# MSP:MiddleSchoolPortal/ENCdl Math Subject List

### From Middle School Portal

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 | |||||

Quadratic | |||||

Rational | |||||

Systems of equations | |||||

Functions | Use when resources focus on meaning of function. Usually appropriate for precalculus work. | ||||

Exponential | |||||

Linear | |||||

Logarithmic | |||||

Piecewise | |||||

Polynomial | |||||

Quadratic | |||||

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 | |||||

Addition | |||||

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 | ||||

Addition | |||||

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 | |||

Addition | |||||

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 | |||||

Reading in mathematics | |||||

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 | ||||

Standard deviation | Measures of spread | ||||

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.

#### Copyright

The Ohio State University holds copyright on all original materials we publish but grants permission for materials to be reproduced or to be adapted and used by others under a Creative Commons 3.0 Share-Alike license. Please contact Kimberly Lightle if you plan on using this resource.

Please use the following format to credit OSU.

Reprinted/Modified from ENCdl Mathematics subject list, version 1.0. Retrieved [insert date], from NSDL Middle School Portal: **ENCdl Mathematics Subject List**. Copyright The Ohio State University.