THE ART OF PROBLEM SOLVING A Process for Finding Solutions

THE ART OF PROBLEM SOLVINGA Process for Finding SolutionsTHE ART OF PROBLEM SOLVINGA Process for Finding Solutions

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THE ART OF PROBLEM SOLVINGA Process for Finding Solutions

Course Objectives

• Learn a problem-solving approach• Review conditions for solving problems• How we should think about problems• Learn to identify issues• Review a process for solving problems• Discuss essential attitudes and behaviors• Understand communication and conflict

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“Problems are opportunities for growth or catalysts for failure—we make the choice.”

– Anonymous

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Math Problem

The math teacher walked into the classroom with a big smile on her face. She had just graded a recent math test and was pleased that over 93% of the class passed. Before returning the exam to the students, the teacher presented the class with the following problem: One-fourth of the class received an “A” on the exam. One-third of those who received an “A” got 100% of the problems correct. How many students got an “A”? How many students received 100%? What fraction of the total students received 100%? What percent of the students received 100%? There are 36 students in the class.

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Math Problem Solving ProcessWhat is the actual problem asking? How many students got an “A”, how many got 100%, fraction of total that got 100%, percent of total that got 100%. What do you know? There are 36 students. One-fourth of all students got an “A”. One-third of all students who got an “A” received 100% on their exam. The teacher is female. She is smiling. Seven percent did not pass the class. What is unknown? How many got an “A”, how many got 100%, fraction that got 100%, percent that got 100%. How many students received a B, C, D or failed . What information is relevant? 36 students, 1/4 got an “A”, 1/3 of all “A’s” received 100%. What information is not relevant? Smiling teacher, % who did not get an “A”, 93% passed, it’s a math class. 5©NLRC


Math Problem Solving Process

Solution: One-fourth of 36 students tells us how many students got an “A” (1/4 * 36 = 9)

Solution: One-third of “A” students received 100% on their exam (1/3 * 9 = 3) Solution: Three students out of 36 received 100% (3/36 = 1/12 of all students received

100%)

Solution: We can determine the percent of a fraction by dividing the top number by the bottom number. The fraction 1/12 equals 1 ÷ 12 or 0.083.

Solution: Change a number to a percent by moving the decimal two spaces to the right. 0.083 equals 8.3%. 8.3% of all students who took the exam answered every question correctly. (The received 100%).

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Water Mains

The city has 1257 miles of water mains; 60% of the mains are over 80 years old with a life cycle of approximately 50 years and are beginning to fail. Main breaks have grown from 5 per year to 17 per year, costing the city millions in repair bills, but many breaks are not in the older pipes. Due to budget limits, there is insufficient funding for large scale inspection or renovation, so targeting potential problem areas for repair seems logical. So far, however, there is no pattern for water main breaks in just the older pipes, but system-wide breaks are becoming more frequent and are causing more damage than ever. What would you do?

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Think it Through

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What do you know?

What are the unknowns?

What information is relevant?

What information is not relevant?

What other information do you

need?

Solve the problem.


General Conditions for Effective Problem Solving

• Interest in exploring the issue• Passion for data & choices• Passion for improvement• Willingness to talk openly about the issue/data• Belief that different views are vital to good decisions

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Practical Reminders

• Remain calm• Don’t get overwhelmed• Think positively• Be creative• Use resources• Stick with it!

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Problems/ Challenges

1. 7.

2. 8.

3. 9.

4. 10.

5. 12.

6. 13.


Issues Identification

INTERNAL EXTERNAL

TANGIBLE INTANGIBLE TANGIBLE INTANGIBLE

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Nature of the problem?

Why is this a problem?

Consequences if not solved?

Probability?

Live with consequences?

Next Steps

Thinking about Problems

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Personal Problem Solving

• Issue exploration• Passion for data and choices• Talk openly about experiences• Willing and able to listen• Honest feelings vs. Conflict

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Problem-Solving Process

Define the Problem

Analyze Potential Causes

Identify Potential Solutions

Select the Best

Options

Develop an Action Plan

Implement Solution and

Evaluate Progress

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Required Attitudes & Behaviors• Ability to use “I” statements – responsibility• Discipline to stay on task• Clear, honest discussion – who, what, when,

where, why, & how• Ability to paraphrase• Willingness to openly state personal preferences• Skill in separating fact from fiction• Ability to identify & discuss feelings• Low levels of defensiveness

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• Willingness to listen – consider all views• Commitment to find best answer/ solution• Low level of competitiveness• Sufficient self esteem to say no• Ability to find mutually supported options• Patience and tolerance• Curiosity to find answers using everyone’s ideas

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Required Attitudes & Behaviors


Problem-Solving Checklist

• Is this truly a problem?• Do I have more than one solution?• What other choices are possible?• Choices I can’t live with?• Eliminated impossible choices?• Choices other side won’t accept?• Eliminated unacceptable choices?• Do I still have more than one option?

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Problem-Solving Checklist

• Can I create additional solutions?• Which solution meets my needs?• Will this solution be acceptable to

others?• What will make the solution

acceptable?• Will other choices work?• Am I ready to present my first choice?• Is anything else needed?

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Communication and Conflict• Humans interpret reality• Celebrate diversity• Don’t discount the simple

solution• Conflict happens• Two different responses• Reactionary• Controlled• Personality styles• Need to interact, solve

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Ten Criteria for Effective Problem Solving

1. Clearly defined problem or issue 2. Agreement on our responsibility

to decide3. Agreement on process and

procedures4. Clarity about our level of

authority to recommend or decide

5. Open, honest communication

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Ten Criteria for Effective Problem Solving

6. Adequate data & information7. Method for achieving consensus8. Appropriate team size and

representation9. A system of building buy-in &

ownership10. Commitment from management to

carry out solution

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Team Problem Solving Rules of Conduct

• Open participation encouraged• No criticism allowed – no ‘discounting’• Equal time for all• Teasing is discouraged if it has an edge• All ideas & people are respected• Different styles respected• Timelines are maintained• No interruptions• No cross-talk (discussions while another is speaking)

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Remember, it is not WHO is right…but WHAT is right that matters. This is where you work – what you do is

important, but the problems are solvable, so relax!

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Summary

• Use a process for effective problem solving• Remain calm; problems were made to be solved• Identify the issues• Issue statement: “So what?”• Have the right attitudes and skills• Conflict is good• What is right

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THE ART OF PROBLEM SOLVING A Process for Finding Solutions

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