New Math Standards: 6–8

As described in the Partnership for Assessment of Readiness for College and Careers (PARCC) Model Content Frameworks for Mathematics:

The two major evidence-based principles on which the standards are based are focus and coherence. Focus is necessary so that students have sufficient time to think, practice and integrate new ideas into their growing knowledge structure. Focus is also a way to allow time for the kinds of rich classroom discussion and interaction that support the Standards for Mathematical Practice.

The second principle, coherence, arises from mathematical connections. Some of the connections in the standards knit topics together at a single grade level. Most connections, however, play out across two or more grade levels to form a progression of increasing knowledge, skill or sophistication. The standards are woven of these progressions. Likewise, instruction at any given grade would benefit from being informed by a sense of the overall progression students are following across the grades.

Another set of connections is found between the content standards and the practice standards. These connections are absolutely essential to support the development of students’ broader mathematical understanding. Mathematics is not a checklist of fragments to be mastered, doing and using mathematics involves connecting content and practices.

Focus is critical to ensure that students learn the most important content completely, rather than succumb to an overly broad survey of content. Coherence is critical to ensure that students see mathematics as a logically progressing discipline, which has intricate connections among its various domains and requires a sustained practice to master. Focus shifts over time.

In middle school, multiplication and division develop into powerful forms of ratio and proportional reasoning. The properties of operations take on prominence as arithmetic matures into algebra. The theme of quantitative relationships also becomes explicit in grades 6–8, developing into the formal notion of a function by grade 8. Meanwhile, the foundations of high school deductive geometry are laid in the middle grades. Finally, the gradual development of data representations in grades K–5 leads to statistics in middle school: the study of shape, center and spread of data distributions; possible associations between two variables; and the use of sampling in making statistical decisions.

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