CHAPTER 2 Flashcards
the system of words, signs and symbols which people use to
express ideas, thoughts and feelings. It consists of the words, their pronunciation and
the methods of combining them to be understood by a community.
Language
is
the system used to communicate mathematical ideas. The language of mathematics
is more precise than any other language one may think of.
Mathematical Language
Numbers, measurements, shapes, spaces, functions, patterns, data and arrangement are regarded as ________
mathematical nouns or object
mathematical verbs
may be considered as the four main actions attributed to problem solving and
reasoning. These actions represent the process one goes thru to solve a problem.
According to Kenney, Hancewicz, Heuer, Metsisto and tuttle (2005), these four
main actions are:
Modelling and Formulating
Transforming and Manipulating
Inferring
Communicating
creating appropriate representations and
relationships to mathematize the original problem.
Modelling and Formulating
changing the mathematical form in which a
problem is originally expressed to equivalent form that represents solution.
Transforming and Manipulating
applying derived results to the original problem situation and interpreting and generalizing the result
Inferring
reporting what has been learned about a problem to a specified audience.
Communicating
is about ideas – relationships, quantities, processes, measurements, reasoning and so on.
Mathematics
According to Jamison (2000) the use of language in mathematics differs from
the language of ordinary speech in three important ways.
✓ First, mathematical language is non-temporal.
✓ Second, mathematical language is devoid of emotional content
✓ Third, mathematical language is precise
Plus
Addition +
The sum of
Addition +
Increased by
Addition +
Total
Addition +
Added to
Addition +
Minus
Subtraction -
Subtracted from
Subtraction -
Decreased by
Subtraction -
Subtracted from
Subtraction -
Multiplied by
The product of
times
Multiplication X, (), *
Divided by
Division ÷ , /
The quotient of
Division ÷ , /
per
Division ÷ , /
It consists of term and separated with other term with either plus or minus.
A single term may contain an expression in parenthesis or other grouping
symbols.
Mathematical Expression
_______ may consist numerical coefficient (the
number together the variable), literal coefficient (the variable itself) and constant (any single number).
Mathematical expression
Combination of two mathematical expression using a comparison operator.
These expressions either use numbers, variables or both.
Mathematical Sentence
The ______ includes equal, not equal, greater than, greater than or equal to,
less than and less than or equal to.
comparison operator
means that it uses variables, meaning that it is not known whether or not the mathematical sentence is true or false.
Open Sentence
______ that known to be either true or false. It can be a TRUE CLOSED SENTENCE and FALSE CLOSED SENTENCE.
Closed Sentence
There are many symbols in mathematics and most are used as a precise form
of shorthand. We need to be confident when using these symbols, and to gain that
confidence we need to understand their meaning.
Conventions in the Mathematical Language
this is the context in which we are working, or the particular topics being studied,
CONTEXT
- where mathematicians and scientists have decided that particular symbols will have particular meaning
CONVENTION
A well-defined collection of distinct object and is denoted by an uppercase
letter
SETS
An object that belongs to a set is called an _________ and it is
usually denoted by lower case letter.
ELEMENT or MEMBER
Method in which the elements in the given set are listed or enumerated, separated by a comma, inside a pair or braces.
ROSTER/ TABULAR METHOD
Method in which the common characteristics of the elements are defined. This method uses set builder notation where x is used to
represent any element of the given set.
RULE/ DESCRIPTIVE METHOD
A = {m, a, t, h}
Roster form
A = {x∣x is the distinct letters in the words “math”}
Rule form
set that has no elements, denoted by Ø or by a
pair of braces with no element inside.
EMPTY/ NULL/ VOID SET
a set with a countable number of elements.
FINITE SET
a set has uncountable number of element
INFINITE SET
the totality of all the elements of the sets under
consideration, denoted by U.
UNIVERSAL SET
set with same elements
EQUAL SETS
set with the same number of elements.
EQUIVALENT SETS
number of elements
cardinality
sets with at least one common element
JOINT SETS
set have no common element
DISJOINT SETS
set wherein every element of which can be found on the second set. ⊂
SUBSET
If the first set equals the second set, then it is an _______
improper subset
symbol for improper subset
⊆
The set containing all the subsets of the given set with n number of elements
is called the______ with 2n number of elements.
power sets
set whose elements are
found in A or B or in both.
UNION OF SETS A and B (denoted by A U B)
set whose elements
are common to both sets.
INTERSECTION of sets A and B (denoted by A ∩ B)
set whose elements are
found in set A but not in set B.
DIFFERENCE of sets A and B (denoted by A - B)
the set of elements found in the
universal set but not in set A.
COMPLEMENT OF Set A (denoted by A’)
