# What to Expect from the NES Math Exam

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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:

• 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.