Choices in Math Class?

Today's lesson was on factoring. Students were shown two methods of factoring. Videos of these methods can be found here:

These methods were meant to give students a step-by-step process to factoring, rather than the old guess and check way.  I told students to use whichever method they liked best. They responded with questions like, "But, which one are we supposed to use on the test?" Again, I explained I wanted to give them options. It was up to them to decide which method they they liked best. It didn't matter to me which one they used.

It occurred to me students are not used to being given choices in math class. They are used to being shown our way of solving problems. On tests, we ask them to show their work, and if their method of solving is different from what we're used to, they lose points. We've taken the creativity out of mathematics. We've made math rigid and have left no room for exploration and discovery. If a student discovers her own solution path, she shouldn't get deducted points. She should be rewarded and praised for her cognition.