When 1+1 doesn't equal 2!

I love math.  I always have.  I know that there is, however, a really large percentage of the population who does not share my feelings about this subject!  When I used to tell people that I was a teacher, the usual second question would come, "What do you teach?"  Upon answering "math," reactions quite frequently turned to revulsion from the person somehow reliving some sort of horrifying math education experiences.
Recently, some other local homeschoolers and I have been talking about the way we teach math.  For many kids, their aversion to math, quite frankly, has come from the way they are taught math.  I don't need my kids to be math geniuses or even share my love of the subject, but I do want them to be able to experience it as more than just a set of tasks to complete or skills to master.  I am one who cringes sometimes at the question, "When will we ever use this?"  To me, learning isn't just utilitarian; some things just help grow your mind, and I want my kids (in all areas) to love learning just for the joy of learning and not always needing it to be "for" something (a set of standards or exams or job preparation, etc.).

That is one of the joys I am finding and learning to embrace with homeschooling.  Sometimes I still get anxious about whether my son's measurable achievement is where it should be (or, if we're being honest, I usually get anxious about whether it is ABOVE where it should be), but when I'm able to let go of that and embrace the freedom we have in this season of life with homeschooling, I love the explorations and deeper learning that we are able to engage.

I had chosen a curriculum for math this year that seemed pretty good.  I wasn't too concerned about it being the "best" because it is a comfortable subject for me to teach and supplement.  But, as we started with the year, I found myself feeling pressured to use the book and felt really unsatisfied with the direction it was taking our math time.  In some attempts to balance, we are still pulling it out some, but I am now scrambling a bit to really put the effort and time and thought into teaching and exploring math the way I would like my son to experience it.  So, we're still getting our feet under us with some new routines, and I'm still working out a lot of it, but I'll try to post a few things as we try them.

Here is one of the first that I took pictures of.  I was inspired by this post from moebiusnoodles (and this follow-up one as well).  If you haven't ever been to that site, I cannot recommend it highly enough!  There is so much brilliance there to help rethink math education and to inspire math learning!
Anyway, there was a recommended picture book that we don't have access to, but I decided to go ahead and just do a simple activity without it.  The idea behind it is to see everyday objects as sets, or collections of objects.  To me, it engages the idea of addition beyond just an algorithm as well.  They have lots of great examples that people have submitted on there.  Being that my son is only 6, we were keeping it in a tangible mode, so I set out pairs of objects, one pair at a time to discuss them.

I started by setting out two Legos and asking him how many I had.  He said, obviously, two.  I said we are used to one plus one being two, right?  What if I told you that one plus one in this case is 10?  He looked at me with big eyes, and then he looked down and really quickly realized I was talking about the raised dots on the Lego pieces.  (In other words, one group plus one other group is equal to 10 individual parts, in this example.)

Here are a few more of the examples I set out for him.  I phrased the problem and asked him to guess what I was actually adding.

One "Tank" plus one "Conductor is 6 (legs).

One turtle plus one dragonfly is 10 (again, legs).

One "Mater" plus one "King" is 8 (wheels).

He was guessing so quickly, and when I set this one out he shouted, "Nine."  It was interesting because I had been thinking of it in terms of legs, so I had thought of it as 8 and 0, but he thought of it as "long, skinny parts," so 9 totally made sense. 

I then asked him if he could think of anything else we could add like that to make problems where 1 plus 1 doesn't equal 2!  He abruptly said, "Get up, please!"  I was caught a little off-guard, but he grabbed my chair and his and said one chair and one chair is 8 (chair legs)!

Ok, now this might be my very favorite one!  He was sort of working it through in his mind and trying to think how to frame it, but he recently got this little Lego Star Wars planet that splits in half.  He had grabbed it, and I ended up helping him figure out how to describe what he was actually adding, but in this case, one plus one EQUALS ONE!  (One half of a planet plus one half of a planet is one planet.)  Ah!  Seriously, made my little mommy math nerd heart skip a beat! Ha.

He started to get excited and silly and lose a little bit of focus on the set concept.  He said, "One boy and one planet is two things!  One boy and four chairs is 5 things!"  I kind of just let him roll with it for a few minutes because, even though it wasn't exactly on the track we had been rolling on, he was still adding things, so WIN!

We worked together to come up with a couple more.  

One box and one notebook is nine (pictures of Lego minifigures).

One clock and one clock is 24.  He asked, "Oh, are you talking about the numbers on them?!"  That was cool because he certainly can't mentally add numbers up to 24 yet, but he was just expanding things conceptually.  So, while it may seem playful, can you see the potential for some really rich math stuff (even beyond the intended concept)?!

Stop Ruining My Plans with Those Great Books

As I've mentioned many a time, I plan.  And, most times, I overplan.  I'm good at adjusting plans and building plans that fit my unique kids, but my strength is not being adaptable in the moment.  Master of Spontaneity, I am not.  My friend once teased me about it, and I said, "I can be spontaneous...as long as I plan to do it."  It actually made sense in my head.

Anyway, recently, my son has totally just bulldozed some of my plans with his darn curiosity and love of a good story!  I adore the Chronicles of Narnia, but I thought he might still be just a tad young for them.  (Sidenote:  One of the challenges I've had in the past reading them to kids in the States was the British English--lots of unfamiliar terms and phrases for things.  Seeing as how Isaiah is around quite a few Brits here, and most often printings of English books we buy or borrow from a school library here are UK printings, so that has actually been not very difficult at all.)
So, I had planned them to be our end of the curriculum year/summer/fun multi-disciplinary unit for next June.  It's written very clearly in my planner, and I was very much looking forward to it.

About a month ago, when we were at the children's home we've been visiting weekly, Isaiah went downstairs with the kids.  I thought they went down to play, but I found him with them watching Prince Caspian (the Hollywood version...in Hindi, mind you).  Given that they seemed to have turned it on right before the huge battle scene (and we would have been very unlikely to have let him watch it), his eyes were as wide as saucers.  On the way home, he started rattling off questions about it.  Well, I certainly couldn't let that Hollywood flick be his sole impression of Narnia!  So, I told him about the books, and he begged to read them.  I was hesitant (hadn't he realized they were not on the calendar for 10 more months?!), but we started The Lion, the Witch, and the Wardrobe, and I half expected that he'd still not quite be ready for them, but he could not get enough of it and would have gladly sat straight through reading them, one after another, if I had let him.  Inside, I kind of panicked!  I wasn't prepared with any of the wonderful activities I wanted to do with the books!  This was supposed to be our whole plan for next June (because, you know how kids hate to read beloved books more than once!).  I had other books planned for us to read.

Thankfully, I was able to reign in my type-A crazies and have thoroughly enjoyed reading these books with Isaiah!  They are such wonderful stories.  How on earth could I ever think this was a problem to have a kid who can't get enough reading and can't tear himself away from a great story?  How could I honestly think it's a problem as I watch his vocabulary expanding and his imagination inspired and stretched?

It is not always an easy part for the personality, but this is one of the true joys of homeschooling--I can let my boys DELIGHT in learning and watch them gleefully engage with books that capture their hearts and minds.  I've even done some fast thinking and pulled out some fun activities to go along with our stories (which I'll share in other posts), much to the further delight of Isaiah.  We are having fun.  With books.  Some of our other stuff got set aside a bit for awhile.  Independent quiet times have turned into reading marathons while little brother is less likely to interrupt.  And, once I finally let go of my precious agenda, I've have had SO much fun with little bookworm, as we've been swept away together into the magical world of Narnia!

My little Narnian Kings, ready for battle