### final considerations FOR THE “PROBLEMATIZING OUR MESSY PROBLEMS” UNIT:

The kinds of thinking that students should be doing with this technology (Virtual manipulatives) should be along the lines of critical thinking, analysis, and problem solving. They should be noticing how their manipulations effect what they are looking at and be able to report back what that means in mathematical terminology. If structured correctly this should be highly transformative since it allows them to directly control variables, coefficients or other aspects of their model and see what happens instantly where if they were doing it with a simple graphing calculator or pencil and paper it would require multiple graphs and the time to create them. (click here for more information.)

Since the learning task and technology for this unit involve noticing changes and turning a real world problem into a mathematical model it may be difficult for some students with special needs. Having a highly structured task card for each segment of the process along with specific details for each student to watch for will help a variety of students in the class. Leveling these task cards with sentence stems, time limits and specific probing questions or bullet points will allow students to better self-manage while working on the over all project. It will also be especially important when working with the virtual manipulatives since they become quite fun to just play with after a while. (Vaughn, Tomlinson)

Another thing to consider is how to allow for students to collaborate on this project. The technology does not allow multiple students to be using it at the same time unless every student has access to a computer (or similar) to use the software. This means the structure of the groupings as well as the time allotted for each member to use the virtual manipulatives needs to be thought of and perhaps given a dry run before you set out on the project as a whole. (Smarter Together)