Throwing Marshmallows

This article in Scientific American got my attention when I was  searching to see if Scientific American has a kids magazine (I can’t seem to find one…anyone know?)

Seems that they have done a study that shows that “young children can crudely add and subtract numbers before they have learned the rules of arithmetic”:

To find out, they gave several groups of children a laptop-based audiovisual test that asked whether one person had more or fewer candies or other objects than another person. The screen showed numbers to be added, such as 21 and 30, or subtracted, such as 64 and 13, followed by another number, such as 34, with which to compare the added or subtracted value.

The children answered correctly from 64 to 73 percent of the time, according to a report published online today by Nature.

Looks like kids without formal instruction in arithmetic can still have a basic understanding of it. My favorite quote from the article was from cognitive psychologist Elizabeth Spelke of Harvard University:

“We never dreamed that you could simply give children the symbols and they will succeed,” she says.

And my second favorite quote:

Teachers were skeptical of the experiment because arithmetic lessons easily frustrate children, but “the kids really loved these problems,” she says. “It looks to us like a big part of the logic of addition and subtraction is already available to them.”

Veeery interesting….I wonder if half the enjoyment was at being asked to try to figure it out for themselves rather then being told how to do it?

~Stephanie

Nope, not the “deadly sin” greed. The dice game Greed! Julie on the Living Math email list (which is an awesome resource for teaching math) forwarded this link to Greed and the boys and I have been having fun playing.

In a nutshell, you have 10 dice. You roll the dice and see what you score. You then have the option to roll again and try to score additional points…the risk however is that if you do not score, then you loose all your points for that turn. So you need to decide if you are going to keep the points you gained on that round or risk them all.

The boys have decided that it is basically “Deal or No Deal” with dice. Funny how much they got a kick out of that aspect of it.

Just thought that I would pass on a fun way to get familiar with how probability works. And just an all around fun game too. Oh and I have to gloat as well that I won the game today! So there!
~Stephanie

I found LivingMath.net at the beginning of this year and have found it to be an absolutely wonderful math resource. From the website:

I want to build a bridge. I’d like to close the gap between math and history, science, literature and humanity created by the isolated way we traditionally approach math education.

In teaching my own children, tutoring and furthering my own self education, I’ve found that math history and literature humanizes math, makes it come alive, and provides the context needed to enjoy and retain learning. Early exposure to real mathematics in real settings without requiring mastery of arithmetic on a set timetable has been a key to the incredible ease my kids have attained mastery when the time is right for them.

The website is chock full of ideas for different ways to approach math and the related email list is a wonderful place to ask questions and get lots of feedback about all sorts of ways to approach math. You will find lots of ways to approach math from a hands-on, holistic pov in addition to lots of discussions about all sorts of different math curricula. I love the mix and it works great with our approach this year of focusing on different math concepts and pulling in a variety of resources.

I especially like her ideas on approaching math from a history and literature perspective. This approach has worked really well with Jason so far…he really likes the Penrose, the Mathematical Cat books and The Number Devil which have been great at exposing him to a variety of math concepts. Reading about them and getting familiar with the concepts will help as we get more and more into them. He seems really drawn to certain concepts like Fibonacci numbers. We have also been reading a bit about the mathematicians themselves and that has given an added dimension to our learning (I personally have been enjoying this aspect as well as I love history!)
I have found that a lot of the folks on the LivingMath.net email list have right-brained/visual-learners. Which makes sense, I think, as we tend to have very non-traditional learners and are always on the look out for new and creative ways to approach math!

Definitely check it out. The website could take you a little while to work through as there are tons of great ideas and especially book recommendations and reviews.

Enjoy!

~Stephanie

Things are still moving along. I am trying to squeeze in enough time to do everything that I want to…not enough hours in the day. We seem to be back on track as far as not being quite so over scheduled. The boys are really enjoying their pottery class and have been making some really neat stuff. Jason has started playing around a bit more with the modeling clay that we have here at home too. He seems to have more patience with it then other art activities.

We have started using Sequential Spelling to help Jason with his spelling. It is not something that he really loves, but he also does admit that his spelling needs a lot of help. Sequential spelling is great for him because it focuses on word patterns rather then straight memorization. It is also not phonics based. Being a right brained learner, learning by seeing the patterns is definitely a better approach. The other nice thing is that there really is no “studying”. We spend a little bit of time most days…I give him the words to spell and correct him immediately if he does not get it right. We talk a little bit about the patterns and rules. Sometimes I wonder (being a phonics gal myself) if this can really work, but he is picking it up. And it seems to make sense to him (which is the important thing).

For math, I have decided instead of completely following one “math curriculum” I will focus on different math concepts and bring in various resources. Right now we are focusing on fractions. We are starting with Key to Fractions which he actually seems to be enjoying. I like the materials too…very easy for him to understand and follow. Again we do spend a short amount of time on it, but he is picking it up very quickly. I also plan to bring in some fraction ideas from Marilyn Burns and other resources. Jason says that he likes fractions much better then multiplication and division. Not surprising. I still work with him some on memorizing his math facts, but I think these will come as he uses them more and more. We are also enjoying reading Murderous Maths and I just picked up some of the Theoni Pappas books that Jason really enjoys. So we are talking/reading a lot about a lot of different math concepts. I have found for Jason that the key is to keep mixing things up and providing variety which he enjoys.

Jason has also been working a little bit out of the Handwriting Without Tears cursive book. Cursive seems to be coming more easily then printing (although his printing is getting better…still not all that great, but better).

Jason’s reading still amazes me. Considering he was “late” (around 8 yo) when he started, you would never know it. He reads mostly for information (catalogs, video game cheats, magazines etc) and I have caught him reading some pretty impressive words. He still is not into reading overly word intensive books (he says that when he reads, he has a harder time “seeing” the story) but he really enjoys comics like The Far Side and Calvin and Hobbes. He seems to also enjoy reading poetry…I think that he likes the cadence in addition to there not being as many words. It is nice now and again to find him sitting on the couch reading…it is all a matter of finding the right book. We also do a lot of audio books as well as Jeff and myself reading to him.

Kyle and I have started doing 100EZ Lessons again. I will need to write another longer post about that because it has been really interesting. We had started doing 100 EZ Lessons last year, and although he enjoyed it, I could tell that it was not clicking for him. So I decided to give him some more time and we stopped the “formal” lessons and just read and played a lot. Fast forward to this year and it is amazing the difference that a little bit of time has made. He definitely is getting it. And getting it pretty easily. I am glad that we did not push it before.

For math, Kyle and I play lots of math games (he still really likes the dice game Pig) and do some work out of his Singapore math book (which he also likes). Can I say that it is actually pretty cool to have a kid who understands my math explanations? (With Jason, I always have to look for other ways to explain math concepts because we think so differently! And while I love this about Jason, it is also nice sometimes to have a kid who understands what I am trying to explain!)

The only thing that Kyle really does not like to do is writing. But he is still pretty young so I am not pushing it. And he does not seem to have the same issues that Jason did at this age. Kyle has a good pencil grip and is pretty good at making his letters. He also likes doing mazes and has started wanting write down his answers when he does math. So for now, I think he is doing fine.

Hmmm…we don’t really sound very “unschooly” lately, but really the above does not take up a huge amount of time and it has come about from seeing what my kids need and working on finding resources that work for them. And it works. Kyle is pretty easy…he reminds me to do his reading and enjoys math workbooks and maze books and the like. And while Jason does not ask to do his math, writing or spelling, he also does not fight me when I say it is time to do them. And when he is working on them, I can tell that he is learning and getting something out of it. Definitely a good experience…and it works because he knows that he does want to learn these things, even if he does not always want to do the work involved. Which is where I come in to remind him and work with him on it. And he sees the results.

I think that this is what Cindy means when she talks about collaborative learning. It is not totally child-led, but it is totally based on the needs of the child. It is not “no structure” but it is structure where it makes sense to have structure. And it feels like the right balance (for now) for us.

And as usual it is getting late and I am getting rambly. So I will say good night for now.

~Stephanie

I love card games. And we discovered a new one this week: Begger Your Neighbor. I had picked up The Book of Cards for Kids card game book at Fun Books while at the VaHomeschoolers Conference and we have been learning lots of new card games out of it. I think that I enjoy it because it is easy to pick up and explain and there is a good element of surprise to it. I also came back from about 1 card left to actually beat Kyle once!

I have several card game books (including one that was my Mom’s when she was a girl). I don’t know what it is about cards but I have always enjoyed playing them. The boys have learned that this is my weakness.

Jason has asked about learning Texas Hold-Em…so I guess that is my next one to learn. And we need to get some poker chips…

~Stephanie

Tags: card games

What did I just say? Yes, we watched a really fun math documentary today. I guess that is what you would call it. The title of the DVD is The Story of 1 (and it is available through Netflix). All about, you guessed it, the history of the number 1. Pretty cool stuff actually. How people started counting using lines on sticks which then progressed to using tokens and the development of math. Takes you from the Sumerians, to the Greeks, to the Romans, the Indians (who invented Arabic numerals we use today and the number 0), and continues on until the importance of binary numbers today. Throws in a bit about Pythagoras, Fibonacci and other important mathematicians. Talks about just why 1 and 0 are so important. (I know that I personally had never given it much thought!)

And they do it in a really fun way…hard to really explain, but it had Jason (9 years old) laughing out loud (always a good thing!) Kyle (6 years old) did not enjoy it as much…found some of it boring. Mainly because much of it went over his head. He did laugh at certain parts and I am sure that he got something out of it. But I could see the connections going off in Jason head as he watched it. At one point when Kyle was complaining about a boring part, Jason told him to be quiet because he really liked it and it was not boring!

When we finished watching it, Jason went back to certain parts to watch them over again. I have noticed that while Jason does not like doing “arithmetic” he actually does grasp (and enjoy!) math concepts very quickly. He also really seems to enjoy the historical aspect of math. We read The Number Devil several months ago (still need to review it here!) and he really liked it and I had a feeling that he would like this as well. They had a similar feel…irreverent and focusing more on math concepts then math facts.

I also want to check out a book called Mathematicians are People Too which sounds like fun. I personally love history and Jason seems to be enjoying the math history that we have done. I love being able to tie everything in together…and it really is the way that Jason learns best. He needs to have some context and interest in what he is learning. I have also heard good things about the Theoni Pappas books like The Adventures of Penrose the Mathematical Cat.

I have to admit that this stuff is as much fun for me as it is for the boys! I know that I am learning tons and I love that I get to learn right along with them. Homeschooling at its’ best.

~Stephanie

The boys and I were playing Cinq-o today which was a lot of fun and reassured me that Jason’s adding and multiplication facts are still progressing. Jason was leading at first with me really far behind. Then I got a great score and the tables were turned. Kyle wound up winning, we me coming in second and Jason third.

After the game, Jason was asking me why he always seemed to loose at dice and card games. We talked a bit about how he did not always loose, but how it could seem that way. And how with most card and dice games it was all about luck. There usually was very little skill involved.

Jason said that he much prefered board games like Risk and card games like Magic and Yu-Gi-Oh, which after thinking about it, makes perfect sense. He has more control over these games…there is some element of luck in the games (dice rolls and draws of a card) but there is also a lot of strategy in them.  Same with his video games. He can practice and work at it and get better/faster/smarter. He can improve his game and work towards winning. In a game like Cinq-o it is all about luck. Luck of the roll or luck of the draw.

Funny thing is that I prefer card games and dice games rather then complex strategy games. I like how the playing field is level…younger players have the same chance as older of winning. I also don’t have to work quite so hard…I don’t have to think 5 plays ahead. They are more straightforward and thus more fun for me.

I am sure that there is a right-brained/left-brained parallel in there…actually it does make sense from that point-of-view. Dice games and card games are more sequential. More straight forward. Strategy games (including video games) require you to see the whole picture…to take into consideration many variables and to see how a move you make now affects the play down the road.

I think that strategy games also play to a right-brained learners’ sense of fairness…after all, if you work harder you will become better and that is only fair. With games of luck, there is no rhyme or reason to who wins really…which is very frustrating to Jason! Mainly because he is just as likely to loose as he is to win. And of course at this point in time, winning is everything. (Although I will say he is much better at loosing now…no getting upset or mad. He just started loosing interest towards the end of the game when he thought he had no chance to win. But he did not ask to stop playing! Big improvement!)

~Steph

This is a recreation of the post I lost the other night…I had the boys re-tell their stories, which they thoroughly enjoyed. The idea was to record some of the small snippets of learning that happened throughout the day. These kind of exchanges happen all the time and help reassure me that the boys are learning constantly.

Kyle and Math

As we were getting ready to go to the Nova Unschoolers park day (why do they always do this when we are trying to get somewhere?) I had this conversation with Kyle:

Kyle: 5 is not an equal number, is it?
Me: (guessing because I am not sure exactly what he is talking about) Do you mean, even?
Kyle: Yeah
Me: You’re right. 5 is not an even number.
Kyle: What is an even number?
Me: It is a number that can be evenly divided by 2 (or in half) with nothing left over.
Kyle: You mean like 20? 
Me: Yes, just like 20.

And then I grabbed some pennies and showed him how if you lined the pennies up in 2 columns, the even numbers lined up evenly and the odd numbers had an “odd” penny left over. Since then he has occasionally come up and verified if various numbers are even or odd.

Jason and Government

We are currently listening to the Children of the Lamp series and really enjoying it. One of the story lines led to a great discussion of the difference between a president and a judge and how our government is set up (three branches, checks and balances etc). Don’t ask how we actually got there, but we did! And Jason was really interested.

Storytelling

I have to remember to do this more often as both boys really enjoy it and it is good practice at organizing one’s thought. Jason seems to really go for subtleness…he put a bit of thought into his stories and really choose the words carefully believe it or not. He also wanted to play around with the capitalization of the letters. We have been talking about what gets capitalized and what does not lately. He remembered in one of his books seeing the capital letters all over the place and wanted to see what that would look like. He decided that it made it harder to read, but he still liked it.

Once you get Kyle’s mind going, you can’t stop him. He actually had about 6 different variations of this story that he wanted to tell. I had to stop him after 3 as we had to get going.

One of the hardest things is to stop Jason from editing Kyle’s stories. He is always giving plot suggestions and correcting Kyle’s verb tenses. I have to remind him that this is Kyle’s story and it is up to him to decide how it goes.

A Short and Dumb Story
by Jason 

OnCe UPoN a TiMe ThErE wAs a GuY. He gOt SquIsHeD By a bOuLdeR.
THe EnD

A Little Bit of a Longer Short and Dumb Story
by Jason

Once upon a time there was a guy. He looked up and saw a boulder. It squished him.
The End.

Rock
by Kyle 

Once upon a time, there was a rock.
The End

Run Away from Big Boulder with Eyes
by Kyle

Once upon a time, there was a guy. He saw a big boulder with eyes. The man saw the boulder going after him. The man turned. The rock turned. And then the man was so tired that he hide behind a bush. Since the boulder was so big, he could see the man. And then the boulder squished the man.
The End.

Run Away from Rock with Eyes
by Kyle

Once upon time, there was a rock. A man saw the rock that had eyes. The man runned and the rock ran after the man. And then the man turned and then the rock turned. And then the man was tired. So he hid behind a bush. Since the rock was so thin he couldn’t see the man behind the bushes. Then the rock keep on running. Then the man hopped on the rock and then the rock felt the man on his back. And then the rock flipped over and squished the man.
The End.

Every so often a discussion comes up on one of my homeschool email list about things that kids must learn. I find these discussions very interesting. Recently, on Homeschooling Creatively, talk turned to the learning of multiplication tables. One mom wrote “I think those tables are pretty darn important. You just can’t get through the math without knowing them.” I thought about this a little bit and on the surface it seemed to make a lot of sense. After all, much of higher math depends on knowing your times tables.

But then I started thinking…but what if you can get by? It is challenging assumptions like this that has helped free my thinking so that I can look at what might work best for Jason. If I think that a skill is critical and must be learned, then we are stuck and can not move forward, when moving forward might be just what we need to do. What if moving forward actually gives him the reason to learn the critical skill? Or what if putting it aside lets him have the time to mature to where he can grasp it?

Right brained kids definitely need to see the why, the whole part, where they are going…so maybe Jason will find the motivation to learn multiplication when he wants to determine the area of something (or wants to know how much money I owe him for 10 weeks of overdue allowances). Or like my friend’s son when he realized that multiplication was way faster then adding to figure things out.

For me, letting go of things that my kids must learn is critical. When I realized that if all else failed, Jason could always use a calculator to do his math facts when he got older, it let me relax. I don’t feel as much pressure to “get him to learn”. This allows me to take the time to look for ways that make sense to him and let him learn it on his schedule.

Does this mean that I think that multiplication facts aren’t important? No. Knowing them definitely (in my mind) makes a lot of things easier. And we do work on them. I just try not to stress over how fast he is learning them and we do not make learning them our sole focus in math. He definitely understands the concept which in my mind is much more important then being able to spout off a memorized answer.

Realizing that if he never learned them, he could still manage to have a productive, successful life has let me back off and give him the space and time that he needs. I have to trust that he will pick them up over time. He still does not really know all his addition facts either and still needs to calculate what 6+7 or 8+5 is (he does this by figuring out that 6+4=10, 7-4=3 and 10+3=13, and he does this pretty danged fast - pretty neat for this left-brained girl!) But I have seen these too gradually come easier and easier for him.

A friend of mine just shared her son’s reading story on a local list. He has CAPD and she tried just about every known reading program including individual tutoring. At 12 (!) he still could not read. At that point, she decided that if he never learned to read that would be ok with her and she backed off trying to teach him. She just started focusing on his strengths and would read whatever he needed read. 6 months later, he picked up a manga book and read it cover to cover. Then he read the instruction manual for a video game he was really into. Now at 14 you would never know that he was not reading 2 years ago.

This set off a storm of posts about how can you say that it is ok if he never learned to read! How can you survive in this world if you can’t read! I think that they missed the point of her story. She was not saying that a parent should not help their child to read if they need help. She was not saying that she did not want her child to ever learn to read and that not being able to read is a good thing. She was saying that no matter what a parent does, if the child is not ready, that child will not be able to read. The child has to be ready. And I would add to that, a child needs to get information in a way that makes sense to him/her.

The biggest thing that I get from her story (and something I try to always keep in mind) is that sometimes you have to let go and trust that your child will learn what they need to learn.

~Steph

Also published in Unschooling Voices #1. 

Before bed this evening, Kyle wanted to tell me something. He said that he figured out what 90+20 was. He then preceeded to explain to me that he first realized that 90+10=100. And 20-10=10. And 100+10=110. Therefore 90+20=110. He was very proud of himself for figuring it out.

Since things have been so busy lately, I had been feeling guilty for not doing more math with him. (He is a strange boy and actually enjoys workbooks!) But it has not held him back…I noticed today when we were trying to kill some time by playing Pig* that Kyle was starting to be able to add the higher numbers. Pretty cool. I love watching natural learning at work.

* To play Pig, roll two dice, add them together and the first one to 100 wins. To make it more interesting, if you roll a 1, you get no points. If you roll double 1 you loose all of your points - Kyle loves it! (And no, I don’t know why it is called Pig!) But it is much more fun then drilling and flash cards that is for sure. We found the game in The I Hate Mathematics Book by Marilyn Burns. I now carry a pair of dice with me so we always have something to play.

~Steph

Still have a major cough and not as much energy, but starting to feel a bit more normal. We had a fun, relaxed day where things just sort of flowed very nicely. We got up and moving this morning and went to Jason’s OT. He enjoyed it and is working on something from there for me for mother’s day, but it is a secret. After that we came home and did a few miscellaneous things.

One thing that we found was a fun tangram website. Jason was way better at this then I was! We played it as a family and between the three of us got pretty good.

After that we decided to go and explore a new-to-us park. I had heard there was one really close by, but had never gone to check it out (don’t ask me why!) Had a really good time…there was a small creek and a path into the woods that we explored a bit. The boys rode their scooters a bit and chased each other all over.

After we got home, we read a bit more from the This Book is About Time by Marilyn Burns and learned about time zones, the international date line as well as the earlier clocks like the sundial and water clocks. The boys really want to make a water clock so I just need to try to round up a few things so we can give it a shot.

We finished up the day with the boys building with their legos and me actually cleaning out our closet. You can actually walk into it now! Definitely an improvement.

The nice thing about the day was that I actually felt like doing things…it has been a couple of days since I have been overly motivated. Colds do have a habit of doing that though, don’t they? And there never seems to be a good time to get a cold…hmmm…I am trying picture what that would look like! A time when lying around in bed all day would be fine, a time when there is nothing else going on, nothing that needs to be done. Do times like those exist? I guess not. If they do, I may need to try to find it…preferably when I am not sick!

~Steph

I am constantly learning lessons during this homeschooling journey we are on (probably more so then the boys!). Often I end up re-learning those lessons many times. But it is good to get a reminder every once in awhile. Really good.

A couple of days ago, the boys decided that it was time to go toy shopping. Between Jason’s birthday, Christmas and over two months of untouched allowances, they each had a bit of money burning their pockets and I had been putting them off for awhile. My only condition was that Jason needed to figure out how much money he had to spend.

Some background…a few years ago I started acting as bank for the boys, mainly because we tend to forget to give them their allowances. This way we have a written record of when we give them their allowance. When they get Christmas or Birthday money they can either keep it in their banks or “deposit” it with me. Then if they are out and want to spend their money, we deduct it from their “account” when we get home.

It had been a while since we had updated their balance, so we needed to add in Christmas money, Birthday money, 10 weeks of allowance (!) as well as deduct for money spent on snacks after swimming and few miscellaneous purchases.

I have to say that I was duly impressed. Jason did adding and subtracting (much of it involving carrying) in his head without missing a beat. No hemming, no “I can’t do this”, no “this is too hard”. He just did it. Because it was real and it would give him an answer to something that he really wanted to know. And that is the lesson that I need to remember.

Jason has a love/hate relationship with math. He is very instinctual and can completely get math concepts but he HATES remembering math facts. My challenge has been to balance these two sides. As he gets better at remembering the math facts, he gets more confidant at figuring things out on his own. But he does need a push now and then. So we do “do math” but not tons of drill and I try to throw in enough “fun math” (he likes the Marilyn Burns books like The I Hate Mathematics Book which focus more on the fun math concepts).

Now that we have started multiplication, we have been having lots of conversations about not seeing why he needs to know math. Part of this I realize is that I tended to do most of the everyday math for him. The idea being that he would see how I used math and start wanting to do it on his own (please don’t laugh…it is working great this way for Kyle! He is constantly telling me to stop so he can figure out things on his own.) But Jason has no problem with letting people do things for him…not because he is lazy, but because he is a perfectionist. If someone can do something easier/better/faster then he can he prefers to let that person do it.

So I now make a point of letting him do the everyday math we come across. It has become a running joke between us and I think that he is seeing that there is a point in knowing his math facts. In fact I think that I scored some points when we talked about how mulitplication would have been a much faster way of calculating how much allowance he was due (he manually added up his allowance 10 times rather then multiplying by 10).

But it is times like these where he does math pretty much effortlessly that help ease my worries that math computation will never be easy for him. It will be. I know that. I just have to remember it. And if all else fails he can use a calculator….

Also published in the 4th Homeschooling Country Fair.

Also published on Life Without School.

OK…So being a right brained learner, Jason is not good with rote memorization. It just is not one of his strengths and it frustrates him. So I have been looking for ways to help him with his math facts. He does fine with the smaller numbers (e.g., 2+4, 5-3 etc) but gets stuck with the higher numbers (e.g., 8+7, 14-6 etc). He has no problem understanding math concepts (like adding/subtracting negative numbers) but when it comes to remembering his math facts he struggles. We have continued on with math, but not knowing these facts slows him down and also has started him thinking that he is “bad” at math. I tried showing him different ways to figure them out, including grouping by 10s (e.g., figuring out 14+7 by adding 3+7 to get 10 and then adding 10+11 to get 21), but nothing seemed to really stick. I had just gotten the Home Educator’s Guide for the Singapore Math program that we have been using and one of the first things that it had was an overview of the many different ways of adding/subtracting (counting up, number line, grouping to ten etc). I figured that it could not hurt, so I showed Jason…not sure what it was (probably that they broke it down somehow more graphically) but it clicked. He totally gets it now. It is so cool…instead of looking at a problem and trying to guess what the answer is, he has a method he can use to figure it out. What is great about this approach is that it utilizes his strengths (puzzle solving and logic) rather then his weakness, memorization.

For example…to figure out 14-8 he subtracts 8-4 to get 4 and then subtracts 10-4 to get 6. I will have to ask him for more examples, because I can’t really remember how he does half of it. LOL! But what counts is he knows! Basically he breaks the equation down into smaller equations that he can do easier. And he is completely able to follow it. There have been a time or two when I really could not follow what exactly he was doing (he still talks out loud as he figures it) but I kept quiet and he came up with the right answer.

I found previously that a similar approach worked when it came to adding double and triple digit numbers. Breaking things down into 10s and 1s really helped. For example, to add 34+55, he breaks it down into 30+50 and 4+5 to get 89. And we actually realized that he understands negative numbers because he would solve a problem like 54-26 as 50-20 and 4-6 to get 30-2 or 28.

The neat thing is that I can see that the light is back on…he sees that he can do this stuff now. He sees it more as a puzzle then this mysterious thing where he was just supposed to know/remember the answer. I can see him manipulating the numbers in his head and he is getting getting faster at it each day.

I have to say…I am not big on formal “curriculum” but Singapore Math has really been a wonderful resource for us. It is really great for explaining concepts to him in a way that he understands. One of the reasons that it works for Jason is that it is very visual…it starts with the “real life” concept…pictures of objects and talks in English about combining them (they call them number stories). It shows several different ways of figuring out an answer and then gradually introduces the symbolic notation. It also seems to be able to explain things in a way that makes sense to him much better then I can! I swear, when it comes to math, we speak two totally different languages and Singapore seems to be able to bridge the gap. I know that I learned this stuff by rote memorization (which luckily I am good at, but even now I still count on my fingers periodically to double check myself). I am so glad to learn that there is a way besides flash cards to figure this stuff out.

And actually I have been starting to use some of these “tricks” myself lately instead of using my fingers….