2. Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—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.
This is a skill we all use every day. Some are much better at quantitative reasoning then others. The ability to think in the abstract, and then apply the knowledge gained to manipulate representative symbols is required in almost all aspects of daily life; imagine the tool maker, programmer or cook. Without this skill we could not accomplish tasks as varied as driving a car or operating the ever present electronic devices filling our lives.
Copernicus, Galileo, Descartes, Newton, Darwin and countless others throughout history have moved Western Man from the static “Dark Age” to a time when science and knowledge are moving so fast we can barely keep up. Their accomplishments depended upon quantitative measurement and reasoning, and then contextualizing knowledge gained to shape a new world view based on phenomenology. Suddenly the secrets of the universe started to be revealed at an ever increasing pace.
Our students will need to continue this accelerated pace utilizing the same skills. The future will depend on their ability to solve problems in the abstract and then apply the knowledge gained. Revealing a “Grand Unified Theory” will lead to technological advances that will make today’s world seem like the dark ages.
It is important to recognize the varied abilities of students when teaching. Many will find such abstract methods of critical thinking incredibly difficult. Finding methods to accurately measure the skill will also be a challenge. The “one size fits all” method of standardized testing will undoubtedly fail to live up to the promise. Those creating the standards and assessments must take this into account. The policy makers must recognize the limitations as well.
James Wheeler – commoncoremath.net