Behind the curtain: the thinking and processes of Mathematics

Mathematics is a language of words and symbols, used as a way to communicate ideas and explanations of numbers, space (geometry), and things that occur in our everday lives.

We encounter graphs and data everywhere in our daily lives, when we read the newspaper, watch television, and in our careers and schooling, that tell us all kinds of information. We must learn and practice how to interpret and analyze this information in order to use it effectively.

A Bar Graph is a visual display used to compare the amounts or frequency of different types of information. Bar graphs can help us make generalizations about data quickly.

A circle graph, also known as a pie chart, is a type of graph used to illustrate the relationship between parts of a whole.

With the increasing prevalence of technology in our society, it now plays an ever important role in helping people communicate ideas about math. We can communicate to help solve problems, present solutions, and analyze all kinds of mathematical topics.

Using a computer spreadsheet for solving math problems allows someone to manipulate data and try different solutions to the problem quickly and easily.

A calculator can help students perform math calcluations quickly and easily. This allows students more time to think about bigger picture stuff, like ideas, patterns, relationships, and problem solving, and less time doing calculations.

The most basic type of calculator, performs the 4 basic functions; addition, subtraction, multiplication, and division.

In addtion to the 4 basic functions, its primary feature is the ability to work with fractions and mixed numbers.

More advanced than the 4 function calculator. Allows the user to complete algebraic and trigonometric problems. Also can help complete more complex statistical problems.

In addition to having the capability to perform all of the functions of a scientific calculator, a graphing calculator can produce graphs of data or information.

Inductive Reasoning involves the use of information from specific examples to draw a general conclusion.

Example: You observe the paperboy delivering the paper every day for a week.

You observe that each day he delivers the paper at 6:00 a.m.

You conclude that "every day the paperboy delivers the newspaper at 6:00 a.m."

A generalization is general conclusion found from using information from specific examples.

A counterexample is an example that shows a generalization to be false.

When you make a generalization using inductive reasoning, you use patterns uncovered by looking at many examples.

Definition: A pattern involving an ordered arrangment of numbers. geometric figures, letters, or other objects. The numbers, figures, letters, etc. that make up a sequence are called the terms of the sequence.

Sequence where the next term is created by adding a fixed number to the previous term.

Sequence in which each term is created from the previous term by multiplying by a fixed number. The fixed number used in the multiplication is called the common ratio.

An example of a patter found in the real world.

Deductive reasoning starts with a general statement or known fact and creates a specific conclusion from that generalization.

A statement is a sentence that is true or false, but not both.

The negation of a statement is the statement not p, as in, (-p)

A type of statement that is in the If, then sentence format: example: If you wear Air Jordan sneakers, then you will play like Michael Jordan. Conditional statements are represented by p >(arrow) q.

Example: If you score at least a 26 on the ACT you will be accepted into the university.

Example: You score a 29. The conclusion is true.

Example: You use a rule of logic to conclude the conclusion is true, you will be accepted into the university.

The converse of a conditional statement is made by switching the hypothesis with the conclusion.

The inverse of a conditional statement is made by negating both the hypothesis and the conclusion.

The contrapositve of a conditional statement is made by switching the hypothesis and the conclusion and negating both.

Two statements that have the same truth value.

One of the most important aspects of math is problem solving. Using math can help us solve real world problems.