“What Would It Look Like If…?” is one of the most powerful tools I use when working with students. Why… because when posing CGI math problems, students tend to draw beautiful models that help them solve problems. However, beautiful drawings are just the beginning.
I could easily tell students what to write, how to write it, and what to say, but their ability to follow directions is not always an indication of their understanding. Instead of telling kids what something looks like, I ask them and together we co-construct mathematical models and meanings.
I, as the teacher begin with something that they already understand very well. After several days and discussions of dividing wholes into equal parts, I might ask students to consider what those equal parts would look like on a number line.
I may have kids count multiple groups 5 and 1 group of 3, and then ask them what would it look like as an equation, where might we put the parentheses, and why? or I might have first graders solve a comparison problem and then imagine what it might look like as a graph (see photo above). And you know what? They are usually very good and figuring it out. Why…because I start with what they know and then connect it to something more abstract like a model or an equation.
In the book, Educational Psychology: Windows on Classrooms, the authors Paul Eggen and Don Kauchak state, “Isolated information imposes a heavy load on students’ working memories, which helps to explain why they may retain little of what they have been taught. The fewer connections there are between ideas, the harder the brain must work to process information. This was a major “aha” for me. What connections are being made in your classroom and how much time are students being given to make those connections?
Mathematicians have agreed upon certain rules for consistent communication. These rules include specific language i.e., product and sum, symbols, and models that do not come naturally to students, and therefore must be explicitly taught.
In addition, the Common Core State Standards (CCSS) and the Smarter Balance Assessment Consortium (SBAC) require students to understand problems from multiple perspectives and in multiple formats. “What Would It Look Like If…?” helps students see and understand these multiple pathways. I love it when I hear students say, “Ohh, I get it.” and you will, too.
We have grade level units in the Teaching One Moore store that take each standard and link it to real world problems, and then on to models and equations. The problems and number choices are specifically scaffolded so that they begin easily and become progressively more challenging. More units and resources are posted every week.