Mathematics for Elementary Teachers

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Sequences

Sequence: an ordered list of objects, events, or numbers

Types of Sequences

Recurrence relationship Sequences

Defines a sequence in which the current term is dependent on previous term(s)

Difference: multiply by 2 then add 1

13 multiplied by 2 equals 26 then add 1

Product of 1st term 13

ex. 6, 13, 27, 55..

Geometric Sequences

Sequence of numbers with a common ratio

common ratio -1/2

ex. 8, -4, 2,-1,..

Arithmetic Sequences

Sequences or numbers with a common difference

Adding 2 to each time will create the next number

common difference of 2, 4, 6, 8 is 2

ex. 2, 4, 6, 8, 10

Composed of elements (objects found within)

Problem Solving

Steps

4. Look back (reflect)

Is there an easier way to solve it?

Does it need to be revised?

Does the answer make sense?

Subtopic

3. Carry out the plan

Revise the plan if necessary

If the solution is not visible, rethink the plan

Be persistant with your current plan

2. Devise a plan

Use a model

Create charts, lists, and use objects

Work backwards

Solve a simpler problem

Use an easier problem based on your current problem

Guess and check

Think of solutions and plug into the problem to check answer

1. Identify the problem

Understand the problem

George Polya (1887-1985)

Major contribution was his work in Problem Solving

"..'solving a problem means finding a way out of difficulty, a way around an obstacle, attaining an aim which was not immediately attainable'.." (Billstein 2)

Quote by George Polya pulled from Mathematical Discovery and re quoted in A Problem Solving Approach to Mathematics for Elementary School Teachers 11th edition by Rick Billstein.

Mathematician and Teacher of 20th Century