November's Math Practice of the Month

Reason Abstractly and Quantitatively

This math practice is an essential focus if we are to get all of our students to the deepest level of mathematical proficiency, the Application and Communication level (level 4).

What's the standard? 

Mathematically proficient students: 

• Make sense of quantities and their relationships in problem situations. 
• Decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols.
• Contextualize—to make meaning of quantities and symbols in terms of a situation. 
• Create multiple coherent representations of the problem attending to the meaning of quantities and units involved, not just how to compute them; and 
• Know and flexibly use different properties of operations and objects.

What does it look like and how do we teach it? 

You can click here for a video and lesson from Inside Mathematics that focuses on representing numerical patterning.

We've also got some great examples of this happening right now in WCSU.  Lisa Hanna, who teaches 6th grade at Doty Memorial School, had students create these poster-sized graphic organizers to demonstrate (and develop!) their fluency between context and abstract representations of ratio problems: 

At U-32, 8th grade math classes are using a "4 Representations of a Function" graphic organizer to develop links between abstract and contextual representations.

Cathy Guiffre (who is out on leave from teaching 7th and 8th grade right now because she is home with her new baby boy!) takes decontextualization one step farther with her "waffle" problems.  Here's Cathy expressing her disbelief that I've never heard of "waffle" problems before:

No, they don't involve breakfast food.  Apparently, "waffle" is the British term for "extraneous information."  Cathy takes a word problem, adds in some extra bits of information and prints all of the bits up on separate cards like this:

Then, she collects the cards into shuffled bundles and hands them out to her students.  Her students' first task is to decide which of the bits of information matter.  Then, they decide how to decontextualize the problem and represent it symbolically.  I should add that this would work at many different grade levels, and students find it very engaging.

I hope this has given you some ideas for how to integrate this math practice into your practice.  As always, if you have questions or something you are burning to share please comment below or send me an email at edorsey@u32.org.

I can't wait to see your ideas!