Reflection on Better Learning Through Structured Teaching - Ch. 2 - Focusing Instruction

I can't even remember how I happened upon the title, "Better Learning Through Structured Teaching" by Fisher & Frey, but I am glad that I clicked the order button.  As I read through this short book, my goal is to reflect on what I already am doing (confirmation) and what I can do to become better.

Focused instruction is not telling but rather explaining.
This goes right along with my over math philosophy..."move your thinking".  Most times, thinking cannot be moved simply by hearing it.  When the "how" and "why it works" are explained along with teacher think alouds, thinking can be moved at a much higher level.

A worthwhile lecture conveys new terms and concepts and draws connections between ideas.
With the introduction of the Common Core standards into my curriculum a couple of years ago, one of my goals has been to truly focus on vocabulary.  Instead of just defining terms, using them and understanding the meaning behind them, has been my goal.  As we strive for precision, using correct mathematical vocabulary is stressed as students explain concepts and procedures.

Forming connections between mathematical ideas is essential as students build on prior knowledge.  As I create lessons, it seems I am constantly putting myself into the students' minds to see how and what the next step should be to help make sense of new concepts.

The common core is teaching thinking.
This has been my biggest hurdle to overcome.  When Math In Context was our curriculum, I saw student thinking at a much higher level then I do in my classroom right now.  For some reason, most of my students do not want to do the thinking it requires to make sense of a problem.  I find myself answering their questions with questions of my own to push them into the problem solving world.  Another strategy I have used that has been met with enthusiasm is using Dan Meyer's Three Act Tasks so students have to figure out what information they need and then how they will use it.  By simply typing up their thoughts attached to their name has spurred many minds into how they can contribute to the lesson as well.

The purpose and learning target...needed for acquiring new knowledge.
Every day, the learning target is posted in my room, and I voice what the purpose or goal of the lesson is going to be.  This is the road map that help students navigate through the lesson instead of just blindly following me.

Thinking aloud allows students to witness the "decision-making tree" experts create and follow as they engage with complex ideas and processes.
This thought rings true as I reflect on a lesson with my Algebra 1 class on explicit and recursive formulas.  After the Common Core changed what was taught in the classrooms, I had to do some brushing up myself on concepts that I had not thought of since high school!  As we looked ahead one class period at what was coming up, I announced to the class that even I was going to have to do some studying on these new concepts.  As I searched the internet for each to follow examples, I got to thinking.  By modeling how I learned about these concepts, would be the perfect way to model to students how to learn new material.  I found some instructional reading with examples that were at my students level and made copies.  When class commenced the next day, I explained to the students that would be learning right along with them.  We did a close read, circling items we did not understand, making notes in the margin to demonstrate what we could connect to, and writing out questions we would need to look up later.  One of the tech guys was working on my cart of iPads quietly in the corner though all this, and after dismissing the class to lunch, he told me that he had never sat through an Algebra class where he had learned so much.  He truly liked my method of covering the material and wished his teachers had been as open about learning as I had been.

Noticing - Expert teacher recognize that noticing their students' thinking reveals the effectiveness of prior instruction and informs their subsequent instructional decisions.
Yes.  Yes.  Yes.
I rarely sit while teaching.  As students work either collaboratively or independently, I am constantly circling the room, listening to their discussions, asking clarifying questions, and keeping mental notes on where the next lesson will go.

"Exit Tickets" or in my case...stickies on the board
This year, I have used the sticky note to assess student thinking.  For example, as students worked through two graphing calculator labs to discovery on their own what m and b stand for in the equation y=mx+b (an equation that has graced my front wall all year long and has prompted wonderings and questions), as they discovered what they believed those variables to stand for, they wrote it out on a sticky with their name, folded it in half, and stuck it on the board either under the m or the b.  As times allowed, I could check their answers, approve of them, or return them for more precision or a correct answer.