Practice and Content Standards

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## Toward greater focus and coherence

These Standards define what students should understand and be able to
do in their study of mathematics. Asking a student to understand
something means asking a teacher to assess whether the student has
understood it. But what does mathematical understanding look like? One
hallmark of mathematical understanding is the ability to justify, in a
way appropriate to the student's mathematical maturity, why a
particular mathematical statement is true or where a mathematical rule
comes from. There is a world of difference between a student who can
summon a mnemonic device to expand a product such as $(a + b)(x + y)$
and a student who can explain where the mnemonic comes from. The
student who can explain the rule understands the mathematics, and may
have a better chance to succeed at a less familiar task such as
expanding $(a + b + c)(x + y)$. Mathematical understanding and
procedural skill are equally important, and both are assessable using
mathematical tasks of sufficient richness.

The Standards set grade-specific standards but do not define the
intervention methods or materials necessary to support students who
are well below or well above grade-level expectations. It is also
beyond the scope of the Standards to define the full range of supports
appropriate for English language learners and for students with
special needs. At the same time, all students must have the
opportunity to learn and meet the same high standards if they are to
access the knowledge and skills necessary in their post-school lives.
The Standards should be read as allowing for the widest possible range
of students to participate fully from the outset, along with
appropriate accommodations to ensure maximum participaton of students
with special education needs. For example, for students with
disabilities reading should allow for use of Braille, screen reader
technology, or other assistive devices, while writing should include
the use of a scribe, computer, or speech-to-text technology. In a
similar vein, speaking and listening should be interpreted broadly to
include sign language. No set of grade-specific standards can fully
reflect the great variety in abilities, needs, learning rates, and
achievement levels of students in any given classroom. However, the
Standards do provide clear signposts along the way to the goal of
college and career readiness for all students.

Follow the links on the left to view the standards.