1. You’ve challenged my thinking process. Initially I associated, “learning without curriculum” to be problem based learning using open teaching methods like constructivism. Now, I see that there is a need for curriculum but it should be revamped in such a way to allow for more flexibility or teacher autonomy.
2. I like your example. It takes away the intimidation of creating a multi-layer project involving various disciplines. Your math example is simple but still allows students to think critically and problem solve. In this case, the manipulatives could serve as part of scaffolding. The ability to choose how to solve the problem would give students ownership over the task. I feel better about my teaching now!