Mat156: Tanya Jaseph

Definition

Engaging in a task for
which the solution method
is not known in advance

Good to Know

A reasonable amount of
tension and discomfort
improves problem solving
performance.

Good Mathematical
Problem Solving
Occurs When...

Students are presented
with a situation that they
understand but do not
know how to proceed

Students are interested
in finding the answer and
attempt to do so

Students are required to use
mathematical ideas to solve
the problem.

4 Steps to Problem
Solving

1.) Understand the Problem

State the problem in
in your own words

What are you trying
to do or find?

What information is missing
or unknown?

What information does the
problem give?

What information is missing
or not needed?

2.) Devise a Plan

Look for a pattern

Compare to a similar problem

Compare to an easier problem

Make a table or a list

Make a diagram

Write an equation

Guess & Check

Work backwards

Break problem down to subgoals

Use indirect reasoning

Use direct reasoning

3.) Carry Out Your Plan

Implement a strategy

Check each step

Is there another method
to solve the problem

Show all your work

4.) Looking Back

Check your results

Could you solve the problem
a different way?

Understand the results in
terms of the original pattern

Find another problem to
practice using this method
to solve

Gearge Cantor created
set theory (1871-1884)

Sets and relations between sets,
are a basis to teach children the
concept of whole numbers and
the concept of "less then" as well
as addition, subtraction, and
multiplication of whole.

Definitions

Set: Any collegtion
of objects

Equal Sets

Two sets are equal if,
and only if, they contain
exactly the same elements

Empty/Null Set

Has nothing in it

{ }

O

the line striking
through should
be diagonal

Finite Set

The cardinal number is Zero
or a natural number

Universal Set

All elements being considered
in a given discussion

Elements

Individual objects
or members of a
set

Cardinal Number

The number of
elements in a set

Methods of
Describing Sets

Listing Method

C = { 1, 2, 3, 4 }

Set Builder Notation

C = { x| x e N where x < 5 }

Set C / is equal to / the set of / all elements x / such that / x is a natural number/ where / x is less then 5