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I am MOST disappointed the school uses the Common Core against grade skipping or acceleration stating the Common Core allows for higher level of thinking within the "curriculum" - yet without the use of higher level content.
Some have suggested that when implementing common core teachers could provide differentiation which requires higher level producibles from gifted students. In some cases, this may use higher level content. For example, differentiation in task demands might consist of some students preparing a report on (easy book) while others prepare a more detailed report on (higher level book). Reference the materials linked at this recent thread. From the view of many parents whose gifted children have experienced this approach, this does not solve the problem, rather it exacerbates the difficulties faced by gifted learners.

Under this approach, the gifted students are not receiving more input/teaching/guidance or acceleration to new material but rather are required to produce more output: read more pages, write longer essays, follow additional rubric constraints. They are required to work at a higher level to receive the same grade as their classmates. They are essentially working at a varsity level to maintain a JV team placement. Both the higher task demands and the grading policy/practice may discourage gifted students and encourage underachievement.

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It is really too bad how poorly the GUIDELINES were implemented. It is equally sad to me to see the misinterpretations of something that could have been somewhat helpful for a foundation.
I agree completely. The way common core was designed was really good, but rather than adopting it as a framework, within which to create an appropriate curriculum, or even within which to modify the current curriculum, textbook makers completely screwed it up and wrote it as the curriculum and school boards adopted it that way.
Please consider that the textbook companies may not have been working independently or at crossed purposes to the common core standards; The creators of common core standards could have withdrawn support of textbook companies and changed direction at any time. Please consider that common core may be a bit of a Trojan horse by design: People gladly welcome guidelines and then are surprised by the onslaught of requirements flowing from it.

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... it could be 10 years before common core is out of classrooms.
Some say that if the common core tests and assessments are dropped then common core is essentially out of the classroom: Curriculum can then be taught as local school boards see fit: using standards as a guideline for a performance floor while exercising discretion with regard to skipping material, condensing material, and otherwise teaching material at the grade levels which seem appropriate to each student.

Some parents have reported that their gifted and/or high-achieving children have not been allowed to work ahead under the common core and were given the reasoning that working ahead may cause the student to be focused on newly acquired skills and information, therefore not have the skills and information currently in mind for the common core grade-level assessments, resulting in performing less than optimally on those assessments, penalizing the teacher/school/district.