### Building Mathematical Comprehension - Chapter 3

Chapter 3 - Making Mathematical Connections
Just like in reading, "learning is intimately linked to the connections we make between our prior knowledge and our new experiences.  Prior knowledge or experiences help learners interpret and construct meaning from newly introduced ideas or concepts." (Sammons)

Even Marzano (2004) says research shows that "what students already know about the content is one of the strongest indicators of how well they will learn new information relative to the content."

While many students are taught from an early age how to make connections, students don't always grasp the idea of how to access the background knowledge needed to make those connections.  Teachers need to explicitly teach how to access this information and make the connections to new information.

Often prior knowledge can be grouped into three categories:
Attitudes
Experiences
Knowledge

Just as in Reading, there are three types of connections:
Math-to-Self Connections
Math-to-Math Connections
Math-to-World Connections

Throughout the chapter, Sammons mentions the importance of explicitly teaching making connections through modeling and think-alouds.  She mentions three important ingredients for making these think-alouds more successful:
proper planning (no more winging it)
authenticity
precise language

Finally, Sammons mentions some strategies for building connections that can also be found in her Guided Math book:
Math Stretches
Mathematical Current Events
Using Children's Literature

The last thing I want to share was an a-ha for me.  If you have ever taught making connections with primary students, you know my dreaded fear - meaningless, loosely-based connections that the students insist are truly important.  Sammons used a series of concentric circles, similar to a bulls-eye approach as a visual for making meaningful connections.  The center (or bulls-eye) was math.  Surrounding that is math-to-self, then math-to-math, and finally math to world connections.  One of her examples of a think aloud included the following statement, "Sometimes the connections I make distract me from thinking about things that help me understand the math concepts." (Sammons)  It seems so obvious, but I'll be honest - I've never thought about modeling that some connections are distracting to me as a reader.  You can bet that statement (in some form) will be added to my teaching tools this year!

Up Next: Chapter 4 - Increasing Comprehension by Asking Questions

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