“Going deep” to meet math standards
By Gene M. Kerns, EdD, Vice President and Chief Academic Officer
With Common Core, like any other complex initiative, we have to first take in the larger, straight-forward ideas before ever considering some of the nuances. Now that most states are years into work with the initiative, some more nuanced discussions are possible. I would like to suggest one such discussion around the mathematics standards.
I believe that Appendix A of the Mathematics Standards is very inappropriately titled. “Designing High School Mathematics Courses Based on the Common Core State Standards” suggests that it’s a document for high school only. But ideas and suggestions contained in the document clearly impact middle schools, and even indirectly impact elementary schools.
In terms of its impacts on middle schools, I am referring to discussions of a suggested “compacted pathway” option where capable students might, after finishing Grade 6, step onto a “compacted pathway” where “nothing is omitted” but they cover Grade 7 and Grade 8 topics, as well as year one of the high school they will attend, all over their two final years of middle school. While the goal of this appendix is to prepare students for high school coursework leading to a full calculus course, the actual work clearly begins in middle school with the identification of compacted pathway candidates and delivery of initial content.
The indirect impact relevant to K-6 is what this appendix means for “enrichment” or “acceleration” or “giftedness.” The compacted pathway is the first time the Standards discuss enrichment or acceleration as moving ahead to higher, more advanced concepts or content. Though not stated directly, the framework of the compacted pathway coupled with the Core’s emphasis on depth, rigor, and application, brings us to a place where we need to redefine enrichment, acceleration, or giftedness in K-6 as “going deeper, as opposed to going ahead.”
To me, this echoes the ideas of education researcher and early learning expert Dr. Amanda VanDerHeyden when she noted that “the classic mistake that many teachers make consistently is moving students on to more advanced content in mathematics when they are somewhat proficient, but before they have truly achieved mastery” (VanDerHeyden, 2013). Similarly, Dr. Mary Ellen McGraw, recently retired from the Delaware Department of Education, often spoke of how we too often “hurry kids along to failure” in mathematics (McGraw, 2013).
What both of these individuals and the Standards are all trying to say is that moving students ahead too quickly in mathematics, particularly in the early grades, is an inherently dangerous enterprise. Kindergarten through Grade 6 is a time of building deep, solid foundations on which to build future success. Building such foundations takes time and the process really can’t be rushed. Concepts must be solid and that means allowing time for things to cure.
The Publishers’ Criteria for Common Core Mathematics K-8 advises that “students who are ‘ready for more’ can be provided with problems that take grade-level work in deeper directions, not just exposed to later grades’ topics” (page 12). Go deeper and build unquestionably deep foundations before you ever consider bringing in topics from later grades.
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