Introduction To Problem Solving

Name: Introduction To Problem Solving
Rating: 4.2 (40 reviews)

In this short course I use 2 problems to illustrate Polya's 4-step problem solving method.

Created byDamon Gang

Last updated 7/2022

English

English [Auto],

What you'll learn

Become Better At Problem Solving
Become More Confident In Math Classes
Become A Better Math Student
Increase In Basic Math Knowledge

Course content

4 sections • 15 lectures • 48m total length

Introduction1:13
Explore fundamentals of problem solving, learn mathematics, and build confidence while developing a personal heuristic to generate solutions using diverse methods at a high school level.
Introduction 23:05
Explore how solving problems improves through experience and effort by identifying the unknown, givens, data, and conditions, and relating new problems to familiar ones to stay in flow.
My Recording Technology And The Enemy Of The Good1:55

The 4 Phases Of Problem Solving3:07
The Diagonal Problem1:53
Phase 1 Understand The Diagonal Problem3:27
Phase 2 Plan The Diagonal Problem's Solution2:23
I said quadratic formula but I meant Pythagorean theorem.
Phase 3 Execute The Plan For Solving The Diagonal Problem2:33
Execute the plan to derive the space diagonal X from A, B, C, showing X = sqrt(A^2 + B^2 + C^2) using A^2 + B^2 = Y^2.
Phase 4 Examine The Solution To The Diagonal Problem4:56

The Handshake Problem3:33
Phase 1 Understand The Handshake Problem1:34
Phase 2 Plan To Solve The Handshake Problem2:33
Do The Plan For The Handshake Problem8:15
The lecture derives the handshake problem, showing how handshakes tally to one plus two plus three, forming triangular numbers, and culminates in the formula n(n-1)/2 for n people.
Examine The Handshake Solution5:30
Examine the handshake solution to verify triangular numbers and their link to Pascal's triangle, then extend the idea by checking results and exploring problem-solving connections.

Requirements

One should be roughly at the Secondary / High School level or higher.

Description

You will see Polya's 4-step method applied to 2 problems. Both problems use mathematics at about the High School level. The first problem will use some basic geometry and the Pythagorean theorem. The second problem uses some basic counting principles. Both problems use some basic arithmetic and algebra. Thus this course should be accessible to most people. The Polya 4-step method is basically to (1) UNDERSTAND the problem (2) to PLAN your solution (3) to DO your Plan and (4) to EXAMINE and look back at what you did.
The two problems I will use to illustrate the Polya 4-step method can be called "The Diagonal Problem" and "The Handshake Problem."
Do you want to be more confident when solving math problems? Then this course is for you!
Do you want to get better at problem solving? Then this course is for you!
Are you stuck on a problem and don't know where to start? Then start with this course!

With just about 30 minutes of your time you can learn, in this short course, a method that could help you the rest of your life!

If you want to learn more about Polya's method then I suggest you read "How To Solve It" by G. Polya. The book has over 20 problems where you can practice his 4-step proven method.

Who this course is for:

This course is for the beginner that wants to get better at solving math problems.

Introduction To Problem Solving

What you'll learn

Explore related topics

Course content

Introduction3 lectures • 6min

The Four Main Phases Of Problem Solving6 lectures • 18min

The Four Phases Applied To A Triangular Number Problem5 lectures • 21min

Conclusion1 lecture • 3min

Requirements

Description

Who this course is for: