I've been thinking quite a bit today about DS's math abilities.  It seems he 'gets' the concept of addition.  He understands that if he has $4 now, on allowance day, he'll have $6.  He can count on his fingers if I give him an oral addition problem.  He knows some without having to count.  But put numbers on a page, and he's clueless.  Well, sort of.  I've given him a sheet of math problems, and he usually can do them without much trouble. 

Yesterday was different though, and what spurred my research into kid's thinking processes. 

We played Kismet.  At the end we were adding up his total score and he had such a hard time with the problems.  I'd write it all out and we'd take it one column at a time (which we just learned about) but the problems he normally knew were just too much.  I'd ask 1+1 and he'd say 14 or something completely random.  Then he'd grasp at straws, just saying random numbers until I had him focus again and count out the answer.  This happened with almost all the problems.  Another problem was 9+7 and I told him he should draw circles so he could count them.  Well, I obviously didn't specify because he just kept drawing circles until he was into 20something and I stopped him and showed him how he should draw 9 and then 7 and then count them to get the answer - which he'd seen me done before. 

The most odd one was 6+6 - he said the answer was 6.  I can see why he said that, but I wondered - why does this kid not see that this is obviously wrong.  It left me (and him) very frustrated. 

 

So it led me to look into the development of children's abstract thought, which brought me to this article. 

http://goliath.ecnext.com/coms2/gi_0199-7823508/Enhancing-early-numeracy-by-promoting.html

It's a bit of a hard read, but interesting (to me anyway)  :) 

 

The premise is that some kids are behind in their abstract though processes due to various reasons, and there are some fun tests (disguised as games ;) that you can do to find out their level of thinking.

So today, for math class, we're going to try it out and see how DS does. 

It was a little disheartening that these tests were done on kindergardeners and DS is 8, but hey, I try hard not to compare, and just focus on where we are now (I get lots of practice at that).

 

Here's the tests

-The oddity principle - Take three objects that are the same and one that is different (shape, color, size, orientation, various).  Have the child pick out the different one.  Do many of these with different objects, but also have the opposites  - ie first problem has 3 big paperclips and one little, second problem has 3 little and one big.  What happens sometimes in the second problem is the child will insist that the little ones are still the 'different' and pick them away from the one big one. 

-Insertion - Show a number line with numbers missing and ask them which number goes in between.  Also have a line of progressively bigger/smaller/redder/etc. objects and ask them to insert objects the correct place in line. 

-Conservation - This deals with the rule that 4 will be 4 forever until someone adds to or subtracts from it.  This can be tested by having a line of 5 beans, then expanding that line and asking if there are more or less or the same number of beans.  Also, have a largely written number, and the same number but written very small, and ask which one has more value. 

 

If you scroll about halfway down the page of the article, it will show specific ways to adminster them and make them more fun. 

I can see these tests coming in handy in the future too when we're learning about alphabetical order, reading, etc.  All of them seem like they'd have some type of letter/reading counterpart. 

 

Voluntary math

DS is doing math problems.  That he asked me to write for him.  

He picked up his math notebook and stared for a while at a page.

Then he came to me and said "I can do this!  Where is a pencil?"

It was the same page wasn't finished a couple of months ago because of a meltdown.  It was the same page that caused me to back off and reevaluate how much he knew about numbers and how we had to just learn to identify the numbers from the very beginning.

Now he's doing addition.  When he ran out of fingers, he drew tic marks to count.  

Seriously, this had him crying just a few weeks ago.  

:)

I had to edit because right after I hit post he figured out my pattern.  I was just going 1+2, 1+3 1+4 etc.  He figured out that they  were in order.  So proud :)

I think what started this is that I let him play How Big is your Brain on Facebook and he can at least guess all of the answers except the numbers section.  Then I have him do the simple addition ones but then I read the harder ones aloud.  I think doing them together with me gave him confidence.  

And now I just got out his abacus so he didn't have to keep making tic marks.

These moments are what homeschooling is for, right?

Attempted reading

Today, in addition to reading a book, and giving him a 'special' word, we tried phonics.  I got this idea from 'The 3 R's' by Ruth Beechick.  We tried this in June, but it ended in tears on the first day so I put it away for the time.

This time we had some success!  

First step is to pick one vowel (A) and three consonants (T,N,S), and put them together to form different, short words.  So we started with AN, AS, AT, then added ANT and ANTS, and then a toughie -  SANTA - which he figured out and earned much praise and high fives.  I'll have to check the book to see what to do next  - I think we just add a couple letters a day and make bigger and better words.  :)

Good job, kid-do!  

Their first language

Andrei has been with our family for 9.5 months.  When we picked him up at the orphanage, he knew 0 English words.  Now, he knows only 5 Russian words.  Everything else he completely forgot, months ago already.   Everyone, including us, is very suprised at this.  We thought about getting a Russian speaking tutor, or we'd need Rosetta Stone to help him learn English, but nope - it came naturally just by living (and watching cartoons).  I thought in High School that I would encourage him to re-learn Russian, but if things are going well in other subjects, we might learn it sooner (although I'd like him to learn Spanish first).  It is amazing to me how quickly the transition went.  And I think it will come back to him quickly as well.

 

Here's Andrei's Russian vocabulary atm:

 

Stoh-be  Not sure what it means - I think 'so'  As in - "I need to put on a coat, stohbe I don't get cold"  It's habit - he doesn't even know he's saying it..

Pi-chen-ya For a while he would ask for this as a snack and we didn't know what it meant, now we figured out it's 'cracker'

Choo-choot Means "little"  We still use it with him, so he knows it

Pree-vyet means Hello

Yah-blah-ka means Apple   -  these last two he knows because he ran into a friend of ours who is studying Russian in college and tried to talk to him.  Andrei had know idea what he said, so I translated for him.  These words stuck.

 

Andrei also tries to look smart by saying - "that means 'shummey' in Russian" - but I know he's making it up (everything is the same word!).  It seems bizzare to me that I know more Russian than my Russian son. 

Daily re-evaluation

I am so glad I did not purchase a curriculum.  So glad.  I have had to scale back my expectations so much, even in the past three weeks.  School stresses him out so much.  I tell him what to do and he starts whining and says he can't do it.  Once I took it away and said he didn't have to do it then (it really was too hard for him), and he started for-real crying.  :(  So we focus a lot on breaking down even the smallest tasks, and even after a horrendous job, I try my best to smile and compliment him on finishing.  The only rule we have is "Don't Give Up!"  I think that is for both of us.

 

So here were my goals, and here's the reality so far:

 

 

Math - our first page was adding simple things with little dots he could count.  The second page I eliminated the dots and he drew them in and counted them.  The third page I had one problem where the number was > 10 and it was too much.  I tried a number line and anything above 10 is meltdown city.  We tried doing "which one is bigger" and it only works at numbers below 10.  I asked him to fill in the blanks like 22,23,24,__, 26, 27 etc.  Nope.  He can orally count to 29, then it gets spotty.  So now, we're practicing writing the numbers - 5 at a time, all the way to 100 - and then play a math/number game like Uno or something. 

 

Reading Practice - we started out reading Little Bear - the same story every day, and by the end of the week he could get most of it. He was actually memorizing it, which I didn't mind, but then he wasn't watching the page, and memorizing it wrong so not really practicing reading at all.  The few times i have tried to encourage him to use phonics to sound out a word, has resulted in meltdown.  Now, we read out of a Beginners Reader Bible book that I had as a kid, and I assign him one word to say when we get to it.  I try to add words from the previous days so he has to pay attention.  I do want to start doing phonics again, but I'm still thinking about a way to make it fun.  I have the 3 R's by Ruth Beechick - I think I might check that out again.  Also www.starfall.com has been good.

 

Writing - this is going really as I expected.  I'm still trying to decide whether it matters to make the letters in the correct order or not.  Not spelling, but the natural way of writing like the little arrows in handwriting books.  I can't really think of a good example.  I really have to cheer him on with a sentence more than 3 words - it looks like too much to him.  So we take it one letter at a time.  

 

Spelling was tortourus for both of us, so I scrapped it completely.

 

Bible, History, Science, Geography - most of these involve me reading a passage, answering his "why" questions throughout, and then afterward he tells me what we read about.  It is hit or miss, really.  The passages are getting shorter and shorter, and now that he knows the gist of what we're reading about, he just repeats that part every day - ex. "He wants to become a knight!.... uhm that's it"  Actually he does really well in Bible stories (and that's the one with no pictures at all - hm) but the rest are eh.  I try and coax it out of him, but when I see we're approaching frustration I just smile and say, "thank you, good job"  He seems to like reading the books, so, I'm not sure what we're going to do.  I think I need to re-think narration, or do some listening exercises or something.  I am sure this is ELL issues. 

 

Bible verse, poetry, and song memorization - going well.  He likes it, I like it.  We just stay on the same passage until he gets it.  Actually we're still on the same passages that we started with, but I think next week we'll move on.

 

Sign Language - he loves this.  We have no trouble doing this.  We need to work on manners around deaf people, but that will only come by doing, I guess. 

 

Art Appreciation.  With Charlotte Mason art, the child would look at an art piece for 10 minutes, and then the parent would take it away and the child would describe it.  I set our goal at 3 minutes.  After about 1 minute he's done.  So I think we'll continue with this, slowly working up the time.  The goal is to increase observation skills so we might also add one of those I Spy book things more often. 

 

All in all, this is not how I imagined.  If I see a system and really like it, I don't like to deviate, so this has been difficult.  We had a 'meeting' after a particularly bad day, listing what he liked and didn't, and he said he like most everything we did.  Under 'not like' he listed Little Bear, and Scary Movies (?).  Under 'maybe' he listed "Numbers, because it's hard but I have to try anyway"  that suprised me. 

And we plug on.

Not a bad leap of logic

Today Andrei wanted to write his name, and then he wanted to write Papa's name (Brent)
So the sheet said

ANDREI

BANDREI

lol pretty good

Let's look from a distance

So I thought we weren't going to do nature notebooks this year, and a perfect opportunity came right in our back yard. Andrei found the beginnings of a wasp's nest under our picnic table.

So I got out my nature notebook and Andrei got his and we both settled down and drew pictures and watched the wasps build their nest. I almost don't want to destroy it, but I also don't want a huge nest by my knees every time I go outside! :shiver: