Yet as she begun to discuss the importance of making connections in terms of mathematical development and supporting number sense I realized how little training and exposure I've had to early math development.
If you asked me right now to write an entire paper on how children develop reading skills- starting from birth on- I could without looking at any references. But until today I could not come close to doing that for math. It shocked me a bit to realize how little I've read about early development of number sense.
Yet Galinsky discusses research that shows babies as young as five month show an understanding of basic mathematical principals and have a sense of magnitude.
Why is this the first time I'm hearing about this?
As the chapter goes on she discusses all the activities that can be done to support this developing early number sense and help children make the connections between their understanding of counting to identifying amounts with numerals.
Here's the thing- Over the years we've noticed that the children at the think-tank have trouble with number sense. This year in our end of year survey the staff asked for more help with teaching number sense. It's something that we've identified school-wide as an area of concern. When I worked with third graders who needed remediation in math a few years ago I was surprised at how their number sense hadn't seemed to improve from first grade (where I was used to working with children). They didn't seem to have any better understanding of number sense than they had two years earlier, they just knew how to do more things with numbers. Not having a strong number sense background certainly slowed them down in everything from fractions to multiplication.
Reading Galinsky's chapter makes me think that we need to re-examine how we teach number sense in the early grades. The importance of sorting, playing board games, and building on executive functioning skills like working memory, self-control and cognitive flexibly (180) can't be overlooked. In letting our end of quarter assessments drive our instruction we've been focused on the end and not the means. What we've been doing is great for getting kids to pass kindergarten assessments, but we're not getting them ready to go beyond that. If our kids are still counting on their fingers in order to add and subtract double, digit addition is about to make their lives really, really uncomfortable. We've skipped an essential step.
Galinsky lists activities that can be done with two year olds and older to help bolster their mathematical thinking and connection making. Many of these tasks are probably done in most middle and upper class households as daily games, simple sorting and playing activities. From my experience with the families I've worked with, few of these games and activities are being done in houses with families in poverty.
As teachers who are getting five year olds whose understanding of mathematics has been hindered by their limited exposure to these basic number-sense tasks we have a lot to make up for.
One of the tasks Galinsky writes about is a Reversed Categorization Task (179) where children are asked to sort one way (mommy's toys go here, baby's toys go here) and then switch it, asking the mommy toys to go where the baby toys went earlier. She states that this task requires three different types of executive function- working memory to remember the rules, self control to follow the rules, and cognitive flexibility to do the opposite of what's been done before. Those aren't simple tasks and all become better with practice.
I've seen five year olds who have trouble with tasks like this one. They are able to sort, but reversing the sort, or adding a twist to the sort creates complete confusion. One of the tasks we ask our kinders to do is to sort by color then using the same objects sort by shape, and then to sort by size. Even if our children can sort by color, shape, and size with separate objects, using the exact same objects to perform this task trips up most of our kids. It isn't that our children cannot sort, it is that they are struggling with their executive functioning skills.
We can't just teach sorting- we have to use it to support teaching these executive functioning skills that will carry with the students throughout their careers.
Activities Galinsky recommends to work on executive functions and number sense:
-Board games that involve counting each space and using a spinner or dice with numerals
-Sorting tasks that involve changing the rules of the sort
-Allowing children to make mistakes and recover for them
-Participating in guided play where the adult is not the boss of the activity but the participant
-Talk about numbers, quantities, and math frequently (calendar time, identifying shapes, putting math observations into daily conversations)
-Encourage children to make numerical predictions and then count to check themselves
-"Build on children's sense of approximate numbers" (195)
I'm not doing the chapter justice, so I highly recommend reading it yourself, particularly if you have a young child or teach younger children. I'm now fascinated by the research on how infants can appreciate number sense. As soon as Baby L wakes up from her nap she's about participate in all kinds of experiments. Poor girl...
Galinksy, E (2010) Mind in the Making: The seven essential life skills every child needs. William Morrow Publishers, New York, NY.