Problem Solving Approaches In Mathematics For Elementary School Teachers Chapter 1 & 2 Terms

Front 1

Inductive Reasoning

Back 1

the method of making generalizations based on observations and patterns

Front 2

Conjecture

Back 2

a statement thought to be true but not yet proved true or false

Front 3

Counterexample

Back 3

a statement given to prove the opposite false in order to prove something true

Front 4

Sequence

Back 4

ordered arrangement of numbers, figures, or objects

Front 5

Common Difference

Back 5

in a sequence, each term, starting with the second is obtained from this number, the distance between each term in a sequence

Front 6

Arithmetic Sequence

Back 6

a sequence in which each successive term is obtained from the previous term by the addition or subtraction of a fixed number

Front 7

Recursive Pattern

Back 7

a pattern where after one or more consecutive terms are given to start, each successive term of the sequence is obtained from the previous term. ex. 3, 6, 9...

Front 8

Recursive Formula

Back 8

the formula that results from a recursive pattern

Front 9

Ellipsis

Back 9

three dots (...) meaning that the sequence continues infinitely using the same pattern it's been using

Front 10

n-th Term

Back 10

any term in the sequence (note it's lowercase)

Front 11

Geometric Sequence

Back 11

a sequence where each successive term is obtained from the predecessor by multiplying by a fixed nonzero number

Front 12

Ratio

Back 12

the fixed number terms of a Geometric Sequence are derived from

Front 13

Exponent

Back 13

the superscript number that indicated how many times the Coefficient multiplies itself by

Front 14

Coefficient

Back 14

the larger number a Exponent indicates to multiply itself by

Front 15

Figurative Sequences

Back 15

sequences that are neither geometric or arithmetic

Front 16

Triangular Numbers

Back 16

one way to represent Figurative Sequences

Front 17

Negation

Back 17

the opposite of a statement, it makes a true statement false and a false statement true

Front 18

Quantifiers

Back 18

words such as "all, some, every, there exists" that make statements more difficult to negate

Front 19

Conditionals/Implications

Back 19

statements expressed in the form, "If p... then q"

Front 20

Hypothesis

Back 20

the "if" part of a conditional

Front 21

Conclusion

Back 21

the "then" part of a conditional, what it fuond as a result

Front 22

Basic Statement

Back 22

if 'p' then 'q'... a=b

Front 23

Converse

Back 23

if 'q' then 'p'

Front 24

Inverse

Back 24

if not 'p', then not 'q'

Front 25

Contrapositive

Back 25

if not 'q', then not 'p'

Front 26

Biconditional

Back 26

'p', if and only if 'q'. in other words, connecting a statement and its converse with the connective and makes (p -> q) ^(q ->p)

Front 27

Valid

Back 27

if the conclusion of a statement follows unavoidably from the hypothesis

Front 28

Direct Reasoning

Back 28

if the statement "if 'p', then 'q' is true and 'p' is true, 'q' must also be true". also called the law of detachment (modus ponens)

Front 29

Indirect Reasoning

Back 29

if we have a conditional accepted as true, and we know the conclusion is false, then the hypothesis is also false

Front 30

Chain Rule (Transitivity)

Back 30

if "if 'p', then 'q'" and "if 'q' then 'p'" are true, then "if 'p' then 'r'" is true.

A=B and B=C; therefore, A=C

Front 31

Set

Back 31

any collection of objects

Front 32

Elements

Back 32

objects in a Set

Front 33

One-to-One Coorospondence

Back 33

if the elements of sets P and S can be paired so that for each element of P there is one element of S and vice versa

Front 34

Equivalent Sets

Back 34

sets that have a One-to-One Correspondence

Front 35

Cardinal Number

Back 35

the number of elements in a given Set

Front 36

Empty/Null Set

Back 36

a Set containing no elements

Front 37

Finite Set

Back 37

a set whose Cardinal Number is zero or a natural number

Front 38

Infinite Set

Back 38

a set where there is no Cardinal Number... the set instead continues on forever

Front 39

Universal Set

Back 39

denoted by a capital 'U' is the set that contains all elements being considered in a given discussion

Front 40

Subset

Back 40

a set within a set, denoted by an underline capital 'C' letter

Front 41

Proper Subset

Back 41

when every element of a given set is contained in another set but there is at least one element of the first set not in the second set

Front 42

Intersection

Back 42

written A (upside down U) B, the set of all elements common for both A & B

Front 43

Disjoint Set

Back 43

if two sets have no elements in common

Front 44

Set Union

Back 44

the set of all elements in two given sets... basically set addition

Front 45

Set Difference

Back 45

the complement of A relative to be, written B - A, the set of all elements in B that are NOT in A

Front 46

Cartesian Product

Back 46

the set of all ordered pairs such that the first component of of each pair is an element of A and the second is an element of B

Front 47

Logic

Back 47

Common Sense