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Math

Our school district has adopted the Houghton Mifflin Series, of which I am using the "Expressions" piece.  Expressions is divided into 10 units.  The concepts and skills taught in these units build from one unit to the next.  Problem Solving is a huge component of this series.  Students are taught to think of possible solution methods and then to use "math talk" to explain their thinking to one another. 

The units in the Expressions series focus on: 

• Unit 1 - Break-Aparts and Partners of a Number/Patterns/Geometric Figures

• Unit 2 - Understanding Addition and Subtraction/Explaining Solution Methods

• Unit 3 - Written Story Problems/Finding Unknown/Counting On

• Unit 4 - Groups of Ten/Tens and Ones/Ten Sticks and Circles

• Unit 5 - Dimes, Nickels, and Pennies/Teen Solution Methods

• Unit 6 - Picture Graphs/Comparison Story Problems/Simple Measurement with Inch Rulers

• Unit 7 - Fractions/Parts of a Dollar/Circle Graphs/Time and Clocks

• Unit 8 - Money/Regrouping Ones to Make a New Ten

• Unit 9 - Problem Solving:  Change Problems/Collection Problems/Multi-Step Problems

• Unit 10 - Measurement and Estimation

 Our district has also offered training in Cognitive Guided Instruction (CGI) through South Dakota Counts.  CGI is a research-based way of teaching mathematics that embraces/encompasses the following components:

• problem solving in meaningful contexts with flexible solution strategies

• building mathematical understanding through questioning based on student prior knowledge

• integration of mathematical concepts

(South Dakota Counts, 2006)

IS

• research-based

• a way of teaching mathematics that enables students to solve problems anyway they choose (there is NOT only one way to solve problems)

• how teachers understand students' mathematical thinking

• a journey or process

• children building meaning based on what they already know

• looking at how students solve problems on their own and how to move them to a higher level

• focused on "individual" understanding of each student

• questioning to get to understanding of each student's thinking

• facilitating student communication

• flexible strategies

• integration of concepts

• a scope and sequence
• a recipe
• a curriculum
• a set of worksheets or computational problems (naked number problems)
• a simplistic approach
• a set of instructional materials
• a prescribed set of strategies and techniques
• formal algorithms
• skills in isolation

• Math Talk Learning Community

• Math Background by 1st grade units