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Are you showing you work? Why critical thinking skills are at the forefront. Since June 2010, Arizona’s College and Career Ready Standards (AZCCRS) in mathematics demand students show their work while solving a given problem, explaining the steps required to arrive at the solution.The Common Core S

Jul 30, 2015

Are you showing you work? Why critical thinking skills are at the forefront.



Since June 2010, Arizona’s College and Career Ready Standards (AZCCRS) in mathematics demand students show their work while solving a given problem, explaining the steps required to arrive at the solution.

The Common Core Standards were adopted by more than 40 states, Arizona being one of them — Governor Jan Brewer ordered they be called Arizona’s College and Career Ready Standards on Sept. 20, 2013. Leaders within the movement toward nationwide standards argued the implementation would give educators throughout the United States the chance to collaborate on curriculum, instructional strategies, and assessments.

“Before the adoption of these standards, educators throughout the country taught different stages of various concepts. Now, the shift in mind-set is setting students up for success on a global level,” explained Andrew Ward, Director of the Master Teacher program at the Arizona K12 Center. “Students’ critical thinking and problem-solving skills are clearly at the forefront now.”

With a few years under their belts, Arizona educators are now more aware of what the standards demand. On the other hand, Nanci Smith, Ph.D., said she works with teachers in trainings that are familiar with the AZCCRS standards, but do not explicitly teach the practices, nor hold their students accountable.

“The math practices are perhaps the biggest change from previous mathematics teaching because it requires much different thinking. Math educators across the country truly believe the standards will change our nation’s ranking in math more so than the content standards. Because of that, I often begin professional-development sessions by explicitly addressing these practices and explaining what they look like in a classroom, and then provide example problems that engage the participants in the practices,” Dr. Smith explained. “I like to remind educators that the eight practices are not for them to do, but are descriptions of what students should be doing as they engage with mathematics.”

Dr. Smith is currently a full-time consultant in the areas of mathematics, curriculum, Common Core State Standards, and differentiated instruction and assessment. Because the Arizona K12 Center understands her excellence in the field, she is often tapped to lead trainings on mathematics for the Center.

Dr. Smith notes there are three to five “shifts” built within the standards, depending upon whose work you read: focus, coherence, rigor, practices, and AZCCRS. She said she aims to fuse all these together when conducting professional-development trainings.

“I try to blend hands-on experiences with problem types and activities with the theoretical understanding as to why certain problems and activities are better matches for the standards in my sessions. The AZCCRS tests given at the end of the year will include open-ended questions and performance assessments, not just multiple-choice questions. Students need to engage with these types of problems,” Dr. Smith explained.

The bottom line is students are now required to produce detailed work. It’s no longer about breadth over depth, but the converse.

“We teach in a new age and a new time,” Dr. Smith said. “I heard a National Council of Teachers of Mathematics president say in the 1980s that we teach math today like we are preparing kids to be 1940 shopkeepers. We haven’t changed that drastically from then until now … except for those that are embracing the practices along with the new standards.”

Dr. Smith encourages educators to learn more about the math standards by participating in professional learning opportunities, especially through the Arizona K12 Center.

“I have worked in 45 states and nine foreign countries. The Arizona K12 Center is easily one of the most professional resources for teachers that I have encountered anywhere in the world,” she exclaimed. “The quality of presenters, materials, training sites, etc. all treat educators as the professionals they are. The Center is a model for lifelong learning, showcasing how enjoyable learning can and should be. I am proud to be part of their resources.”

For three days in June, Arizona educators will have the opportunity to attend the Arizona K12 Center’s Summer Math Institute, in partnership with the Arizona Department of Education. Although Dr. Smith will not be leading the Institute, two of her professional colleagues, Dan Meyer and Susan O’Connell will.

June 2–4 will enlighten participants by allowing them to engage, learn and collaborate alongside experts in the content of mathematics. There will be grade-level strands, led by knowledgeable and experienced educators from across Arizona, as well as the country. Attendees will learn to design units, lessons, activities and assessments to address Arizona’s College and Career Ready Standards.

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