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!
The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.—Common Core State Standards for Mathematics, p. 8 CSS.MP1 Make sense of problems and persevere… Continue Reading
Last week, our Early Math Team here at the AIMS Center partnered with Fresno EOC Head Start to spend a day devoted to children’s mathematics. I had the privilege of sharing a few thoughts at the beginning of the day to help shape our time and work together over the coming year. In this keynote,… Continue Reading
This blog post is the third in a series concerning technology in education stemming from the Jean Piaget Society Conference I attended in June. The theme of this year’s conference was “Technology and Human Development.” It provided a venue to discuss technology through a variety of different academic disciplines and research frames of reference all… Continue Reading
Chris Brownell flies solo this week, as he declares an end to Summer 2017. He reflects upon three events that he was involved in and what they have meant to him. The need for humility, and openness when it comes to learning was driven home this summer it seems. These qualities are implied in the… Continue Reading
If you were asked to describe the best professional learning experience you have ever had, what would you say? Would you say it fit your needs perfectly? Would you say you were provided with individualized considerations? Would you say you were able to take the experience and share it with your colleagues? Would you say… Continue Reading
Some of the most precious and meaningful memories I have from teaching kindergarten came from a classroom stuffed bear I called Mr. Teddy. He was part of six kindergarten classes. He would go home with a new student every Monday and return to class on Friday with a new story to tell that had been… Continue Reading
In my last post I wrote about one of my first experiences teaching math to second graders. At the time (way back in 1996!), the math adoption we were using was MathLand, which was very conceptually based. I had several teacher friends that were also educators comment that they loved MathLand and felt it really… Continue Reading
As I watched my children play at the park one day this summer, my attention quickly focused on a small voice saying, “one, two, three, four, five…” I looked over and observed a game of hide-and-seek in progress. Even my youngest is self-motivated to recite the number sequence more accurately when she is playing. This,… Continue Reading
Jason Chamberlain is a Research Associate who was working with the Early Math Team this past Spring. He talks with me about how he saw children progress through the earliest formal stages of counting and describes a game that this team developed to reflect these stages. His enthusiasm and passion for this process are abundant… Continue Reading