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The goal of this map is to outline the foundations of math education; detailing how we use math to communicate, reason, and problem solve, by providing background knowledge, resources, and examples to help teachers gain perspecitives on the basics of Mathematical thinking.
One of the most important aspects of math is problem solving. Using math can help us solve real world problems.
Deductive reasoning starts with a general statement or known fact and creates a specific conclusion from that generalization.
Two statements that have the same truth value.
The contrapositve of a conditional statement is made by switching the hypothesis and the conclusion and negating both.
The inverse of a conditional statement is made by negating both the hypothesis and the conclusion.
The converse of a conditional statement is made by switching the hypothesis with the conclusion.
3. Use a rule of logic to determine the truth of the conclusion.
Example: You use a rule of logic to conclude the conclusion is true, you will be accepted into the university.
2. Note the given info about the truth or falsity of the conclusion.
Example: You score a 29. The conclusion is true.
1.Start with a true statement, often in if,then form.
Example: If you score at least a 26 on the ACT you will be accepted into the university.
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.
The negation of a statement is the statement not p, as in, (-p)
A statement is a sentence that is true or false, but not both.
Inductive Reasoning involves the use of information from specific examples to draw a general conclusion.
When you make a generalization using inductive reasoning, you use patterns uncovered by looking at many examples.
Fibonacci Sequence
An example of a patter found in the real world.
Sequence
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.
Geometric Sequences
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.
Arithmetic Sequences
Sequence where the next term is created by adding a fixed number to the previous term.
A counterexample is an example that shows a generalization to be false.
A generalization is general conclusion found from using information from specific examples.
3. Conclude that the relationship is probably true for all other examples and make a generalization.
You conclude that "every day the paperboy delivers the newspaper at 6:00 a.m."
2. Observe that the relationship is true for every example checked.
You observe that each day he delivers the paper at 6:00 a.m.
1. Check several examples of possible relationships.
Example: You observe the paperboy delivering the paper every day for a week.
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.
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.
Types of calculators
Graphing
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.
Scientific
More advanced than the 4 function calculator. Allows the user to complete algebraic and trigonometric problems. Also can help complete more complex statistical problems.
Fraction
In addtion to the 4 basic functions, its primary feature is the ability to work with fractions and mixed numbers.
4 function
The most basic type of calculator, performs the 4 basic functions; addition, subtraction, multiplication, and division.
Using a computer spreadsheet for solving math problems allows someone to manipulate data and try different solutions to the problem quickly and easily.
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 circle graph, also known as a pie chart, is a type of graph used to illustrate the relationship between parts of a whole.
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.
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.
