Sort of a rambling post. But trying to make some sense of my thinking…
I always appreciate posts from @emergentmath. This particular post made me pause, I had just completed the MARS task, Boomerangs, he references. We are in the midst of our systems unit.
I plan to use Geoff’s suggestion for a matching/sorting activity this werk for students to see the benefits of each type of tool to solve systems.
But where I struggle is with this standard:
I am experiencing some pushback from a handful of students who are able to reason and solve a system without actually modeling it algebraically.
Their reasoning is correct. They verify their solutions and interpret them correctly. They can sketch a graph yet “refuse” to model as a system of equations. I struggle because “their math” is right on. I realize places where algebraic models can help but I honestly can’t tell them my way is better…yet the standard says…
It feels almost like I am punishing them if I make them model it algebraically.
Then I have others who are not sure where to start. The equations model provides them a tool, yet they will not embrace it.
How do others handle this situation in your classrooms?
I use graphical, alongside a numerical table of values, with solving/verifying with the equations, letting them see their own connections eventually.
My biggest goal for systems is to provide enough modeling for students to actually “see a context” to connect/make sense of a naked system of equations.
This is where I believe skill/drill has ruined the power and beauty of math. Finding an intersection point but what in the world does in mean? It’s a point on a graph. Whoopee. Why isn’t it all taught in context as a model?