problem solving management theory

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In This Article Expand or collapse the "in this article" section Problem Solving and Decision Making

Introduction.

• General Approaches to Problem Solving
• Representational Accounts
• Problem Space and Search
• Working Memory and Problem Solving
• Domain-Specific Problem Solving
• The Rational Approach
• Prospect Theory
• Dual-Process Theory
• Cognitive Heuristics and Biases

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Problem Solving and Decision Making by Emily G. Nielsen , John Paul Minda LAST REVIEWED: 26 June 2019 LAST MODIFIED: 26 June 2019 DOI: 10.1093/obo/9780199828340-0246

Problem solving and decision making are both examples of complex, higher-order thinking. Both involve the assessment of the environment, the involvement of working memory or short-term memory, reliance on long term memory, effects of knowledge, and the application of heuristics to complete a behavior. A problem can be defined as an impasse or gap between a current state and a desired goal state. Problem solving is the set of cognitive operations that a person engages in to change the current state, to go beyond the impasse, and achieve a desired outcome. Problem solving involves the mental representation of the problem state and the manipulation of this representation in order to move closer to the goal. Problems can vary in complexity, abstraction, and how well defined (or not) the initial state and the goal state are. Research has generally approached problem solving by examining the behaviors and cognitive processes involved, and some work has examined problem solving using computational processes as well. Decision making is the process of selecting and choosing one action or behavior out of several alternatives. Like problem solving, decision making involves the coordination of memories and executive resources. Research on decision making has paid particular attention to the cognitive biases that account for suboptimal decisions and decisions that deviate from rationality. The current bibliography first outlines some general resources on the psychology of problem solving and decision making before examining each of these topics in detail. Specifically, this review covers cognitive, neuroscientific, and computational approaches to problem solving, as well as decision making models and cognitive heuristics and biases.

General Overviews

Current research in the area of problem solving and decision making is published in both general and specialized scientific journals. Theoretical and scholarly work is often summarized and developed in full-length books and chapter. These may focus on the subfields of problem solving and decision making or the larger field of thinking and higher-order cognition.

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Organization and Management Problem Solving A Systems and Consulting Approach

• James T Ziegenfuss, Jr - Pennsylvania State University, Middletown, PA
• Description

Based on a broad range of case studies, Organization and Management Problem Solving is an insightful text designed to improve the application of organization theory and systems thinking in teaching and practice. This book illustrates the five key themes in the nature of organization and management—technical, structural, psychosocial, managerial, and cultural—through the analysis of measured incidents tested by students.

A clear theoretical framework supports the case studies, allowing the text to have practical relevance to contemporary settings and to be recognized as a model for describing, analyzing, and responding to organization and management problems. The model integrates the thinking of many writers on organization and problem solving including Ackoff, Blake, and Mouton; Schein, Kast, and Rosenweign; and Mitroff and Lippitt. The approach eliminates causal conditions and emphasizes responsive problem solving. Theory is applied and expanded as needed to a broader social context, engaging the reader in a thorough understanding of the nature and development of organization theory and problem solving.

This book is relevant to consultants, academics, and professional managers in a number of settings (academic, military, business organizations, and research institutes) and disciplines (including development and change, management, human resources, social psychology, communication, sociology, and psychology).

See what’s new to this edition by selecting the Features tab on this page. Should you need additional information or have questions regarding the HEOA information provided for this title, including what is new to this edition, please email [email protected] . Please include your name, contact information, and the name of the title for which you would like more information. For information on the HEOA, please go to http://ed.gov/policy/highered/leg/hea08/index.html .

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Management Science Theory: Definition, Contributors, and Pros/Cons

Table of Contents

What is Management Science Theory?

Management Science Theory, also known as Operations Research or the Quantitative Approach, is a problem-solving approach that uses mathematical and statistical methods to tackle complex business challenges. It’s like having a toolbox filled with mathematical tools to fix intricate problems in an organization.

Unlike other management theories that focus on human behavior, Management Science Theory is all about crunching numbers and analyzing data. The theory employs various techniques such as linear programming, queuing theory, game theory, and more, to optimize processes and decision-making.

With the help of computers and advanced communication tools, the impact of Management Science Theory on businesses has grown significantly. It’s like having a superpower to process vast amounts of information and find the most efficient ways to operate.

Overall, Management Science Theory empowers managers to be like problem-solving superheroes, using mathematical tools to navigate complexities and make informed decisions that drive organizational success. It’s a powerful approach that complements other management theories and equips managers with a diverse set of tools to tackle the challenges of today’s dynamic business world.

Who are the Major Contributors To Management Science Theory?

The major contributors to Management Science Theory are as follows:

• George Dantzig (1914-2005) : An American mathematician who is often referred to as the “father of linear programming.” He made significant contributions to the development of linear programming techniques, which are essential in optimization problems.
• John von Neumann (1903-1957) : A Hungarian-American mathematician and economist who played a key role in the development of game theory, a fundamental tool in decision-making involving multiple parties with conflicting interests.
• Tjalling Koopmans (1910-1985) : A Dutch-American economist who contributed to the field of Operations Research and made significant advancements in the theory of linear programming.
• Russell L. Ackoff (1919-2009) : An American organizational theorist and systems thinker who made contributions to problem-solving methods, including systems thinking and operations research.
• C. West Churchman (1913-2004) : An American philosopher and systems theorist who emphasized the importance of addressing complexity and uncertainty in decision-making through a systems approach.

These scholars, among others, have played crucial roles in shaping Management Science Theory by introducing mathematical and quantitative methods to enhance decision-making and problem-solving in various fields, including business, engineering, and military operations.

Related : What is the Decision Theory of Management?

Pros and Cons of Management Science Theory

Let’s explore some pros and criticisms of the management science approach.

• Optimized Decision Making: The theory equips managers with mathematical tools to analyze data and evaluate multiple options. This leads to more informed and optimized decision-making, like finding the most efficient route to reach a destination.
• Improved Efficiency and Productivity: By employing quantitative techniques like linear programming and queuing theory, businesses can streamline processes, allocate resources effectively, and maximize productivity. It’s like fine-tuning a well-oiled machine to run at its peak performance.
• Resource Allocation: Management Science Theory aids in resource allocation, ensuring resources like manpower, inventory, and finances are used optimally. It’s like allocating funds wisely to get the best return on investment.
• Effective Planning and Forecasting: The theory’s mathematical models enable businesses to forecast future trends and outcomes. This helps in making strategic plans and mitigating potential risks, like using a weather forecast to prepare for a storm.
• Proactive Problem-Solving: Management Science Theory provides a proactive approach to problem-solving. Businesses can anticipate and address potential issues using predictive analysis and optimization techniques, like fixing a machine before it breaks down.
• Overemphasis on Quantitative Methods: Critics argue that Management Science Approach tends to prioritize quantitative methods over other qualitative aspects. This may lead to overlooking critical human and social factors, like employee motivation and organizational culture.
• Assumptions and Simplifications: The theory often relies on unrealistic assumptions and simplifications to create mathematical models. Critics contend that these models may not accurately represent real-world complexities, leading to potentially flawed decision-making.
• Limited Application: Management Science Theory is most effective in well-structured and repetitive environments. Critics argue that it may not be suitable for dealing with uncertain and dynamic situations, where factors are constantly changing.
• Resistance to Change: Some organizations may resist adopting Management Science Theory due to a perceived shift in decision-making power from managers to data-driven approaches. This resistance can hinder the theory’s implementation and potential benefits.

Read Next: Human Relations and Behavioral Science Theory of Management

By profession, Sujan Chaudhary is a BBA (Bachelor in Business Administration) graduate, and by passion a blogger. He loves to share his business knowledge with the rest of the world. While not writing, he will be found reading and exploring the world.

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Problem-solving and Learning for Public Services and Public Management

Theory and Practice

• © 2024
• Tony Kinder   ORCID: https://orcid.org/0000-0003-2769-3655 0 ,
• Jari Stenvall 1

Tampere University, Tampere, Finland

You can also search for this author in PubMed   Google Scholar

• Enables readers to apply learning frameworks to problem-solving in public services
• Introduces user-focused approaches to improving service efficiency and effectiveness
• Explains how people at diverse organisational levels can play key roles in organising service improvements

Part of the book series: Springer Texts in Business and Economics (STBE)

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Table of contents (12 chapters)

Front matter, introduction.

Tony Kinder, Jari Stenvall

Problem-Solving and Public Services

Public value, values, and public services, e-public services, local public sector innovation, organising in self-organising ecosystems, learners, teachers, and leaders, entrepreneurial activity, knowledge flows and services improvements, governances and sustainability dialectics, inequality, climate, and dialectical problem-solving, conclusions, back matter.

• Learning frameworks
• Public services providers
• Policy-making
• Service models
• Artificial intelligence
• Digitalisation
• E-technology
• Sustainability
• Public goods
• Service users
• Communal living
• E-democracy

About this book

Authors and affiliations, about the authors, bibliographic information.

Book Title : Problem-solving and Learning for Public Services and Public Management

Book Subtitle : Theory and Practice

Authors : Tony Kinder, Jari Stenvall

Series Title : Springer Texts in Business and Economics

DOI : https://doi.org/10.1007/978-3-031-43230-9

Publisher : Springer Cham

eBook Packages : Economics and Finance , Economics and Finance (R0)

Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024

Hardcover ISBN : 978-3-031-43229-3 Published: 16 February 2024

Softcover ISBN : 978-3-031-43232-3 Due: 18 March 2024

eBook ISBN : 978-3-031-43230-9 Published: 15 February 2024

Series ISSN : 2192-4333

Series E-ISSN : 2192-4341

Edition Number : 1

Number of Pages : XXI, 454

Number of Illustrations : 41 b/w illustrations, 40 illustrations in colour

Topics : Public Administration , Public Policy , Knowledge Management , Governance and Government , Economics, general , Business and Management, general

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Watch CBS News

Teens come up with trigonometry proof for Pythagorean Theorem, a problem that stumped math world for centuries

By Bill Whitaker

May 5, 2024 / 7:00 PM EDT / CBS News

As the school year ends, many students will be only too happy to see math classes in their rearview mirrors. It may seem to some of us non-mathematicians that geometry and trigonometry were created by the Greeks as a form of torture, so imagine our amazement when we heard two high school seniors had proved a mathematical puzzle that was thought to be impossible for 2,000 years. 

We met Calcea Johnson and Ne'Kiya Jackson at their all-girls Catholic high school in New Orleans. We expected to find two mathematical prodigies.

Instead, we found at St. Mary's Academy , all students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is alive with colorful parades, replete with floats, and beads, and high school marching bands.

In a city where uniqueness is celebrated, St. Mary's stands out – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the school instills in them they have the ability to accomplish anything. 

Christina Blazio: That is kinda a standard here. So we aim very high - like, our aim is excellence for all students. 

The private Catholic elementary and high school sits behind the Sisters of the Holy Family Convent in New Orleans East. The academy was started by an African American nun for young Black women just after the Civil War. The church still supports the school with the help of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were working on a school-wide math contest that came with a cash prize.

Ne'Kiya Jackson: I was motivated because there was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is a lot of money. So I-- I would like to at least try."

Both were staring down the thorny bonus question.

Bill Whitaker: So tell me, what was this bonus question?

Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a proof.

The seniors were familiar with the Pythagorean Theorem, a fundamental principle of geometry. You may remember it from high school: a² + b² = c². In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told  them  was there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked at the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah. 

Bill Whitaker: What motivated you to say, "Well, I'm going to try this"?

Calcea Johnson: I think I was like, "I started something. I need to finish it." 

Bill Whitaker: So you just kept on going.

Calcea Johnson: Yeah.

For two months that winter, they spent almost all their free time working on the proof.

CeCe Johnson: She was like, "Mom, this is a little bit too much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson:   So then I started looking at what she really was doing. And it was pages and pages and pages of, like, over 20 or 30 pages for this one problem.

Cal Johnson: Yeah, the garbage can was full of papers, which she would, you know, work out the problems and-- if that didn't work she would ball it up, throw it in the trash. 

Bill Whitaker: Did you look at the problem? 

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause most of the time I don't understand what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I write this? Does this help? ax² plus ….

Their math teacher, Michelle Blouin Williams, initiated the math contest.

Bill Whitaker: And did you think anyone would solve it?

Michelle Blouin Williams: Well, I wasn't necessarily looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was just looking for some ingenuity, you know—

Calcea and Ne'Kiya delivered on that! They tried to explain their groundbreaking work to 60 Minutes. Calcea's proof is appropriately titled the Waffle Cone.

Calcea Johnson: So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So then what we do next is we draw a second congruent, which means they're equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Calcea Johnson: Am I going a little too—

Bill Whitaker: You've been beyond me since the beginning. (laughter) 

Bill Whitaker: So how did you figure out the proof?

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Ne'Kiya Jackson: Okay, I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that's basically what I used for the proof. That's the proof.

Bill Whitaker: That's what I call amazing.

Ne'Kiya Jackson: Well, thank you.

There had been one other documented proof of the theorem using trigonometry by mathematician Jason Zimba in 2009 – one in 2,000 years. Now it seems Ne'Kiya and Calcea have joined perhaps the most exclusive club in mathematics. 

Bill Whitaker: So you both independently came up with proof that only used trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you math geniuses?

Calcea Johnson: I think that's a stretch. 

Bill Whitaker: If not genius, you're really smart at math.

Ne'Kiya Jackson: Not at all. (laugh) 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

Ne'Kiya Jackson: Well, our teacher approached us and was like, "Hey, you might be able to actually present this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah. 

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but just a minute for word of their accomplishment to go around the world. They got a write-up in South Korea and a shout-out from former first lady Michelle Obama, a commendation from the governor and keys to the city of New Orleans. 

Bill Whitaker: Why do you think so many people found what you did to be so impressive?

Ne'Kiya Jackson: Probably because we're African American, one. And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part.

Bill Whitaker: So you think people were surprised that young African American women, could do such a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd like to actually be celebrated for what it is. Like, it's a great mathematical achievement.

Achievement, that's a word you hear often around St. Mary's academy. Calcea and Ne'Kiya follow a long line of barrier-breaking graduates. 

The late queen of Creole cooking, Leah Chase , was an alum. so was the first African-American female New Orleans police chief, Michelle Woodfork …

And judge for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told us Calcea and Ne'Kiya are typical St. Mary's students.  

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told us the students hear that message from the moment they walk in the door.

Pamela Rogers: We believe all students can succeed, all students can learn. It does not matter the environment that you live in. 

Bill Whitaker: So when word went out that two of your students had solved this almost impossible math problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, there were many naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not have done it. African Americans don't have the brains to do it." Of course, we sheltered our girls from that. But we absolutely did not expect it to come in the volume that it came.  

Bill Whitaker: And after such a wonderful achievement.

Pamela Rogers: People-- have a vision of who can be successful. And-- to some people, it is not always an African American female. And to us, it's always an African American female.

Gloria Ladson-Billings: What we know is when teachers lay out some expectations that say, "You can do this," kids will work as hard as they can to do it.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She told us an encouraging teacher can change a life.

Bill Whitaker: And what's the difference, say, between having a teacher like that and a whole school dedicated to the excellence of these students?

Gloria Ladson-Billings: So a whole school is almost like being in Heaven. 

Bill Whitaker: What do you mean by that?

Gloria Ladson-Billings: Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, "I'm not going to be anything special." What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. Here, there's no test to get in, but expectations are high and rules are strict: no cellphones, modest skirts, hair must be its natural color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told us they appreciate the rules and rigor.

Rayah Siddiq: Especially the standards that they set for us. They're very high. And I don't think that's ever going to change.

Bill Whitaker: So is there a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So when you're here, there's just no question that you're going to go on to college.

Rayah Siddiq: College is all they talk about. (laughter) 

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges where every senior has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% college acceptance rate?

Pamela Rogers: That's correct.

Last year when Ne'Kiya and Calcea graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Bill Whitaker: So wait a minute. Neither one of you is going to pursue a career in math?

Both: No. (laugh)

Calcea Johnson: I may take up a minor in math. But I don't want that to be my job job.

Ne'Kiya Jackson: Yeah. People might expect too much out of me if (laugh) I become a mathematician. (laugh)

But math is not completely in their rear-view mirrors. This spring they submitted their high school proofs for final peer review and publication … and are still working on further proofs of the Pythagorean Theorem. Since their first two …

Calcea Johnson: We found five. And then we found a general format that could potentially produce at least five additional proofs.

Bill Whitaker: And you're not math geniuses?

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News.

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