HoB icon

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

 

 

Top