Mathematical Language and Symbols

Chapter 2 - Mathematical Language and Symbols

Lesson Title

A. Characteristics of mathematical language: precise, concise, and powerful.
B. Expressions vs. sentence
C. Conventions in the mathematical language
D. Four basic concepts: sets, function & relations, binary operations
E. The Real Number and Its properties

Lesson Overview

  • Language is a system of words, signs, and symbols used to express ideas, thoughts, and feelings.
  • It consists of words, pronunciation, and methods of combining them for community understanding.
  • Language is a systematic means of communicating ideas or feelings through conventionalized signs, sounds, gestures, or marks with understood meanings.

Desired Learning Outcomes

  1. Discuss the language, symbols, and conventions of mathematics.
  2. Explain the nature of mathematics as a language.
  3. Perform operations on mathematical expressions correctly.
  4. Acknowledge mathematics as a useful language.

Lesson Content

  • Every science has its own lingo and word usage.
  • Mathematical language is the system used to communicate mathematical ideas and is more precise than ordinary language.
  • It has its own grammar, syntax, vocabulary, word order, synonyms, negations, conventions, idioms, abbreviations, sentence structure, and paragraph structure.
  • Mathematical language includes a large component of logic and uses symbolism.
  • Apt language is key to making mathematics comprehensible and understandable.
  • This language consists of ordinary language using technical terms and grammatical conventions, supplemented by specialized symbolic notations for mathematical formulae.
  • Advanced courses involve understanding interrelationships among sophisticated concepts.
  • All human languages have grammatical structures distinguishing between nouns and verbs.
  • Numbers, measurements, shapes, spaces, functions, patterns, data, and arrangements are mathematical nouns or objects.
  • Mathematical verbs may be modeling and formulating, transforming and manipulating, inferring, and communicating.
Mathematical Verbs:
  • Modeling and formulating: Creating appropriate representations and relationships to mathematical the original problem.
  • Transforming and manipulating: Changing the mathematical form in which a problem is originally expressed to equivalent forms that represent solutions.
  • Inferring: Applying derived results to the original problem situation, and interpreting and generalizing the results in that light.
  • Communicating: Reporting what has been learned about a problem to a specified audience.
  • Expertise in mathematical language requires long and supervised experience.
Characteristics of Mathematical Language
  • Mathematics is about ideas – relationships, quantities, processes, measurements, reasoning, and so on.
  • The use of language in mathematics differs from ordinary speech in three important ways:
    • Mathematical language is non-temporal (no past, present, or future).
    • Mathematical language is devoid of emotional content.
    • Mathematical language is precise.
  • Mathematical notation is highly compact, conveying much information in little space, and focused, conveying only important information.
  • However, symbols can refer to many ideas, which can be a disadvantage for learners.
  • Students must learn to articulate what they learn and answer