Developing Ways of Thinking – The Common Core Standards

Posted: February 27, 2014 in Teaching and Learning Philosophy
Tags: ,

Our good friend, Dr. Ted Coe, had the following article published on


Why Arizona needs Common Core standards

Math professor: It’s all about how we think and learn

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By Ted CoeMy TurnTue Feb 25, 2014 12:54 PM

In a recent surveyconducted by Expect More Arizona, 43 percent of the state’s likely voters said they favor Arizona’s College and Career Ready (Common Core) Standards, which define the knowledge and skills necessary for K-12 students to succeed in college and careers.

After being given a short description of the standards, support rose to 71 percent.

Yet just last week, the state Senate Education Committee passed bills to abolish or allow schools to opt out of these standards and literally revert back to the level of standards from the last century. This is not the direction Arizona should be moving.

To understand why, you must first understand three key areas of mathematics teaching and learning: ways of doing, ways of thinking and habits of thinking.

Ways of doing: I have been a math educator for 20 years. I have seen how our culture views mathematics simply as ways of doing. Consider the typical math classroom experience: A teacher explains a particular mathematical process and students complete the process 30, 40 and sometimes up to 100 times.

The next day, the teacher introduces another mathematical process, perhaps unrelated to the previous one. Students collect these pieces for up to five months and the system rewards those who are able to memorize the greatest number of processes.

Think about it: When you finished the last of your mathematics classes, did you see math as a collection of random pieces or as a completed puzzle?

Ways of thinking: For too many, math ends up being merely a collection of random pieces, when in reality the pieces should always fit together. After all, mathematics is the one academic subject that makes logical sense.

Unfortunately, many lose the notion that what we do in math should follow from how we think about math. Our ways of doing need to develop from ways of thinking.

Arizona’s College and Career Ready Standards set a new expectation in this regard because they are built on progressions of thinking. That is, the standards emphasize not only the mathematics processes but also conceptual understandings that are consistent across the grades.

Math instruction should make sense both day-to-day and year-to-year. Teachers who use clever shortcuts to supplant thinking do their students a disservice in the long run.

Habits of thinking: It is important to encourage good mathematical habits of thinking. Arizona’s College and Career Ready Standards will develop mathematical practices such as problem-solving, persevering, reasoning abstractly, constructing arguments and attending to precision. The standards will require our students to think about and apply their math skills to real-world contexts.

Educating our state’s future leaders has never been more important. Arizona’s College and Career Ready Standards provide a framework that will ensure our youth get the quality education needed to prepare for college and the workplace.

In the realm of mathematics, that means doing more than helping students ace an exam. Rather, it’s about encouraging and supporting ways of doing, grounded in ways of thinking, while developing essential mathematical habits.

Dr. Ted Coe is an assistant dean at Grand Canyon University, a member of the Partnership for Assessment of Readiness for College and Careers Math Operational Working Group and a co-director of the Arizona Mathematics Partnership, an $8.7 million National Science Foundation grant to promote excellence in middle school math and improve student achievement.


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