### Math Think Alouds

 The Teaching-Learning Cycle (modified)
The Teaching-Learning Cycle is fundamental to our work in Mathematics for Elementary Teachers II. One of the projects assigned in this course asks the future teachers to focus on the Planning and Instruction phases of the Cycle. For three different learning landscapes (Number Sense, Addition, and SubtractionMultiplication and Division; and Fractions, Decimals, and Percents), teachers select a big idea, a model, and a landmark strategy to research and teach.

However, lesson planning and instruction are more than knowledge of the mathematical topics being studied. Learners are the most important thing to consider. Unfortunately, the teachers in this course do not always have easy access to learners. Consequently, we concentrate on developing what Fisher and Frey call Purpose & Modeling lessons in the Gradual Release of Responsibility (see figure at right). So we imagine that our learners need a demonstration of the big idea, model, or landmark strategy and plan a Think Aloud.

The goal of the Think Aloud is to make our thinking visible to learners so that they might attend to important aspects that might otherwise go unnoticed. At the risk of getting too meta, I try to do Think Aloud demonstrations because many of the teachers never experienced this approach in math class. I develop a plan using various frameworks and then record my instruction using varying formats.

On the Number Sense, Addition, and Subtraction Landscape, I decided to focus on hierarchical inclusion (big idea), open number line (model), and using constant difference (landmark strategy) because they were topics the teachers this semester identified as areas they could learn more about.

The plan for the first Think Aloud on hierarchical inclusion can be found here. And below is how I tried to implement it as instruction using the ShowMe App. As I told the teachers, this is a draft version and there are plenty of things to change if I were to make it the version I would use in class - consider yourself warned. The Common Core State Standards (CCSS) addressed in this Think Aloud are K.CC.B.4, K.CC.B.4.C, AND MP.7.

For the second Think Aloud I wrote a narrative plan (here) and went "old school" in my instruction - just me and my white board. This is also a draft and would require some revising if I were to use it with children. The CCSS addressed in this Think Aloud are 2.NBT.B.7, 2.NBT.B.8, AND MP.4.

My final Think Aloud focuses on using the landmark strategy called constant difference. I used PowerPoint to organize my plan and Jing to capture the presentation from my computer screen. Do I need to say it's a work in progress? The CCSS addressed in this Think Aloud are 2.NBT.B.5 and MP.8.