Synthesize! Math?

Welcome to Chapter 8 of Building Mathematical Comprehension....Synthesizing Information.

"The process of synthesizing information may be the most complex of comprehension strategies" (P. 227). Well. I would agree with that! Synthesizing seems to be the most difficult for my kiddos to grasp. 
What does synthesizing look like in math? 
Well, for starters.....there's a whole lot of thinking that goes on during math!

Consider this all of this that needs to go on in those little brains--
  • Conceptual understanding - they need to have a functional grasp of mathematical ideas
  • Procedural fluency - when & how do you use all those procedures?
  • Strategic competence - they've got to be able to form, represent, & solve math problems
  • Productive disposition - they must be able to see that math makes sense & is useful (again--- it's not hereditary!)
  • Adaptive reasoning - we want kiddos to be able to think about & make connections between concepts & relationships.
One of the things that I'm really appreciating about this book is that Sammons points out "What Students Need to Know About ________" (whatever the skill is). One of the (many) things I need to improve upon is making kiddos aware of what & why they need to know whatever it is we're working on. (Isn't that what metacognition is all about?).

Here are what kiddos need to know about synthesizing--
Mathematicians (and we're all mathematicians!)
  1.  are aware that mathematical ideas change with additional experiences.
  2. synthesize ideas when they think about new experiences they have.
  3. understand that synthesis is the sum of all the information gained from old & new math experiences.
  4. realize that their own knowledge of math will continue to grow & change as you come across new ideas.
  5. can explain how using synthesis can help you better understand. 
That's a pretty big order!
If you're like me, you're already thinking about how you can help your kiddos develop this skill. Here are some of the ideas Sammons gives:
  • Modeling & Think Alouds- During reading, we pause every now & then to think aloud to let kiddos hear our thinking. We need to do the same thing with Math! Kiddos need to hear/see how all the different facets of math work together when one is working on a problem.
  • Create Concrete Experiences - I know I'm preaching to the choir-- we all know that kiddos need to anchor abstract on to concrete. I like the example of 
    • Nesting Dolls - as an object lesson for synthesis. Line the dolls up according to size & have kiddos come up with how that relates to our thinking (Your thinking changes & gets bigger with more experience). Amanda Nickerson, from One Extra Degree has a fabulous product on TpT that does just that!

    • Bake a Cake! All the separate ingredients go in together to make a new whole food. I've got some ideas a-cookin' for this one! Make sure you come back to check it out!!

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