Friday, July 26, 2013

Building Mathematical Comprehension- Chapter 9

Second to last post of this book study. Crazy!! Catch up on my old posts by going here:

Chapter 9-  
Monitoring Mathematical Comprehension

The good news: Many students take part in this mostly subconscious act of self monitoring meaning as they read and do math. 

The bad news: Not ALL students are able to do this on their own.  In fact, in the beginning of the chapter Sammons says that so many children don't expect to understand math. (249) If I don't expect myself to be able to understand, then I'm not going to have much motivation to persevere when it gets hard. It's easy to give up when the expectation isn't there. This really speaks to the importance of building a safe learning environment in our classrooms and having high expectations for ALL students!

This great anchor chart from First Grade Brain Sprinkles can easily be adapted for math.  

The great thing is that this strategy of metacognition encompasses all the other strategies!

Metacognition in math, however, is twofold. First, students must monitor their conceptual understanding (252). Then, students must monitor their understanding of the meaning of the problem (254). Many math students are so engrossed in procedural understanding that conceptual understanding suffers, thus problem solving suffers.

Here's what students need to know about monitoring mathematical comprehension:

1. They are responsible for their own understanding. Students must be aware of times when they don't understand. 

2. Students need to know when they don't understand. 

3. They can pinpoint their misunderstanding. In other words, students know what got them confused in the first place. 

4. Students can use strategies to fix their comprehension. 

5. Strategies should be used flexibly. When one doesn't work, student know to reevaluate and try something new. 

Concrete Example: When a car breaks down, we don't try to keep driving it. We fix it! When our comprehension breaks down, we don't keep working, we stop and fix our comprehension first. (258)

Red Flags Students Should Watch For:
  • My internal voice isn't working 
  • I can't visualize the problem
  • My mind is wandering and I can't focus
  • I can't recall the details
  • When I ask questions to clarify, I can't come up with an answer (259)
Here are some great thinking stems to assist with metacognition.
no source for the above Pinterest pin :(

Red Flags Teachers Should Watch For:
  • Students who rush through their work
  • Students who don't make mathematical connections
  • Students who give up easily (260)
Strategies for Monitoring Mathematical Comprehension

Have students put a post it with the word "huh" written on it next to the confusing part of the text. If the confusion is cleared up they add a light bulb. The teacher can walk around and see what areas of the text/work should be addressed. (263) 

Ticket Out the Door
This strategy requires students to solve a problem, rate their understanding, or show their understanding in some other way before leaving the class. The teacher then uses that formative assessment when planning the next day's lesson. (264)

(Ticket Out The Door poster from Teach-A-Roo)

Color-Code Math Stretch
Similar to the Ticket Out the Door, students rate their understanding of the day's lesson on color coded sticky notes. Green if they understood it well, yellow for moderate understanding, and orange for very confused. On the note students write a quick statement about the concept. (266)

Here's a bit of a spin on this math stretch from Timeouts and Tootsie Rolls.  

So, so, so much to take in. After giving your brain a little break you can check out these other links too! 

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