Author Archives: Jason Chamberlain

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!


What is Five?: Foster a Flexible Understanding of Number

What an opportunity I have here at the AIMS Center!  We have been afforded the time and resources to read mountains of research about how children come to understand number, replicate that research, and then begin designing mathematical learning opportunities that help children along while eliciting their mathematical thinking.  After a period of reflection upon… Continue Reading

The (Math) Things Kids Say

Children’s thoughts about mathematics are reflections of their experiences (Steffe, von Glasersfeld, Richards, & Cobb, 1983). Let’s take a look: In the AIMS blog, there has been a good bit of talk about the “mathematics of children” (Steffe, 1991).  This covers a lot of ground.  When we talk about the way that children construct math… Continue Reading

Meet the Children Where They Are: Episode 4

Narrator:  “Although this series makes this interaction seem like a long period of time, it was actually only about 3 minutes…well, maybe 5!  Time flies when you’re having fun, okay?  Anyway, can Bob count two hidden piles of rocks?  Let’s get back to the action.” (Math research associate narrates…) RA:  So it was the bottom… Continue Reading

Meet the Children Where They Are: Episode 3

Narrator: “Last time on Meet the Children Where They Are: Has Mr. Unnamed nerdy-looking stereotypical math Research Associate (RA) found 5-year-old Bob’s zone of potential construction (ZPC)? Bob has counted 12 rocks and he came up with three different solutions.” (from title screen — video of construction site with concrete truck backing up) (fade to… Continue Reading

Meet the Children Where They Are: Episode 2

Narrator: “Last time on Meet the Children Where They Are: Mr. Unnamed nerdy-looking stereotypical math Research Associate (RA) is down in the mud getting ready to do some math with an unsuspecting 5-year-old child named Bob. Can he find Bob’s ZPC without damaging the child for life? Let’s head back to the construction site where… Continue Reading

Using Fingers to Build Number Sense

It has been a lot of fun to get back into the classroom during the last few weeks!  The Early Mathematics research associates have been interviewing students (3- and 4-year-olds) to see how they say the number word sequence, how they count objects, and how they subitize.  These were our initial interviews from which we… Continue Reading


Why? Why do you go to work daily? Why are you good at what you do? Why are you reading this mathematics blog? Why are students engaged in some math lessons and not others? Why do some students do well in school while some fall behind? I’m going to leave you, the reader, to answer… Continue Reading