How to go about accelerating?

[IsabelC]

Hi, I'm not usually posting here as most of my concerns are special needs related. However, as we start planning for bring my youngest child (currently in prep, AKA 5yo kinder, at school), I'm finding it's not much easier to plan for her than for the others. I'm a little at sea with how to teach a faster learner.

 

I have no idea whether she is very gifted, or just a little gifted, or - as you sometimes say here - "just bright". We haven't had any assessments for that, however her teacher said she has never seen a child like her in all her years of teaching. She is like a knowledge hoover. Whatever you give her, she sucks it in, at about ten times the speed of her siblings. She seems to learn everything faster and more easily than her peers, too. Her teacher has been great with giving her as much individualized work as possible, but told me that she still thinks Ms. 5 is sometimes bored; she thinks in a whole different way to the other kids. But, she doesn't have any strong interests apart from reading, and she will read indiscriminately if we don't suggest things. 

 

I have known for a while that she's on the faster side academically, but I think she's learning significantly below where she "should" be, even with all the extension the school can offer. I can see this child is going to need some proper accelerating when we bring her home. However, she is socially and emotionally immature (ASD stuff), so I want to start moving her fast enough to maintain interest, but also gently without a lot of pushing or exposure to things she can't deal with (I was a bit horrified a while ago to find her reading a university obstetrics textbook full of graphic illustrations of very sick/deformed babies - I actually got rid of that book, but that's typical of how she will get interested in anything that's around). And of course, she is sometimes just as silly as any 5yo.

 

Anyhow, how you figure out where your child is "at", and what do you do about it? For example, she said her math at school is boring and too easy. So I tried her on some grade 1 math, but she did 7 pages in a few minutes and said that was just as easy as the school stuff. So should I let her do it as fast as she wants and gradually get ahead? Or do I only give her half the problems, or just the review lessons, until we reach a point where she is challenged? Or should I maybe simply give her a placement test and start her on whatever book she places in regardless of grade level? Or is it better to broaden out instead, maybe spend a couple of terms redoing LoF or playing mathy games? 

 

[Arcadia]

For math, we went broader with stuff like tangrams, pentominoes, pascals triangle, Fibonacci numbers, origami, abacus, Mayan number system, Roman numerals ...

 

Pentominoes template

http://www.cleavebooks.co.uk/trol/trolxp.pdf

 

Tangrams template

http://www.cleavebooks.co.uk/trol/trolxk.pdf

 

For science, The new way things work book as well as the way things work DVD set are interesting and safe for any age. Nothing gross or scary. His other books have lovely illustrations.

http://www.amazon.com/gp/aw/d/0395938473

 

The DVD set is old and your library might have it. The book is a revised edition.

 

For placement in math, I just let my kids test out with the end of year reviews tests I found in public school textbooks which my local library have.

[EndOfOrdinary]

Initially we did the same thing for math and just pikes of books about darn near anything he wanted. The library is our friend. We got a zoo membership and attended at least once a week.

 

I will say that DS was a horridly immature little deviant until he was challenged. Once I started actively schooling him at where he needed to be, it was like all the energy could be channelled. That an LOTS of activity. Just the physical act of wearing m out. You might be amazed at what could happen with a little mental struggle and academic interest.

[IsabelC]

Thanks for the suggestions :)

 

For math, we went broader with stuff like tangrams, pentominoes, pascals triangle, Fibonacci numbers, origami, abacus, Mayan number system, Roman numerals ...

Pentominoes template
http://www.cleavebooks.co.uk/trol/trolxp.pdf

Tangrams template
http://www.cleavebooks.co.uk/trol/trolxk.pdf

For science, The new way things work book as well as the way things work DVD set are interesting and safe for any age. Nothing gross or scary. His other books have lovely illustrations.
http://www.amazon.com/gp/aw/d/0395938473

The DVD set is old and your library might have it. The book is a revised edition.

For placement in math, I just let my kids test out with the end of year reviews tests I found in public school textbooks which my local library have.

Yes, she likes roman numerals and tangrams, so I think she'd probably be interested in other extra bits and pieces. I hadn't seen Pentominoes before, but I know she'd like them because she likes to play Blokus and that has similar shapes.

 

I'm wondering with regards to testing out in math, what about the 'manipulative stage'. Many people seem to suggest that's it's very important for kids to do things with blocks, rods, or whatever before doing mental arithmetic. But if the kid is already doing problems mentally, is it necessary to make them use manipulatives? Or pictures, for that matter? We have, in the past, used MAB base ten blocks to make sure she understood hundreds, tens and units, but I failed to get her interested in using number lines.

 

 

 

Initially we did the same thing for math and just pikes of books about darn near anything he wanted. The library is our friend. We got a zoo membership and attended at least once a week.

I will say that DS was a horridly immature little deviant until he was challenged. Once I started actively schooling him at where he needed to be, it was like all the energy could be channelled. That an LOTS of activity. Just the physical act of wearing m out. You might be amazed at what could happen with a little mental struggle and academic interest.

How long did it take to find the right level for that little bit of struggle? I am keen to get my daughter to a point where at least some stuff is challenging. (My experience of schooling was that I spent so long not being challenged that it was an almighty shock to the system when I reached about 9th grade and had to learn how to cope with not knowing the answer instantly. I don't want to be pushy, but I don't want her to coast so much that she doesn't learn to cope with challenge, iykwim.)

 

 

 

Since she has already done LoF, you could go thru the topics and see what was retained, using a chapter review kind of approach. From there, pick any topic and enjoy learning.

We only went through the elementary set (Apples to Jellybeans, I think?) but I'll probably go back to the beginning and start again. She will enjoy it and probably understand / remember more on the second go-round.

[IsabelC]

You have to be careful that the student didnt memorize instead of learn. If they can explain solutions to their stuffed animals with manipulatives or pictorial, or solve problems, they probably know it. The manipulative, or concrete stage is for beginners approachng a new concept, who dont know enough to begin abstractly. For ex, if I want to teach you how the organs fit inside the abdomen, you might do better if you had the real thing or a model available, as you would have a better idea of size relationships and packing then if I just told you about it.

 

Number lines come pretty easily after use of a ruler and the concept behind it is learned.

 

That's funny, I was saying how my kid doesn't like concrete stuff, then you gave the example of organs and I was reminded that she loves unpacking and repacking the thoracic/abdominal contents of my anatomy doll  :laugh: 

 

Yes, I suspect that she does just memorize some stuff. She seems to know multiplication facts (presumably from hearing her brother learn them, as I haven't taught her) but I'm not sure she has fully grasped how multiplication works and why it is commutative. I might try testing understanding by getting her to 'teach' her stuffed animals. 

[Arcadia]

I'm wondering with regards to testing out in math, what about the 'manipulative stage'. Many people seem to suggest that's it's very important for kids to do things with blocks, rods, or whatever before doing mental arithmetic. But if the kid is already doing problems mentally, is it necessary to make them use manipulatives?

My boys kind of did the "manipulative stage" as toddlers with Legos. They also had the 100 beads "board" (10 rows of 10 beads on a wooden frame) as a baby toy which they had more fun dismantling and putting back.

 

If a young child who does math mentally can explain how the child interpret and solve the problem verbally with or without manipulatives, I consider that good enough for me. Besides anyone that has handed my kids math manipulatives have found that my kids would build structures out of those instead.

 

Number lines are useful for negative numbers. However my boys prefer to explain negative numbers using money so negative numbers are IOUs.

 

They figured out commutative, associative and distributive properties using M&Ms from their Easter and Halloween stash before they were taught. So in a way they did show they were competent enough in use of manipulatives.

[Mike in SA]

Here is a challenge to try out...  It will tell you how ready your child is to abstract.  It might be more challenging for the parent than the child.  :)

 

Start with a uniform pile of legos (one domain).  Now, create an "operation" on two blocks from set A.  Does the result belong in set A?  If the range is a subset of A, then you have a closed operation.

 

Come up with a few sets and operations that result in open and closed operations.

 

When your child gets this process, they are ready to learn formal mathematics.  The ability to abstract is the key.  If the exercise is very difficult, then keep playing a bit longer.

[IsabelC]

Now could you please explain the procedure in English? :lol: 

 

As I have mentioned before, I am not a mathy person. I am learning along with my kids, after getting right through school (and doing well, strangely enough) without any understanding of even the most basic mathematical concepts.

 

So could you give an example of this activity please? (Maybe I need to go back to playing! :D)

[Mike in SA]

Now could you please explain the procedure in English? :lol:

 

As I have mentioned before, I am not a mathy person. I am learning along with my kids, after getting right through school (and doing well, strangely enough) without any understanding of even the most basic mathematical concepts.

 

So could you give an example of this activity please? (Maybe I need to go back to playing! :D)

 

I did say it would be tougher for the parent than the child!  ;) 

 

Ok, here is how it might play out:

 

"Let's make a pile of the little legos (1x1s).  Don't stick any together.  We'll leave all the other legos in the bucket.  Stuck-together legos belong in the bucket -- only non-stuck legos can go into our pile."

 

When that is done...  "Now, let's make up an 'operation.'  We'll call it 'sticking.'  If we take any two of the little legos, we can do a 'sticking' operation, and put them together.  But then, they won't be able to go back into our pile.  They'll have to go into the bucket, because our pile is only non-stuck little legos."

 

"But, we could make up another operation, called 'turning.'  We could turn any of the little legos, and they'd still be little legos, and can stay in our pile."

 

The math of it: the domain is the set that you start with (the pile of little legos), and the range is the set of possible results (either the little pile, or the bucket).  "Sticking" would be an open operation on a set of unstuck little legos.  "Turning" would be a closed operation on a set of unstuck little legos.  Here, "closed" just means that the range is a subset of the domain.  This concept is the basis for all of our regular arithmetic operations (+,-,/,x).  For example, you can't always divide two whole numbers and end up with a whole number -- you might have a remainder, or the two numbers may not be divisible.

 

If you change your domain to include stuck-together little legos, then "sticking" becomes a closed operation -- they won't get back to the bucket, because stuck-together little legos are still allowed...

 

Kids can be quite creative.  She will probably be able to come up with a couple of domains, and dream up some operations that are closed under that domain.  And she will be able to use those terms while doing so!  When she wows you with this skill, she's ready for the real deal.

[Erin]

WRT manipulatives, if she's got something, just skip it.  Only go back to them when you actually need to.  

 

When Buck was working on more challenging equations in Algebra, he would forget to keep it balanced.  We used manipulatives (or at least the picture of) to show that the equal sign means an equation has GOT to remain balanced or you screw up that whole equals thing!

 

On the flip side, I was an example of a kid who "got" multiplication very early because I memorized my facts.  However, it wasn't until I was in my teacher ed. classes in college that I understood multiplication to be talking about sets of things.  And I got it then because the prof was showing us how to teach with manipulatives.  lol

 I've often wondered how much easier my high school math classes might have been if I'd had a more concrete base in my younger years.  

[lewelma]

I did not do any formal math with my older until he was 6.5 but started at 5.5 with my younger.  For each child, I just sat with him at the table for 20 minutes each day (for like a year), and had him do 1 problem of each type.  If he got it, we moved on; if he didn't, I have him do 3 more.  Typically 3 was enough (out of a section of of 20, or a unit of 5 pages). Sometimes it was not, and then I had the kids do the entire unit. After a year or so, I had each child at the appropriate level for him, and they could work at a more expected pace. 

 

As for manipulables, I had made all sorts of really cool thing from Montessori. In fact, I spent weeks threading golden beads.  And do you know what?  My older never touched them; there was simply no need.  I don't think he has used a manipulable in his life.  Now my younger has used a few here and there, but mostly he just uses pictures of pizzas for fractions and stuff like that.  He never had to actually cut up paper pizzas to understand fractions. I think it really depends on the kid.  So I definitely disagree that all kids must use manipulables.  Diagrams, yes; actual manipulables, no.

 

Ruth in NZ