Espanola Public Schools
Introduction and Information
Mathematic Curriculum and Pacing Guides

Curriculum Alignment Matrices are guidelines used by educational professionals to determine what should be taught and when it should be taught. These documents provide details that should be extremely useful to instructional leaders and teachers.

• New Mexico's standards with benchmarks are extended to the performance objective level in the first column.

• Next appears the Pacing Guides which are designed to link recognized best practice in Reading/Language Arts, Mathematics, Science, and Social Studies to the New Mexico Standards with Benchmarks and accompanying Performance Objectives through an appropriate scope and sequence. The scope and sequence was developed using the New Mexico Standards with Benchmarks and accompanying Performance Objectives, a research base of 5 state-wide scope and sequences, input from curricular experts with in the Espanola Public Schools, and best practices in the specific field which link to the best practices and "big ideas." The letter "I" refers to the Introduction of the Performance Objective, the letter "D" refers to the continued Development of the Performance Objective, the letter "M" refers to the Mastery of the Performance Objective and the letters "M/E" refers to the Mastery/Extension of the Performance Objective.

• The next column contains importance indicators. An L (low), H (high), or M (medium) in the NMSBA/CRT/DIBELS column is meant to signify the relationship between the performance objective and success on the assessment.

• Performance objectives marked H must be taught prior to the testing window, those marked M ought to be maintained throughout the year and those assigned L may be introduced at any point, but will not be essential for success on this year's assessment.

• The 4th column lists Resources and Materials that can be utilized during instruction to meet the Performance Objectives. This includes, but is not limited to, academic vocabulary, video lessons which show teachers using best practices to teach Performance Objectives, and instructional materials.

• Column 5, labeled "Suggested Assessments," gives examples of what teachers can do in the classroom with students, to meet Performance Objectives. These are activities that will help students demonstrate knowledge and understanding of Performance Objective.

• Last three columns addresses Procedural Knowledge, Conceptual Knowledge, and Contextual Knowledge:

Procedural Knowledge

• Knowledge of formal language or symbolic representations

• Knowledge of rules, algorithms, and procedures

Conceptual Knowledge

• Knowledge rich in relationships and understanding

• It is a connected web of knowledge, a network in which the linking relationships are as prominent as the discrete bits of information.

• Examples concepts - square, square root, function, area, division, linear equation, derivative, polyhedron

• By definition, conceptual knowledge cannot be learned by rote. It must be learned by thoughtful, reflective learning.

Conceptual knowledge refers to a person's representation of the major concepts in a system. Examples include being able to answer questions such as, "What is the difference between the units-column and the tens-column in two-column addition problems such as 39+45=___?"

Conceptual knowledge is also known as: The kind of knowledge that may be transferred between situations.

Contextual Knowledge

Contextual knowledge is of a set of features, and environment, or setting within which a learner makes connections, comparisons and analogies. Contextual knowledge is cognitively complex and requires a great deal of information processing from learners trying to interpret schema. It requires both declarative and procedural knowledge to derive understanding of an environment.

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