# Adaptive Reasoning Part 3: Talk in Whole Group and Guided Math Groups

We have been talking about fostering adaptive reasoning among our students. Donovan and Bransford have defined it as the “Capacity for logical thought, reflection, explanation and justification” (p. 21). So this means students are thinking, reflecting, explaining and justifying themselves both publicly and privately. We build this by doing it as a whole group, as small groups, as partners and then as individuals. We must scaffold this type of thinking. The landmark report Adding It Up notes that even very young children from the ages of 4 and 5 can “demonstrate sophisticated reasoning abilities” if given the appropriate experiences (http://www.nap.edu/openbook.php?record_id=9822&page=129).

It goes on to note that “Research suggests that students are able to display reasoning ability when three conditions are met: They have a sufficient knowledge base, the task is understandable and motivating, and the context is familiar and comfortable” (http://www.nap.edu/openbook.php?record_id=9822&page=130).

Furthermore, it adds that one important “manifestation of adaptive reasoning is the ability to justify one’s work. ” But it clarifies that there is a difference between justify and prove noting that proofs are more complete whereas justifications are less formal. So, proofs would be where we would make the students write it down and explain it through a series of logical arguments whereas justifications would be more talking about it (http://www.nap.edu/openbook.php?record_id=9822&page=130). So for example, we might have students prove that a number is even or odd. We also might have them prove that 6 + 7 is a doubles +1 fact. We could have them prove that 1/4 is smaller than 2/3.

I challenge all of us to think about how we might start doing this in our elementary math classrooms. How might it look in your kindergarten classroom? How is that the same and/or different from how it would look in a 6th grade classroom? I think there are many possibilities.

Here is an example from an upper elementary classroom:

http://mason.gmu.edu/~jsuh4/teaching/posterproofs.htm

Here is a great example of having students write a CONVINCE ME paper:

http://mason.gmu.edu/~jsuh4/teaching/convince.htm

Remember IT’S ALL IN THE QUESTIONING….

http://mason.gmu.edu/~jsuh4/teaching/resources/questionsheet_color.pdf

Accountable Talk Icons

http://mason.gmu.edu/~jsuh4/teaching/resources/discourse.pdf

More Question Prompts for Problem Solving:

http://mason.gmu.edu/~jsuh4/teaching/resources/mathjournals.pdf

References

How Students Learn: History, Mathematics, and Science in the Classroom By National Research Council (U.S.). Committee on How People Learn, A Targeted Report for Teachers, Suzanne Donovan, John Bransford Edition: illustrated Published by National Academies Press, 2005 ISBN 0-309-08949-2, 978-0-309-08949-4

Adding It Up: http://www.nap.edu/catalog.php?record_id=9822#toc

I am up for the challenge, and I will in turn challenge and coach the teachers to stretch themselves to use the strategies you suggest. The Proof Posters are for Grades 4-6?? and Convince Me for Grades 1/2 and up? I am still grappling with how this would look in Kdg – pictures, and interactive writing??

Lisa PietrosimoneOctober 4, 2010