Standard 2: Reason Abstractly & Quantitatively
Clip 2/13: Standard 2: Reason Abstractly & Quantitatively Using Number Operations Part D
Mathematically proficient students make sense of quantities and relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualization to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
A group of transitional kindergarten students struggle to represent the problem. Tracy Sola asks students from other groups to come and analyze the struggling group’s work. After repeating the problem—a squirrel had five nuts and shared one with his friend—she asks the students which student’s work represents the problem.The students are decontextualization of a problem situation and contextualization of the representation back into the context of the problem. They analyze the struggling group’s work and use the context of the problem to find who represented the problem correctly. Tracy Sola supports this practice by asking the students in the class to represent another problem situation.