Dave Hewitt & mathematical awareness

 In the videos we watched in class, the three things that made me stop and think were:

1) Hewitt's ideas that students will naturally find the correct answers, they just needed guidance to get there faster. That if left to their own devices, mathematical thinking comes naturally, it is only that the pace needs to be quickened

2) The idea of a group choir makes a lot of sense. I especially enjoyed that for tricky answers the unison would break and then the group as a whole would understand that further thought had to be put into this question.

3) I loved that Hewitt did not tell his students what was right and what was wrong, he was only a guide. He was constantly asking if the students thought they were right. In honesty, I remember being a student and being decently upset with teachers who did this. I remember feeling cheated, why was I doing their job for them? But i recognize now the significance of framing the relationship with students in this way.

I think that the fraction problem is a great inquiry problem that doesn't have any correct answer, at least not at the start. It is obvious that Hewitt has a particular fraction in mind, but by framing the question in terms of multiple steps, students feel much more agency. Just finding a fraction in between 5/7 and 3/4, there are infinite answers. By making the problem more concise, he is controlling which fraction the students give as an answer, but it still does not feel like agency is removed from the student.

I have already incorporated group choir into my teaching because I felt like it is a good way for students that have self doubts to more easily play along; they are just one voice in a group of 30. It make me happy to see that someone so professional as Hewitt approves of this teaching style.