# MiddleSchoolPortal/ENCdl Math Subject List

In 1998, content specialists at the Eisenhower National Clearinghouse began a review of the existing ENC mathematics subject list with a task force that has evolved into the present Mathematical Sciences Conference Group on Digital Educational Resources. The goal was to establish a vocabulary that reflected the needs of both K-12 educators and university mathematics and statistics educators. Based on the existing ENC mathematics subject list and with input from the Mathematical Sciences Conference Group, ENC content specialists created a vocabulary list suitable for our K-12 audience that also can be mapped to the Core Subject Taxonomy created by the Mathematical Sciences Conference Group. The ENCdl Mathematics Subject List is a working vocabulary that is mathematically correct, reflects the NCTM standards, and will serve the resource discovery needs of K-12 mathematics educators.

Subject Terms, Level 0 Subject Terms, Level 1 Subject Terms, Level 2 Subject Terms, Level 3 Scope Notes Equivalent and/or Related Terms
Algebra
Abstract algebra Usually used for resources beyond K-12. Groups, rings, fields, ideals
Algebraic manipulation Appropriate for working with algebraic expressions. Expressions
Exponents
Factoring
Fractions
Order of operations
Algebraic proof
Equations Use when resource is about solving equations or graphing equations. Appropriate for first algebra course.
Exponential
Slope
Logarithmic
Parametric
Polynomial
Rational
Systems of equations
Functions Use when resources focus on meaning of function. Usually appropriate for precalculus work.
Exponential
Linear
Logarithmic
Piecewise
Polynomial
Rational
Step
Graphing techniques Techniques capable of producing animated graphing sequences based on mathematical formulas (ERIC) Graphing utilities (ERIC)
Inequalities
Linear algebra
Linear programming Subject encompasses optimizing a function under fixed constraints. Optimization
Linear transformations
Matrices Matrix, matrix algebra
Systems of linear equations
Vectors
Sequences and series
Calculus
Continuity
Differentiation
Functions Use when a resource is designed to build understanding of functions in the context of continuity, limits, and differentiation.
Integration
Limits
Multivariate
Series Fourier series
Discrete mathematics
Algorithms
Chaos
Combinations and permutations
Game theory Method for analyzing situations of strategic interaction between competing agents or parties, where an agent's payoff from competition is affected not only by its own actions but also by the actions of its competitors. (ERIC)
Graph theory
Recursion and iteration
Geometry
Analytic geometry
Cartesian coordinates Cartesian plane
Circles Assign when the resource builds understanding about equations of circles and their algebraic properties.
Conics
Distance formula
Lines
Planes
Polar coordinates
Surfaces
Fractal geometry Assign for fractal resources that may explain self-similarity or the generation of a fractal image and the related mathematics.
Geometric proof
Plane geometry If resource focuses on quantitative, see Measurement. Euclidean geometry
Angles
Circles For resources about circumference and area of circles, see Measurement.
Congruence
Construction
Lines and planes
Polygons For area and perimeter, see Measurement.
Pythagorean theorem
Quadrilaterals For area and perimeter, see Measurement.
Scale Use when the resource is about enlarging or shrinking a shape. Proportional
Similarity
Symmetry
Tilings and tessellations
Transformations Substitution of one mathematical configuration or expression by another in accord with a mathematical rule. (ERIC)
Triangles Assign for resources about triangle theorems. For area and perimeter of triangles, see Measurement.
Solid geometry
Cones
Cylinders
Polyhedra
Prisms
Pyramids
Spheres
Logic and foundations
Methods of proof
Propositional and predicate logic
Sets and set operations Set theory
Venn diagrams
Mathematics history
Biographies of mathematicians
Early number systems Assign for specific cultural number systems with unusual notation or counting systems other than base ten
Famous problems
Measurement Process of obtaining a numerical description of the extent to which persons, organizations, or things possess specified characteristics. (ERIC)
Angle measure Angular measurement
Area
Area of circles
Area of polygons
Nonstandard shapes
Surface area
Circumference
Length Distance
Money
Perimeter
Rate Speed
Scale Scale drawing
Systems of measurement Units of measurement
English Standard units, customary units
Metric
Nonstandard Nonstandard units may include paperclips, unifix cubes, finger length, etc.
Temperature Celsius, Fahrenheit
Time Assign to resources about topics such as telling time, elapsed time, reading a calendar, or reading a schedule. Calendar
Volume
Weight and mass
Number and operations Computation
Arithmetic
Comparison of numbers
Composition and decomposition of numbers Expanded form
Counting Skip counting
Decimals
Division
Multiplication
Subtraction
Exponents Powers
Factorials
Factors Assign when working with numbers, not when working with expressions or equations. Greatest common factor, least common multiple
Fractions Mixed numbers
Division
Equivalent fractions
Multiplication
Subtraction
Number sense Assign to resources about the development of early math skills such as recognizing groups of objects, matching names and numerals, or developing the concept of one-to-one correspondence.
Operations Assign for a discussion of operations with any subset of the real numbers not specific to decimals or fractions. Computation
Division
Multiplication
Properties of operations Associative, commutative, distributive, equality, transitive
Subtraction
Percent Percentage
Place value Number bases
Ratio and proportion Proportional
Roots Cube roots, square roots
Number concepts
Complex numbers Imaginary numbers
Famous numbers
e
Golden ratio Golden mean
i
Pi
Zero
Integers Negative numbers, positive numbers
Irrational numbers
Prime numbers
Rational numbers Assign as subject when resource discusses fractions, repeating or terminating decimals, and integers as part of one set.
Real numbers
Whole numbers Counting numbers
Patterns and sequences
Arithmetic sequence A sequence with a constant common difference between terms.
Fibonacci sequence
Geometric patterns
Geometric sequence A number sequence with a nonzero constant ratio between terms.
Number patterns Can be assigned to patterns arranged spatially such as magic squares. Pascal's triangle
Number theory Includes the study of algebraic and transcendental numbers.
Cryptography The study or analysis of codes and coding methods. (ERIC, use Technology)
Modular arithmetic
Primes Assign to resources with information about prime numbers such as types, theories, patterns, etc.
Probability
Combinations and permutations
Conditional probability
Distributions Tables or graphs of observed, predicted, or theoretical data indicating either the probability or the number of instances to be found along successive intervals of an ordered scale -- also, the mathematical functions of distributions. (ERIC, use Statistical Distribution)
Binomial distribution
Continuous distributions
Discrete distributions
Expected value
Normal distribution
Variance
Experimental and theoretical probability
Independent events
Limit theorems
Central limit theorem
Law of large numbers
Random variables
Sample space and events
Process skills Broadly transferable intellectual skills, appropriate to all scientific endeavors -- includes basic process skills (e.g., observing, inferring, measuring, communicating, classifying, predicting, using time-space relations, using numbers) and integrated process skills (e.g., controlling variables, defining operationally, formulating hypotheses, interpreting data, experimenting, formulating models). (ERIC, use Science Process Skills)
Algorithms Use when resource addresses the use or development of algorithms
Communication
Mathematical language
Writing in mathematics
Concept formation
Connections Resources may demonstrate connections within different fields of mathematics or to subjects outside of math.
Estimation The act or method of calculating or estimating through the use of number operations and/or other mathematical processes. (ERIC, use Computation)
Mental calculation
Problem solving
Strategies
Word problems Mathematical problems expressed in narrative form -- answered by conversion of the circumstances to equivalent computations or equations, which can be solved arithmetically, algebraically, or with symbolic logic. (ERIC)
Reasoning Interrelated, generally "higher-order" cognitive skills that enable human beings to comprehend experiences and information, apply knowledge, express complex concepts, make decisions, criticize and revise unsuitable constructs, and solve problems -- used frequently for a cognitive approach to learning that views explicit "thinking skills" at the teachable level. (ERIC, use Thinking Skills)
Critical thinking
Deductive reasoning
Inductive reasoning
Representation Can be applied to both processes and products.
Algebraic representation
Modeling Spatial representations, models
Visual representation Can refer to graphic representation.
Spatial sense Assign when a resource supports developing understanding of relationships in either two or three dimensions.
Visualization Assign when resource supports the understanding of an abstraction through the use of an image.
Real world applications
Cartography and surveying Triangulation
Consumer mathematics Finance, interest
Engineering mathematics
Mathematics for biology
Mathematics for computer science
Mathematics for social science Social science fields include psychology, sociology, and political science.
Mathematics for the physical science Physical science fields are chemistry and physics.
Statistics Branch of mathematics dealing with collections of quantitative data. (ERIC)
Data analysis Preparation of factual information items for dissemination or further treatment (includes compiling, verifying, ordering, classifying, and interpreting). (ERIC) Statistical analysis
Bayesian statistics Procedures that combine data from new observations with prior observations or estimates to derive new and more precise estimates. (ERIC) Bayes' theorem
Confidence intervals
Data distribution Range
Error analysis
Hypothesis tests Significance testing
Mean, median, and mode Measures of central tendency
Regression and correlation Linear regression
Data collection
Data and measurement issues
Experimental design The underlying plan or organization of a research project or study that determines its scope and approach -- also, the process of planning and organizing research activities. (ERIC, use Research Design) Bias
Sampling and surveys Selecting a representative part of a population to draw inferences about the characteristics of the whole population. (ERIC, SN is only for Sampling, not for Surveys)
Data presentation
Bar graph
Box and whisker plot
Frequency graph
Histogram
Scatter plot
Stem and leaf plot
Table
Topology Study of the properties of geometric forms that remain constant under such transformations as bending or stretching. (ERIC) Knots
Trigonometry
Angles
Inverse trigonometric functions
Trigonometric equations
Trigonometric functions Periodic functions
Trigonometric identities

#### Disclaimer

The ENCdl Mathematics Subject List was created by the Eisenhower National Clearinghouse for Mathematics and Science Education. ENC was funded at least in part through Contract No. RJ97071001 with the U.S. Department of Education. The ideas and opinions expressed here do not necessarily reflect the positions or policies of the U.S. Department of Education.