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**Grand Canyon University**- B.S. in Mathematics for Secondary Education

The National Evaluation Series (NES) are national examinations aligned to nationally recognized standards, such as those established by the National Council for Teachers of Mathematics. The NES examinations are computer-based examinations that are taken year-round, by appointment only, through the NES nationwide network of testing centers.

There are two mathematics examinations designed to assess a prospective teacher’s content knowledge in mathematics:

- Middle Grade Mathematics
- Secondary Mathematics

## National Evaluation Series Math Exam: Middle Grade Mathematics

The NES Middle Grade Mathematics examination, which is currently utilized by a few State Boards of Education, consists of 150 multiple-choice questions. Test takers have 4 hours and 15 minutes to complete this examination. The National Benchmark Score for the Middle Grade Mathematics NES exam is 220, and the cost of the exam is $95.

The test framework for the Middle Grade Mathematics examination consists of four content domains (and their percentage of the test score):

*Number Sense and Operations: 17 percent*

Number sense and operations deal with:

- Understanding numbers
- Understanding operations

This content domain may therefore include: analyzing the relationships between the subsets of real numbers; analyzing the use of estimation; and translating between different representations of numbers, among others. It also deals with understanding operations, which include analyzing relational and operational properties and solving a variety of problems involving integers, fractions, decimals, ratios, proportions, and percentages.

*Algebra and Functions: 33 percent*

Algebra and functions deal with:

- Understanding patterns, relations, and functions
- Understanding algebraic techniques and applications
- Understanding linear relations and applications
- Understanding nonlinear relationships and concepts of calculus

This includes analyzing a variety of patterns; solving linear and non-linear equations and inequalities; manipulating algebraic expressions, equations, and inequalities; and analyzing direct and inverse proportional relationships.

*Measurement and Geometry: 25 percent*

Measurement and geometry deal with:

- Understanding measurement principles, procedures, and applications
- Understanding Euclidean geometry in two and three dimensions
- Understanding coordinate and transformational geometry

This includes applying the Pythagorean theorem and its converse; applying principles of similarity and congruence; analyzing properties of points, lines, planes, and angles; and calculating or estimating measures of lengths, areas, and volumes, among others.

*Statistics, Probability, and Discrete Mathematics: 25 percent*

Statistics, probability, and discrete mathematics deal with:

- Understanding principles and techniques of statistics
- Understanding principles of probability and techniques for determining probability
- Understanding principles of discrete mathematics

This includes using appropriate formats for organizing and displaying data; using counting principles to calculate probabilities; analyzing the effects of bias and sampling techniques; applying set theory to solve problems; and applying concepts of permutations and combinations to solve problems, among others.

## National Evaluation Series Math Exam: Secondary Mathematics

The NES Secondary Mathematics examination, which is currently being utilized by a few State Boards of Education, consists of 150 multiple-choice questions. Test takers are given 4 hours and 15 minutes to complete the examination, and the cost of the examination is $95. The National Benchmark Score is 220.

The test framework for the Secondary Mathematics examination consists of five content domains (shown here with their percentage value):

*Mathematical Processes and Number Sense: 19 percent*

Mathematical processes and number sense deal with:

- Understanding mathematical problem solving
- Understanding mathematical communication, connections, and reasoning
- Understanding number theory

As such, content assessment may involve analyzing the group structure of real numbers; analyzing the properties of numbers and operations; recognizing connections between mathematical concepts; and solving mathematical and real-world problems involving integers, decimals, percentages, and fractions, among others.

*Patterns, Algebra, and Functions: 24 percent*

Patterns, algebra, and functions deal with:

- Understanding relations and functions
- Understanding linear, quadratic, and higher-order polynomial functions
- Understanding exponential and logarithmic functions
- Understanding rational, radical, absolute value, and piece-wise defined functions

This section may therefore involve analyzing real-world problems involving linear, polynomial, and high-order functions; solving systems of linear equations or inequalities using a variety of methods; applying the laws of exponents and logarithms; interpreting different representations of functions; and performing operations with functions, including compositions and inverses, among others.

*Measurement and Geometry: 19 percent*

Measurement and Geometry deal with:

- Understanding measurement principles and procedures
- Understanding Euclidean geometry in two and three dimensions
- Understanding coordinate and transformational geometry

Assessment in measurement and geometry may therefore include: analyzing two- and three-dimensional figures using coordinate systems; using the properties of polygons and circles to solve problems; analyzing precision, error, and rounding in measurements and computed quantities; and applying the Pythagorean Theorem and its converse, among others.

*Trigonometry and Calculus: 19 percent*

Trigonometry and calculus deal with:

- Understanding trigonometric functions
- Understanding differential calculus
- Understanding integral calculus

Assessment in this area may therefore include: applying integration to solve real-world problems; calculating the integrals of functions; evaluating limits; demonstrating knowledge of continuity; and applying trigonometric functions to solve problems involving distance, angles, and the unit circle, among others.

*Statistics, Probability, and Discrete Mathematics: 19 percent*

Statistics, probability, and discrete mathematics deal with:

- Understanding principles and techniques of statistics
- Understanding principles and techniques of probability
- Understanding principles of discrete mathematics

As such, assessment in this area may involve: applying set theory to solve problems; analyzing uniform, binomial, and normal probability distributions; performing operations on matrices and vectors; and analyzing the effects of bias and sampling techniques, among others.

## NES Mathematics Examinations: Content and How to Prepare

Individuals can best prepare to take the NES examinations in mathematics by thoroughly reading the test framework:

Pearson Testing offers free videos and tutorials that guide test takers on how to prepare for the examination and what to expect when taking the NES computer-based examinations:

Further, NES Prep Interactive Study Guides (There is a fee for access to this service.) allow test takers to experience sample questions and understand their strengths and areas that need improvement.