The 5 Practices

As I was reading the beginning of the 5 Practices book, I remembered certain times in my own education where math lessons seemed unconnected or had unclear goals. I don’t remember having to do nearly as much thinking as this book suggests, but the importance of pushing students in this direction is clearly needed in many of today’s classrooms. When faced with problems that don’t require much more than recalling an algorithm and using it repeatedly, it is clear that this is not “doing” mathematics. “Doing” mathematics involves higher levels on both axes of the Cognitive Rigor Matrix as described in the NCTM article. In an effort to develop in students the ability to handle the increased cognitive demand associated with higher-level problems,
In a way, I was following the second practice of monitoring. However, I had never thought of the first practice of anticipating solutions. Certainly, planning is critical and I am much more comfortable with any activity when I have a chance to get things prepared beforehand, but when the 5 Practices book suggested to come up with different equation rules for the Patio Problem on page 18, it seemed beneficial when it came to looking over the different student answers in chapter 3. It is clear that, much like mathematics in general, the practices must build upon one another for effective discussion-based
I think the general idea of taking large amounts of class time throughout the school year to focus on single questions can be beneficial, but the 5 Practices book stresses that the question itself is just as important as all the work done with it. Finding the balance can be difficult, especially with students of varying degrees of ability and prior knowledge. The key is to include as many students as possible and to ensure you are asking questions in a purposeful way, which certainly comes with experience. All of this talk about student-centered, inquiry-based instruction is certainly exciting, but when you have a list of standards that must be covered and tests you must prepare your students for, it can seem like a daunting task. I hope to learn more about this type of instruction and be able to implement it into my future classroom successfully, as it is much needed - especially when it comes to students being able to develop a STEM mindset and see the meaning and beauty behind