Things are really hopping around the AIMS Center. Everyday becomes better than the last. I wake up and I’m challenged and excited by what I get to do during the day. As most people know, we really want to find a way to share what research tells us about children’s construction of number with classroom teachers here in our valley. At first I thought that sounded like a reasonably basic idea. Every day I realize just how awesome that charge is. Now that I have worked here a couple of years, I am able to reflect on my time here and make some sense of the work we’ve accomplished and the work we have yet to do.
The first year and a half we were all about reading and learning the research we chose to translate for classroom use. Reading it was not as simple as I thought it would be. It took talking with others, acting out some of the examples, and working with real children to understand what it was that the authors were describing. Working with children helped me to see that the children of our valley react in the same way that the researchers described they would.
Now that we have a reasonable expectation as to how the children will react, we have to be familiar enough with the research that we can “walk around in it”. We needed to be able to apply it to any child, in any classroom, at any time. We wanted to move away from a script and be able to engage children and adapt our teaching to their needs. We did this with small groups outside of the classroom first and then went into classrooms and began working with entire classes of children who rotated through math “centers.” In order to work with a classroom full of children, we needed some kind of engaging activities or tasks. We wanted those to be flexible so that they can be adapted for each individual child. We wanted them to look uniform across the room so that no child felts singled out, behind, or ahead. We wanted the tasks to be easy for the children to use and easy for the teacher to prepare and use with students. Most importantly, the goal of the tasks is to be the medium by which we learn about and foster the child’s number sequence rather than the task itself being some kind of goal. This is what my teams continues to spend most of their time working on.
It makes sense that we needed to learn the research around a child’s construction of number so that we could leverage that knowledge to adapt the lesson with any given child, on any given day. Our next goal is to learn how teachers come to know about children’s construction of number. There’s less research about this. We want to adapt our translation to the needs of each teacher so that it is relevant and meaningful for each. Together with those who conducted the research on children’s construction of number, we forge ahead in sharing what we have gained with all of you.
Counting-on is one of the things I have come across in Les Steffe’s research that is crucial, but not necessarily an obvious goal to have for students. It would seem that if a student could count-on (ex: given the problem 6+5, would start at six and count-on five more rather than starting from 1 and… Continue Reading
In my last blog, we discussed how the student needs time to imagine counters, or use something that can stand in the place of counters, so the child will gain enough experiences to make just the numeral meaningful. How can we encourage students to do this? Let’s imagine a child has the goal of figuring… Continue Reading
In school mathematics, we spend a lot of time making math very formal, very sophisticated, and very unreachable for most people because it doesn’t feel real. Perhaps more time should be spent playing with math, exploring math, and making math real for everyone. In ancient times, people often did very sophisticated math problems, but they… Continue Reading
We at the AIMS Center have been digging into research on how children come to know number. What I realize is that knowing the journey from perceptual to conceptual which children must take is important for teachers to understand, in order to effectively help children on their path to understanding number. We have discussed the… Continue Reading
Hopefully last week you read the blog by Tiffany Friesen in which she discussed perturbation. In it, she gave a couple of examples from her own experience. Both of the situations that she mentioned were familiar enough to her that she had the capacity to resolve her confusion. She had familiarity with making the cookies… Continue Reading
We know that children do not learn simply because we have given them information that we find to be important. And I hope that we know that just because we list the objectives on the board, cover each one with diligence, and check it off doesn’t mean that we have taught the objective. So what… Continue Reading
When you hear the term partitioning, you might think about partitive division or partitioning a discrete set of objects, like dividing a dozen cookies among four people. Partitioning also applies to continuous intervals. An example would be the task of equally sharing a candy bar among 5 friends. The outcomes for how a child would… Continue Reading
This month kicked off with a bang! It started with a trip to the beautiful Monterey Peninsula for the California Mathematics Council (CMC), North Section – Asilomar Conference 2016. If you have not been before, switch over to your calendar right now and mark off the first weekend of December for the conference. Then you… Continue Reading
If you are an elementary school teacher, I am sure that you are already familiar with skip counting. We want students to learn how to count by 2’s, 5’s, 10’s, etc. We think of this as preparing them to understand and efficiently multiply. I have recently learned from the research that if we add a… Continue Reading