MATHEMATICS AS A LANGUAGE Mathematics in the Modern

MATHEMATICS AS A LANGUAGE Mathematics in the Modern World

Wait! Before we talk about “MATH” Lets PLAY A GAME!

Ooopss… …just a game of what’s next!!!

WHAT’S NEXT? ANSWE R:

WHAT’S NEXT? ANSWE R: 12, 345, 654, 321

1 3 7 15 31 WHAT’S NEXT? ANSWE R: IS THE ONLY EXPLANATION?

WHAT’S NEXT? ANSWE R:

WHAT’S THE PATTERN IN THE GIVEN SET OF EQUATIONS ?

LETS BEGIN!

How did you learn your native language? (Filipino/Chinese English/Japanese Korean…)

MATHEMATICS AS LANGUAGE A LANGUAGE is a systematic means of communicating by the use of sound or conventional symbols. It is the code we all use to express ourselves and communicate to others.

Components of a language: q. Vocabulary of symbols or words q. Grammar or rules of how these symbols are used q. Community of people who use and understand these symbols q. Range of meanings that can be communicated with these symbols.

• ENGLISH LANGUAGE MATHEMATICAL LANGUAGE • Symbols: English Letters/ Arabic Numerals • Vowels and Consonants Variables and Constants • Words • Phrases • Sentences Term Algebraic Expressions Mathematical statements: Equations, Inequalities, etc

ELEMENTS OF THE MATHEMATICAL LANGUAGE •

• The Language of Mathematics was designed so we can write about: 1. Things like Numbers, Sets, Functions, etc. 2. What we Do with those things (add, subtract, multiply, divide, join together, etc. )

SYMBOLS Mathematics uses symbols instead of words: q. There are the 10 digits: 0, 1, 2, . . . 9 q. There are symbols for operations: +, −, ×, /, . . . q. And symbols that "stand in" for values: x, y, . . . q. And many special symbols: π, =, <, ≤, . . .

LETTER CONVENTIONS • Often (but not always) letters have special uses: Examples What they usually mean Start of the alphabet: a, b, c, . . . constants (fixed values) From i to n: i, j, k, l, m, n Positive integers (for counting) End of the alphabet: . . . x, y, z variables (unknowns) • Those are not rules, but they are often used that way.

Example: y = ax + b • People will assume that a and b are fixed values, • And that x is the one that changes, which in turn makes y change.

NOUNS, VERBS, SENTENCES • Even though we don't use the words "noun", "verb", or "pronoun" in Mathematics, you can imagine these similarities to English: q. Nouns could be fixed things, such as numbers, or expressions with numbers: 15 2(3 -1/2) 42 q. The Verb could be the equals sign "=", or an inequality like < or >

NOUNS, VERBS, SENTENCES q. Pronouns (things like it, he, you, etc. ) could be variables like x or y: 5 x-7 xy 2 -3/x q. And they could be put together into a Sentence like this: 3 x + 7 = 22