# Building the Mathematical Mind

Watching a young child’s mathematical knowledge grow is analogous to watching a house being built.

When I was in my teens, my dad, along with my brother and I,  BlogAugPt2 BlogAugPt1built our new home. I remember the exciting days of noticeable growth, such as when we poured the concrete slab, framed the walls, or put the roofing on. I also recall days of monotony and lack of evident progress, at least from my point-of-view. Really, though, there were a lot of essential things happening during those not-so-glamorous days: digging footings for the foundation, plumbing, wiring, fire blocking, etc. These were the underpinnings for a strong, safe, efficient home, yet being so close to the daily construction process, it was hard for me to appreciate a difference.

As teachers, we have those electrifying moments when we can say students have made marked progress. We also have the periods of time when we wonder if we are making a difference at all.

Reflecting on the past year -my time in the classroom, the research readings I have discovered, and the qualitative data our team has gathered- I would certainly say that we were able to provide children with the opportunities to make exciting growth in number sense. Even though we had days that left us wondering if we were on the right track, retrospective analysis makes clear the overall growth made possible by some of the less obvious construction going on in all of those young minds.

During review, I came across some video of this little guy. You will notice he began the school year (September 2016) with very little awareness of quantity or subitizing accuracy. Take a look.

As you can see, he couldn’t tell us how many dots there were when we showed him three. Some parents or educators freak out and speak of developmental delays or dyscalculia. But neither of those things were true in this case. He just needed opportunities. Opportunities to count lots of different things, opportunities to guess (yes, guess) and eventually estimate the quantities of items before counting, and most of all, goals he set for himself.

We found that by letting this child take the lead, he would set goals for himself that we would tweak just a little (mathematize). For instance, he loved board games, so why not let him play a lot of board games? His goals eventually found a nice intersection with our mathematical goals for him. Soon, he had his own set of mathematical goals. Kids love math if they can be in the driver’s seat. Watch what happened at our last interview with him in May 2017. The same child that couldn’t tell us that there were three dots on a card was now counting two sets of imaginary cookies!

And just like that, even though we were in a busy classroom with a whole bunch of preschool children, they were each building their own mathematical house. For this child, the mental groundwork has been laid, the footings and foundation poured. Now he’s ready for kindergarten!