I stumbled across a new app today called Mathination. This app takes different expressions and equations and allows students to manipulate them by hand. For example, a student can drag variables and numbers around and see what happens to the expression or equation. Dragging a number across an equation changes its sign:
Then, dragging the coefficient 3 underneath the 9 automatically gives us x = 3.
Mathination also allows the user to expand and factor expressions, and square root and square equations.
I have mixed feelings about this app. On one hand, I think it is a great way for students to explore solving equations and simplifying expressions. However, on the other hand I think that this app does not help students understand why these algebraic steps are correct. For example, dragging the 3 to the other side of the equation to isolate x does not help students understand that dividing by 3 on both sides gives us a 1*x, which is equal to x.
The app also allows you change the equation or expression in ways that do not lead to solving or simplifying, for example I was able to change this simple equation:
Before finally isolating a correctly:
I actually think Mathination will be most helpful in the classroom for exploring these equivalent expressions and equations that lead students off the path of simplifying/solving. Instead of having students practice the right way to solve/simplify, Mathination gives them the freedom to explore the algebraic rules to become convinced of the most efficient method for simplifying/solving. Mathination also takes arithmetic proficiency out of the picture, allowing students the freedom to explore within the time constraints of the curriculum and school day. If you have read some of my earlier posts, this type of conceptual exploration is what I have been looking for!
I think I will use this app with my Algebra I students when we get to rational expressions - not to teach the skill of simplifying expressions or solving equations, but to explore the rules for simplifying and solving after we have already practiced using pen and paper. I will keep you updated on how it goes!