MiddleSchoolPortal/ENCdl Math Subject List

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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.

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