What does it mean to be good at math? This is something I’ve been musing over for some time now.
I used to think that someone who was good at math was someone who could solve many different types of problems. By hand. The long way. The way I was taught to do it.
I’m not too sure anymore. There are tools available that help us solve equations. That let us solve by graphing. That let us solve with CAS. Why isn’t it okay to use these to get beyond the symbolic manipulation that often frustrates students? Why isn’t it okay to use the tools that let them get to the real problem solving?
Is solving for x the real skill we’re trying to teach?
If a student can read a word problem, understand what it is asking, set up equations to model the situation, use a graphing calculator to get the solutions, and evaluate the reasonableness of the solution why isn’t that enough? For the “average” student, does it matter if they say the answers are or if they say approximately 1.412 and -0.079?
If a student can solve a problem by hand and get the answer of is that not enough? Why is a better answer?
I want my students to understand the relationship between the graph, the table, the equation, and the situation. I want my students to be able to explain and defend their answers. I want them to be able to evaluate the reasonableness of the solutions proposed by others.
There are tools that let more students have access to these ideas. Why do we insist they do it by hand?