ZAC or Zone of Actual Construction: what the student will be able to accomplish or solve unassisted.
ZPC or Zone of Potential Construction: the range determined by the modifications of a concept a student might make in, or as a result of, interactive communication in a mathematical environment.
This year we are excited to be taking our learning into the classroom. Our goal is to is to find ways to turn what we discovered last year into manageable classroom experiences that teachers can implement in a real setting.
We will be working with 2nd and 3rd grade classes, using the tasks from last year’s small groups. We know that the goal is not to “give” information to the children, so we are aiming to find ways for teachers to organize the math opportunities in a manner so that each child is working within their Zone of Potential Construction (ZPC) or Zone of Actual Construction (ZAC). To find each child’s ZPC and ZAC, we will be utilizing the initial interview we constructed last year and creating groups based on our findings. We were able to use this as a tool to help us make homogenous groups in the last study, and will use it for the same purpose this year.
Once we have our groups set, we will run a station in two classrooms. We will focus on the manageability of the tasks we present, as well as ensuring that the presentation of the task allows for teachers to observe student behavior in order to better develop second order models of the students mathematics. A second order model is our interpretation of the students’ mathematical understanding. We believe that we need to try to look from the students’ perspectives as much as we can in order to know where to start with their learning. These models also inform us as to what sort of math opportunities might help them to construct new mathematical ideas and concepts. Lastly, we will be looking to see if the tasks we create effectively provide these opportunities for students to construct mathematical understanding beyond what they began with.
It is not enough that we saw growth with groups of students last year. We want to have the experience as a real teacher might, facing all of the obstacles within a classroom. Only then will we be able to say that the research is viable for actual mathematics instruction. Another team at AIMS is already entering that next stage. They are entering the classrooms as actual teachers, responsible for all the standards, teaching kindergarten and first grade on a daily basis. I love working for AIMS, where value is given to re-enacting the research we do, ensuring the work is valid in classrooms as it is in research studies. I look forward to providing updates through this blog on the progress of our study. Please feel to ask any questions you might have in the comments below or tell us what you’re most looking forward to about the results we find.