Essential Mathematics Understandings
Content, Process, and Principles
Content: (formerly “Essential Mathematics Understandings in 10
discrete categories)
Students will understand that:
 Algebraic Reasoning: Patterns and Functions – Patterns and functional
relationships can be represented and analyzed using a variety of
strategies, tools and technologies.
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Numerical and Proportional Reasoning – Quantitative relationships can
be expressed numerically in multiple ways in order to make connections
and simplify calculations using a variety of strategies, tools and
technologies.
Geometry and Measurement – Shapes and structures can be analyzed,
visualized, measured and transformed using a variety of strategies, tools
and technologies.
Working with Data – Data can be analyzed to make informed decisions
using a variety of strategies, tools and technologies.
Process: (formerly Habits of the Mind)
Students will understand these habits of the mind:
 One must understand the underlying structure and relationship of
numbers and operations in order to compute, estimate, and solve
mathematical problems in a meaningful way.
 To be a successful problem solver, one needs to acquire a variety of
mathematical problem soling strategies, and to know how to select the
appropriate strategies based on context and purpose.
 Reasoning is essential to all mathematical understanding in order to
arrive at, justify, and prove appropriate solutions.
 Mathematics requires the effective and appropriate use and application
of a variety of constructed, drawn, written, and oral communication
tools.
 Making connections among mathematical concepts is necessary to
strengthen and further mathematical understanding.
 Representation is central to the study of mathematics and should be
developed in order to build new understandings of concepts and
relationships and serve as tools for thinking about and solving problems.
Principles:
Teachers will understand:
 Equity – Excellence in mathematics education requires high
expectations and strong support for all students.
 Curriculum – A curriculum should be more that a collection of
activities: it must be coherent, focuses on important mathematics,
and well articulated across the grades.
 Teaching – Effective teaching requires what students know and need
to learn and then challenging them and supporting them to learn it
well.
 Learning – Students must learn mathematics with understanding,
actively building new knowledge from experience and prior
knowledge.
 Assessment – Assessment should support the learning of important
mathematics and furnish useful information to both teachers and
students.
 Technology – Technology is essential in teaching and learning
mathematics; it influences the mathematics that is taught and
enhances students’ learning.
Principles and Standards for School Mathematics, NCTM, 2000.