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## Saturday, April 5, 2014

### The Fuzziness Continues

Taken from  the New York State Testing Guide’s Educator Guide to the Regents Examination in Geometry (Common Core)

Students will be expected to know grade-level mathematical content with fluency and to know which mathematical concepts to employ to solve real-world mathematics problems. Students will be expected to know grade-level mathematical content with fluency and to know which mathematical concepts to employ to solve real-world mathematics problems.

Upon reading this statement I immediately became focused on the word “fluency”.  Just to check my vocabulary, I went to http://www.merriam-webster.com/dictionary/fluency and found two definitions.
1)    the ability to speak easily and smoothly; especially : the ability to speak a foreign language easily and effectively
2)      the ability to do something in a way that seems very easy

 I suspected that definition #1 was not relevant (unless the regents Exams will be oral exams), so definition #2 has to be the meaning intended. But is it? Imagine the mathematical content in a Geometry course actually being described as “easy” by the end of the year. What a goal! What a target! Is it realistic as an expectation? Being a natural skeptic, I went searching for more information. I checked the NYS Testing Guide for Algebra 1 (here) and found this: Students will be expected to know grade-level mathematical content with fluency and to know which mathematical concepts to employ to solve real-world mathematics problems. In both documents, the statements were attached to categories labelled Shift 5: Application and Shift 6: Dual Intensity.  So naturally I needed to delve more. When I wade through the http://www.engageny.org/ site I find that “Shift 6: Dual Intensity” is the tag for this:   Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. What does that mean? I get the practicing and understanding, but what do “more than a balance” and “occurring with intensity” mean?  I find these phrases being used all over the country in all kinds of “Common Core” related documents. This is scary stuff. Do a google search on this statement: “Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity.”  It’s an education in the making.

As a sample, this is from El Toro High School in California:
 Shifts in Mathematics Shift 1 Focus Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom.  They do so in order to focus deeply on only the concepts that are prioritized in the standards Shift 2 Coherence Teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. Shift 3 Fluency Students are expected to have speed and accuracy with simple calculations, teacher structure class time and/or homework time for students to memorize through repetition, core functions. Shift 4 Deep Understanding Students deeply understand and can operate easily within a math concept before moving on.  They learn more than the trick to get the right answer.  They learn the math. Shift 5 Application Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Shift 6 Dual Intensity Students are practicing and understanding.  There is more than a balance between these two things in the classroom – both are occurring with intensity.

Note these are called “shifts.” The implication is that it is all new and different. Some are not new, but some might be, depending on the meaning of the words used. What is the meaning of “Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom”?  I can guess at what it is supposed to mean: fewer concepts so those dealt with can be handled better.  But does it mean that? I cannot tell.  I do know that the authors of that statement did not display much fluency with it.

 The more I delve into Common Core documents at the state, district, and school levels the more I see a strange and unfortunate gathering of words. Delaware even says “Mathematics is not a list of disconnected tricks or mnemonics.” That can be found here.

Oops! Sorry Delaware! That idea was previously written as “Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts. Therefore, the standards are designed around coherent progressions from grade to grade.” This appears in in the original Common Core postings.

I find it insulting that such a statement appears. Thinking it is fine, even encouraged, but to find it relevant and meaningful enough to place in a formal document is an insult to all the people who have been teaching mathematics. If you need to insult some, so be it. But to insult all? That’s terrible.

Am I against the Common Core? Absolutely not. Am I pleased with it as it is? Absolutely not.