of books.

 

Karen

 

Are these mysteries?

[Laura in CA]

They particularly appeal to boys (my sons are 12 & 13). One of my sons won first place in a math contest (and $100 ;-) and I know that things he learned from MM definitely helped (one of the questions in the contest had to do with how many pieces result from cutting a pizza all the way across with a certain number of cuts, and that was in MM -- but the books are so full of interesting facts that I'm sure the books also helped in less tangible ways). My kids will start trig this fall, and we're planning to read the MM trig book (I think it's called the Fiendish Angletron or something) over the summer as preparation.

 

You can get the books from Ray at Horrible Books --

 

http://www.horriblebooks.com/

 

http://www.horriblebooks.com/horriblebooklist.htm

 

He orders them from England every few months. If you order from him by May 31st (his next order) you should receive them sometime around the end of June. He has great service and free shipping.

 

You can also get them from

 

http://www.bookdepository.co.uk/search?searchTerm=murderous+maths&search=search

 

They also have good prices & free shipping. I've ordered from both places and have been very happy with both.

 

~Laura

Edited May 25, 2009 by Laura in CA
clarity

[kpupg]

They particularly appeal to boys.

 

Yes, I didn't mention this ... in my mind, these books are sort of in the same category as Life of Fred for humor etc.

 

The author is Kjarten Poskitt (I think), who is English, and if you have to have the books right now, you can get them through amazon.co.uk, though you will pay for the shipping. American book sellers don't always have them available, but there are ... I don't know ... close to a dozen books in the series maybe? So there is usually something available domestically at any given time.

 

These are the books my son read in bed before we discovered Life of Fred for a "real" curriculum LOL. My son learned all his trig concepts from that Angeltron book and will only be filling in around the edges when he does trig "officially" :) He still picks one up and re-reads it now and them -- great fun for him.

 

Karen

[VanessaS]

Excellent article (AOPS). I completely agree!

 

My DH and I are engineers (software and electric) and we use mostly algebra, geometry, number theory, strategy, economic theory, and statistics but at a very advanced level. No calculus in sight! I was in AP Calculus in high school and went on to College Algebra and bombed. A tough Algebra course is much more difficult than high school Calculus.

 

We're planning on spending 2 years on each topic with our kids, rather than one.

Even now (with my 4 yo) when we do math problems we try to find as many possible ways to get to each answer: counting manipulatives, moving the counters in form groups (how he discovered multiplication), using a number line, counting on our fingers, counting aloud (forwards and backwards), etc. We're noticing the patterns and properties. It's so much more fun that way. We can learn the "math facts" when he's school-age and we start a formal curriculum, if he hasn't memorized them all already.

[Sarah CB]

We've dealt with this as well. Dd finished Singapore 6B when she was 9. We tried NEM but I had a new baby and couldn't wrap my brain around it and she wasn't ready for it. So, we spent a couple of years trying out different things. Eventually we found Russian math 6 - it's well worth it. Then we did about half of NSM before moving on to NEM without a problem. She finished NEM 1 and then half of NEM 2 before starting with a tutor. This year she is in grade 7 and will write the Provincial exam for Principles of Math 10 (Canadian). She wants to do math 11 over the summer and then do math 12 next year. I'm not sure what we'll do after that - or what the rush is. I'd rather see her work through Gelfand's algebra or some geometry proofs or some other really interesting sounding math that I don't understand :)

[Storm Bay]

This year she is in grade 7 and will write the Provincial exam for Principles of Math 10 (Canadian). She wants to do math 11 over the summer and then do math 12 next year. I'm not sure what we'll do after that - or what the rush is. I'd rather see her work through Gelfand's algebra or some geometry proofs or some other really interesting sounding math that I don't understand :)

 

 

Do you like the Principles of Math, or are you in a province where you need to do certain things in order to graduate? She could rush through those tests and then go onto something more interesting. The AMS (American Math Society, but there may be a Canadian equivalent) has some interesting books for advanced high school math students. There are other things, as well.

[Sarah CB]

Do you like the Principles of Math, or are you in a province where you need to do certain things in order to graduate? She could rush through those tests and then go onto something more interesting. The AMS (American Math Society, but there may be a Canadian equivalent) has some interesting books for advanced high school math students. There are other things, as well.

 

I'm not really sure if I like PofM or not... In our province we have "essentials", "applications", and "principles" with "principles" being the more "academic" option. Dd is enrolled in a program that is geared towards graduation. She was the one who wanted to do Math 10 this year. I was happy with working through NEM. She did do all sections of NEM 2 and 3 that relate to Principles of Math. I'd like her to work through the remaining sections of NEM 2 and 3 over the summer, before she starts math 11.

 

I'll take a look at the AMS stuff and then see if we have a Canadian equivalent.

 

Thanks,

Sarah

[Storm Bay]

I'll take a look at the AMS stuff and then see if we have a Canadian equivalent.

 

Thanks,

Sarah

 

 

Look for the high school page--I can't seem to find the link quickly.Oneof the titles includes Mathematical Circles (which you can get at Amazon.com), so you'll know you're on the right page. I hope to get that one and one on ciphers this year.