Posted in family life, learning together

## learning together: counting in binary

Limerick has been interested in different base systems for several months now; he’s enjoyed playing place value games in bases other than 10, converting between bases, counting in alternate bases, and so on.

The other day he came up to me and told me that he’d figured out a new way to count on his fingers. Holding up the pinky finger on one hand, he told me that was 1. Just the ring finger extended was 2; the ring and pinky together was 3. The middle finger on its own was 4, middle and pinky together was 5, middle and ring together was 6, and middle, ring and pinky all at once was 7.

It may be easier to see his logic with 0’s and 1’s, where a finger curled down represents a 0 and a finger extended represents a 1.

00000 00001 (one pinky extended)
00000 00010 (ring extended)
00000 00011 (pinky and ring extended)
00000 00100 (yeah, this one looks wrong, but he’s six so he has no clue)
00000 00101 (middle and pinky)
00000 00111 (middle, ring, and pinky)

And so on.

It’s binary! Assigning each finger one place in the binary place value system, he figured out how to count on his fingers to 1023 (which would be all fingers extended). In addition to showing how natural this aspect of mathematics is to him, it also shows a good foundational understanding of computer science – because electric signals are either on or off, just like Limerick’s fingers could either be extended or curled down, and therefore represent data in this same bitwise manner. It is so amazing what kids can think of and create when they are given the chance to deeply explore something they love.

(We tried developing a base 3 counting system but found it was too difficult to keep some fingers folded only halfway down when the fingers next to them needed to be extended or completely curled – someone with more fine motor control might have more luck though!)

Posted in family life, sqt

## {sqt} – finding community and playing board games

I’m linking up with This Ain’t the Lyceum again today for seven quick takes! I’ve had a bit of writer’s block this week and having a format laid out for me helps get the words flowing again 🙂

1. I’ve been feeling a lot more isolated lately. Rondel (and even Limerick) are older than the kids who show up to the weekly church playgroup, all of their friends from church are in school or therapy most of the time, and I’m having trouble finding a homeschool group that is relaxed enough to accommodate our family’s needs. I mean, field trips and classes aren’t going to help the boys make friends, and park days where the kids are expected to play away from the adults is going to be hard with the little kids (and Rondel’s tendency to zone out and lose track of where he is and how to find his way back to me). And honestly, I don’t need a whole group, just one or two families who can walk through life with us right now.
2. Sometimes I think our family falls into so many different/radical/tiny niche categories that I will never find anyone who really gets it on all levels. There’s the large “autism family” blanket – but oh wait, they don’t know how to handle an autistic parent, and they tend to support ABA therapies that are described as abusive by a lot of autistic adults who have experienced them (perks of an adult diagnosis here…). There’s the homeschool blanket – but we are using ESA funds from the state to help pay for speech therapy and curriculum, which puts us in a special legal category, and is apparently reason enough for several of the larger state groups to exclude us. And we’re Christian of course, but I’m uncomfortable in a lot of the Christian homeschooling circles (they can swing fundamentalist and Calvinist), and I want my kids to be exposed to the diversity of ideas and backgrounds that a secular group might offer – but I still want them to know (and hopefully believe) what I believe to be true about God. I could try to get all the pieces in different places but that is so much socializing and I don’t think I can handle that many people/groups/acquaintances!
3. Mostly I just want Rondel to find a best friend. He told me he would like to play more with other kids but he ends up just watching them and doing his own thing a lot of the time because he isn’t sure how to join in. And I don’t know how to help him 😦 I just sort of clung to my best friend through most of childhood and depended on her to navigate social events. So I keep hoping he will meet someone to be that kind of friend… if you are ever wanting to pray for our family, that would be at the top of my list right now.
4. In other news, we have been making more and more board games until they seem to be everywhere. We have number boards up to 100, 195, 223, and 550 (Limerick keeps requesting more and more numbers with smaller and smaller squares, but I think 550 is the limit even using our smallest game pieces). We have a traditional path-format board game with colored squares, a spiral snake with colored squares, a loop board game with the letters of the alphabet, and most recently a sting ray-shaped board with a colored path twisting along his body. My favorite game is called “LEGO Monsters” and we play it on path or spiral snake boards: each square gets one or two LEGO pieces of the same color as the square, and if a player’s piece lands on a square they get to collect the pieces and use them to build a monster. We all start with a head and eyes to make sure we aren’t missing those crucial elements, and we end up with some crazy creations! This game also has the advantage of removing the winning/losing element 🙂
5. While I may get tired of playing the board games all day long, I have to admit they were the cause of the least stressful visit we have ever had to the pediatrician. Usually the boys have a lot of trouble keeping their hands off of things, leaving the light on, staying quiet when the doctor is talking, and so on – but this time they each brought a board game and were able to play contentedly even though we had to wait quite a while (not due to any fault of the doctor; Aubade has a UTI and we had to wait for her to pee so they could test it). Even the doctor complimented them on how well they behaved, which is definitely a first at this office!
6. Another side effect of the board games is that Limerick is beginning to internalize a lot of the numbers and their relationships. He can do quite a bit of addition now without having to count to make sure, especially with numbers 1-6 (thank you dice) but also with larger numbers because of his number boards. It’s neat to see his understanding of the numbers deepen – when I watch him think about the sum of his three dice, for instance, or about what number he’ll be moving to after adding his roll to his current position, I can almost see him manipulating the numbers in his head, breaking them up and recombining them, becoming friends with them.
7. And finally, we have been counting. Counting and counting and counting. We drove to church and Rondel counted the whole time drive and all the way to Sunday School (he made it to 1025). We drove to speech therapy and Rondel almost cried when we asked him to take a break from counting for his appointment and pick up again afterwards (poor guy – it is hard to stop when you’re in the middle of something and going strong!). I’m not sure what he likes about it, since he isn’t nearly as in love with numbers as Limerick, but hey, he’s never going to forget those numbers now!

How has your week been? Do you have tips for making connections and building community? How about any favorite board games (non-competitive games in particular)?