David Hewitt and Mathematical Awareness

 One stop I had while watching the video is the idea of powers of the mind. Hewitt brings up a good point that students are often relying solely on memory in the classroom rather than thinking and working out why math works the way it does. I think a lot of this comes from the traditional teaching technique of stand and deliver, students are able to take the backseat while the teacher is doing all the thinking and hard work. Using thinking classrooms can help put students in the driver's seat and take control of their learning. 

I also enjoyed that Hewitt did not explicitly tell students if they got the question correct but instead lets them figure it out on their own. I think this is important in the classroom because it moves away from the idea that the teacher is the holder of knowledge and rather encourages students to be independent. 

Finally, I also liked the idea of doing math verbally. I can see that working very well for certain students who are auditory learners. It can also work well for students who get overwhelmed by mathematics when it has been written down. However, I can also see how for certain students this method of learning can be inefficient because they get confused when things are not written down. 

In my own classroom I would love to try out thinking classrooms and fostering independence in students. I feel these methods are quite beneficial for students because it helps them take accountability for their learning. 

To solve the fraction problem of finding a number between 5/7 and 3/4 my first step was to make sure they both had the same common denominator. So the numbers would now be 20/28 and 21/28. Hence a number between 5/7 and 3/4 could be 41/56. 

I think Hewitt created these problems to be solved as a problem of day or as a way to start off an inquiry-based lesson. All the problems in the video are great examples of problems that have multiple correct answers which can help students understand that there are multiple ways to approach even one problem!