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
 
While you wait, head on over to see what other bloggers are saying about this chapter:
 




 
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2 comments:

Amanda said...

It's been awhile since I last talked to you! How are you? Super glad its summer time :) I am excited you are doing a book study on this book. I have it and haven't had a chance to sit down and dive into it. I think this might be the perfect time since I would have someone to talk to about it! :) Hope to catch up with you this summer!

Amanda
Reaching for the TOP!

Beth said...

Great post.
Beth
Thinking of Teaching

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