Math Representation in Language

Math representations in language

The single biggest problem with communication is the illusion that it has taken place.

George Bernard Shaw

Overview

The following table summarizes different representations in the language of mathematics!

The mathematical objects (nouns) being operated upon by a mathematical action which can be represented as a manipulation (verb) in a manner in which we believe is appropriate for elementary students and therefore a necessary part of an elementary curriculum. See additional resources

Mathematical Objects (nouns)	Mathematical Actions (verbs)
Types of objects	Properties of objects	Practicle use	Operations on objects
Number/quantity integers rational numbers real numbers measures of: length area volume time weight	order between-ness part/whole relationships units dimensions	counting measuring	Arithmetic operations addition subtraction multiplication division expotential
Shape/space metric - value between two points lines/segments polygons circles conic sections spherical shapes topological properties - geometric properties and spatial relations unaffected by the continuous change of shape or size of figures.	distance location symmetry similarity connectedness enclosure	mapping and traveling designing and building objects	translation rotation reflection covering, packing, & tessellating scaling projection inversion conformal mapping homotopies/deformations
Pattern/function linear quadratic power rational periodic transcendental	input/output domain/range continuity boundedness rate of change, curvature, etc. maxima and minima rate of accumulation linear-root, slope/intercept quadratic-roots, axis of symmetry power-roots, asymptotic behavior rational-roots, singularities, asymptotic behavior periodic-frequency, phase transcendental-"growth" constant	expressing how something depends on another - one or more other things resolving constraints (solving equations and inequalities)	identifying and describing repetitive relationships arithmetic operations (functions on Rn) comparison equations inequalities identities composition translation reflection dilation/contraction
Arrangements combinations permutations graphs networks trees	adjacency enumeration vertices and edges of graphs/networks	organizing discrete information	tends to be closely connected to the idea of repetitive pattern at this level
Chance/data discrete continuous	determinism randomness relative frequency distribution moments	dealing with uncertainty dealing with lack of precision	sampling (by counts and/or measures) composing representing

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