5. Use Appropriate Tools Strategically.
Math proficiency standard 5 requires students to use appropriate math tools and use them strategically. Tools used for mathematics are varied and include pencil and paper, calculators, computer software, Ipads with programmed instruction lessons, rulers, compasses, protractors, manipulatives and countless other items. Students should show proficiency using all applicable tools. Showing proficiency requires realizing what tools can be used, and how they should be used dependent upon the problem being solved. Students should recognize the tool’s value and limitations.
Tools help students better visualize and understand problem solving by providing a deeper level of learning. Students are able to look at problems in different ways and compare solutions by using the data provided by utilizing mathematical tools. This supports learning at higher levels, and facilitates a more comprehensive approach to solving both mathematical and everyday problems. Carpenters, tool-makers, scientists and countless other professions require the proficient use of mathematical tools to complete projects.
While many bemoan the fact today’s students utilize computers and calculators, like the slide-rule and trigonometric tables of old, these tools allow students to solve problems using extremely large numbers or great amounts of data. The graphing calculator and internet allow students to explore mathematical content that in the past would not have been possible until much later in the educational process.
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
A review of social media reveals many NCCS detractors either do not understand the program, or feel it is a federal takeover of local school systems. This indicates a need for better communication regarding the goals and components of the program. The majority of Americans are not really sure what the term “Common Core Standards” even means. Unfortunately, this lack of knowledge leads to resentment and distrust. What should be viewed as a straightforward plan for increasing students’ critical thinking skills and improving education across the United States, is too often seen as a socialist plot to indoctrinate our children.
Organizations such as the conservative Heritage Foundation and Republican National Committee feed into the campaign of misinformation by spreading stories of classrooms where answering a math problem incorrectly is acceptable and the social sciences are redesigned to support a leftist agenda. Facts be damned; opponents “feel” the Common Core is a partisan plot which must be stopped. Of course, as is always the case, there are those on both sides of the partisan divide who would scrap the NCCS for various reasons, and others who support the new standards fully.
This is not a new phenomenon. Every attempt at improving education in this country, whether top down or bottom up, has met resistance. Often, detractors have been correct in their opposition. Just as often, improvements in method have been abandoned due to lack of understanding and support from parents, organizers and politicians. Educators themselves have sunk numerous efforts at improvement in the classroom.
While the National Common Core Standards will probably not be a panacea, almost any effort to improve K-12 education in America is worth a try. Success will depend on buy-in from educators, politicians and citizens of all ages and backgrounds. Cooperative effort will undoubtedly lead to positive results. Tweaking will be required, but the goal is a good one, and can be achieved. Partisan bickering and misinformation campaigns can only lead to a continuation of the downward spiral currently leaving so many American students behind.
America’s ability to educate cannot afford to lag as the speed of information technology continues to advance. High tech societies will not thrive in an environment of low tech workers. It is inherent on our government and educators to inform the masses, ensuring they understand the NCCS effort, and its desired affect. Anything less can only lead to another failure.
James Wheeler – commoncoremath.net