Assessments: Conceptual Understanding vs. Procedural Fluency

I was at the beginning of my teaching career when the "turmoil" over the common core standards was in full force.  My state had changed their standards to the "Utah Core Standards," but they were really the common core standards in disguise.  They were trying to avoid the terminology "common core" and all the political problems it was causing, but the truth was that the state recognized that these were quality standards, and it would benefit the students in my state if they were implemented.  

Before the 1960's arithmetic was the majority of what was taught in math class.  Then the United States entered the space war with Russia...the USA was determined to become the best.  As a result, the "new math" was introduced.  The "new math" dove into matrices, trigonometry, geometry, and more all on a very conceptual level.  The "new math" eventually received a lot of push back as many people thought it would be more beneficial for students to learn a little about a lot of math.  The curriculum then changed to "a mile wide but an inch deep."  At this point, math became less conceptual and more algorithm based.  The students that naturally had good math reasoning were still pushed along and entered Calculus during high school, but every one else started to get left behind.  This became evident when they entered college. The basic level math classes at the the Universities were full and many students were struggling.  

It was clear that the standards were failing many students.  Purely conceptual wasn't a solution, and purely procedural didn't work either.  The new standards were created with the goal of valuing conceptual and procedural.  With these new standards, the hope of many educators is to not lot students get left behind.  To allow all students to succeed. First, teach at a conceptual level so students can reason through the mathematics and perhaps even discover an algorithm.  Encourage procedural fluency, but only after they have mastered conceptual understanding.  

With these ideas in mind is how I create all of my resources.  Valuing both conceptual understanding and procedural fluency.  If you are interested in some math assessments that assess both conceptual understanding and procedural fluency you can click on the links below. They are also editable for use year after year. 

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