Chapter 8: Enacting the Mathematics Lesson
Similar to the lesson planning phase, this is something I have learned a lot about in graduate school, even if I haven't actually enacted that many - we just talked about a lot of these concepts, so there wasn't a lot of new information in here for me.
One new topic for me was the idea of persistent questions - which of course I understand already; this was just a new title for me. Further, the authors suggested having students write persistent questions to each other, which seems a great idea to check for understanding, make them think about others' solutions, etc, while also making sure even the shy kids have a chance to participate.
There's also a great checklist in this chapter for maintaining a high level of demand, which can be hard to do, especially when you are pressed for time. Right now, I'm asking a lot of my Upward Bound students to discover things on their own through exploratory labs, and they are struggling a bit. I know that helping them through these labs is lowering the cognitive demand, but since I only have then 10 days, I can't afford to have them take too long on any one topic because we won't get them covered before the final project. If it was an ordinary class, I would let them take longer and lengthen the whole unit, but that's not an option for me right now.
When it comes to issues with maintaining this high level of demand, the authors suggest targeting specific areas - which helps avoid taking on too much - and enlisting your students to help you. I definitely think that's a great idea, because I might think I'm accomplishing a goal, when from the students' perspectives, I'm not.
Some of the teacher moves that we have hashed out and rehashed here at WVU were mentioned in this chapter too, so that wasn't anything new. However, the authors did suggest having students use some of these moves, particularly asking "adding on" questions to their classmates, which seems to be a great idea, especially for more advanced classes, to help students take more ownership of their learning.
One new topic for me was the idea of persistent questions - which of course I understand already; this was just a new title for me. Further, the authors suggested having students write persistent questions to each other, which seems a great idea to check for understanding, make them think about others' solutions, etc, while also making sure even the shy kids have a chance to participate.
There's also a great checklist in this chapter for maintaining a high level of demand, which can be hard to do, especially when you are pressed for time. Right now, I'm asking a lot of my Upward Bound students to discover things on their own through exploratory labs, and they are struggling a bit. I know that helping them through these labs is lowering the cognitive demand, but since I only have then 10 days, I can't afford to have them take too long on any one topic because we won't get them covered before the final project. If it was an ordinary class, I would let them take longer and lengthen the whole unit, but that's not an option for me right now.
When it comes to issues with maintaining this high level of demand, the authors suggest targeting specific areas - which helps avoid taking on too much - and enlisting your students to help you. I definitely think that's a great idea, because I might think I'm accomplishing a goal, when from the students' perspectives, I'm not.
Some of the teacher moves that we have hashed out and rehashed here at WVU were mentioned in this chapter too, so that wasn't anything new. However, the authors did suggest having students use some of these moves, particularly asking "adding on" questions to their classmates, which seems to be a great idea, especially for more advanced classes, to help students take more ownership of their learning.
Chapter 9: Reflecting on the Mathematics Lesson
Reflection is such an important part of teaching, and it really isn't emphasized enough in teacher education programs, I think. I know personally I have trouble writing really good reflections - partially it's because I've already thought of it in my head, so I don't feel like writing it down. Sometimes it's because the lesson when horribly awry and I don't want to admit it to myself - but I have to!! The authors say that we have to have evidence of good and bad things and a desire to discover surprises (both good and bad) in order to really change our beliefs and teaching. I'm trying to do that.
Reflection in some sense is about evaluating, and I think that maybe I need a more concrete "rubric" from which to evaluate my lessons. Sometimes reflection is hard because I might forget certain aspects of a lesson, or focus too much on one - perhaps I should write a rubric with all of my overall goals on them to see how I am meeting those goals. This would lead to the first of six steps in the reflection cycle: identifying and describing the problem.
Reflection in some sense is about evaluating, and I think that maybe I need a more concrete "rubric" from which to evaluate my lessons. Sometimes reflection is hard because I might forget certain aspects of a lesson, or focus too much on one - perhaps I should write a rubric with all of my overall goals on them to see how I am meeting those goals. This would lead to the first of six steps in the reflection cycle: identifying and describing the problem.