Identify Goal
Define Problem
Define Problem
Gather Data
Define Causes
Identify Options
Clarify Problem
Generate Ideas
Evaluate Options
Generate Ideas
Choose the Best Solution
Implement Solution
Select Solution
Take Action
MacLeod offers her own problem solving procedure, which echoes the above steps:
“1. Recognize the Problem: State what you see. Sometimes the problem is covert. 2. Identify: Get the facts — What exactly happened? What is the issue? 3. and 4. Explore and Connect: Dig deeper and encourage group members to relate their similar experiences. Now you're getting more into the feelings and background [of the situation], not just the facts. 5. Possible Solutions: Consider and brainstorm ideas for resolution. 6. Implement: Choose a solution and try it out — this could be role play and/or a discussion of how the solution would be put in place. 7. Evaluate: Revisit to see if the solution was successful or not.”
Many of these problem solving techniques can be used in concert with one another, or multiple can be appropriate for any given problem. It’s less about facilitating a perfect CPS session, and more about encouraging team members to continually think outside the box and push beyond personal boundaries that inhibit their innovative thinking. So, try out several methods, find those that resonate best with your team, and continue adopting new techniques and adapting your processes along the way.
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Cognition ; Problem typology ; Problem-based learning ; Problems ; Reasoning
Problem solving is the process of constructing and applying mental representations of problems to finding solutions to those problems that are encountered in nearly every context.
Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to vexing and complex social problems, such as violence in society (see Problem Typology ). Second, finding or solving for the unknown must have some social, cultural, or intellectual value. That is, someone believes that it is worth finding the unknown. If no one perceives an unknown or a need to determine an unknown, there is no perceived problem. Finding...
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Jonassen, D.H., Hung, W. (2012). Problem Solving. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_208
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In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.
Podcast transcript
Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.
Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].
Charles and Hugo, welcome to the podcast. Thank you for being here.
Hugo Sarrazin: Our pleasure.
Charles Conn: It’s terrific to be here.
Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?
Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”
You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”
I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.
I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.
Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.
Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.
Simon London: So this is a concise problem statement.
Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.
Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.
How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.
Hugo Sarrazin: Yeah.
Charles Conn: And in the wrong direction.
Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?
Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.
What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.
Simon London: What’s a good example of a logic tree on a sort of ratable problem?
Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.
If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.
When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.
Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.
Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.
People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.
Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?
Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.
Simon London: Not going to have a lot of depth to it.
Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.
Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.
Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.
Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.
Both: Yeah.
Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.
Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.
Simon London: Right. Right.
Hugo Sarrazin: So it’s the same thing in problem solving.
Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.
Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?
Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.
Simon London: Would you agree with that?
Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.
You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.
Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?
Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.
Simon London: Step six. You’ve done your analysis.
Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”
Simon London: But, again, these final steps are about motivating people to action, right?
Charles Conn: Yeah.
Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.
Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.
Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.
Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.
Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?
Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.
You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.
Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.
Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”
Hugo Sarrazin: Every step of the process.
Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?
Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.
Simon London: Problem definition, but out in the world.
Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.
Simon London: So, Charles, are these complements or are these alternatives?
Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.
Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?
Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.
The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.
Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.
Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.
Hugo Sarrazin: Absolutely.
Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.
Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.
Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.
Charles Conn: It was a pleasure to be here, Simon.
Hugo Sarrazin: It was a pleasure. Thank you.
Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.
Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.
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This page continues from Problem Solving an Introduction that introduces problem solving as a concept and outlines the stages used to successfully solve problems.
This page covers the first two stages in the problem solving process: Identifying the Problem and Structuring the Problem .
Before being able to confront a problem its existence needs to be identified. This might seem an obvious statement but, quite often, problems will have an impact for some time before they are recognised or brought to the attention of someone who can do anything about them.
In many organisations it is possible to set up formal systems of communication so that problems are reported early on, but inevitably these systems do not always work. Once a problem has been identified, its exact nature needs to be determined: what are the goal and barrier components of the problem? Some of the main elements of the problem can be outlined, and a first attempt at defining the problem should be made. This definition should be clear enough for you to be able to easily explain the nature of the problem to others.
Looking at the problem in terms of goals and barriers can offer an effective way of defining many problems and splitting bigger problems into more manageable sub-problems.
Sometimes it will become apparent that what seems to be a single problem, is more accurately a series of sub-problems. For example, in the problem:
“I have been offered a job that I want, but I don't have the transport to get there and I don't have enough money to buy a car.”
“ I want to take a job ” (main problem)
“ But I don't have transport to get there ” (sub-problem 1)
“ And I don't have enough money to buy a car ” (sub-problem 2)
Useful ways of describing more complex problems are shown in the section, ' Structuring the Problem' , below.
During this first stage of problem solving, it is important to get an initial working definition of the problem. Although it may need to be adapted at a later stage, a good working definition makes it possible to describe the problem to others who may become involved in the problem solving process. For example:
Problem | Working Definition |
The second stage of the problem solving process involves gaining a deeper understanding of the problem. Firstly, facts need to be checked.
Problem | Checking Facts |
“I want to take a job, but I don’t have the transport to get there and I don’t have enough money to buy a car.” | “Do I really want a job?” “Do I really have no access to transport?” “Can I really not afford to buy a car?” |
The questions have to be asked, is the stated goal the real goal? Are the barriers actual barriers and what other barriers are there? In this example, the problem at first seems to be:
Goal | Barrier 1 | Barrier 2 |
Take the job | No transport | No money |
This is also a good opportunity to look at the relationships between the key elements of the problem . For example, in the 'Job-Transport-Money' problem, there are strong connections between all the elements.
By looking at all the relationships between the key elements, it appears that the problem is more about how to achieve any one of three things, i.e. job, transport or money, because solving one of these sub-problems will, in turn, solve the others.
This example shows how useful it is to have a representation of a problem.
Visual and verbal representations include:
Chain diagrams are powerful and simple ways of representing problems using a combination of diagrams and words. The elements of the problem are set out in words, usually placed in boxes, and positioned in different places on a sheet of paper, using lines to represent the relationship between them.
Chain Diagrams are the simplest type, where all the elements are presented in an ordered list, each element being connected only with the elements immediately before and after it. Chain diagrams usually represent a sequence of events needed for a solution. A simple example of a chain diagram illustrates the job-transport-money example as as follows:
TAKE JOB |
Flow charts allow for inclusion of branches, folds, loops, decision points and many other relationships between the elements. In practice, flow charts can be quite complicated and there are many conventions as to how they are drawn but, generally, simple diagrams are easier to understand and aid in 'seeing' the problem more readily.
Tree diagrams and their close relative, the Decision Tree , are ways of representing situations where there are a number of choices or different possible events to be considered. These types of diagram are particularly useful for considering all the possible consequences of solutions.
Remember that the aim of a visualisation is to make the problem clearer. Over-complicated diagrams will just confuse and make the problem harder to understand.
Listing the elements of a problem can also help to represent priorities, order and sequences in the problem. Goals can be listed in order of importance and barriers in order of difficulty. Separate lists could be made of related goals or barriers. The barriers could be listed in the order in which they need to be solved, or elements of the problem classified in a number of different ways. There are many possibilities, but the aim is to provide a clearer picture of the problem.
1. Get money |
A visual representation and a working definition together makes it far easier to describe a problem to others. Many problems will be far more complex than the example used here.
Continue to: Investigating Ideas and Possible Solutions
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OpenAI made the last big breakthrough in artificial intelligence by increasing the size of its models to dizzying proportions, when it introduced GPT-4 last year. The company today announced a new advance that signals a shift in approach—a model that can “reason” logically through many difficult problems and is significantly smarter than existing AI without a major scale-up.
The new model, dubbed OpenAI o1, can solve problems that stump existing AI models, including OpenAI’s most powerful existing model, GPT-4o . Rather than summon up an answer in one step, as a large language model normally does, it reasons through the problem, effectively thinking out loud as a person might, before arriving at the right result.
“This is what we consider the new paradigm in these models,” Mira Murati , OpenAI’s chief technology officer, tells WIRED. “It is much better at tackling very complex reasoning tasks.”
The new model was code-named Strawberry within OpenAI, and it is not a successor to GPT-4o but rather a complement to it, the company says.
Murati says that OpenAI is currently building its next master model, GPT-5, which will be considerably larger than its predecessor. But while the company still believes that scale will help wring new abilities out of AI, GPT-5 is likely to also include the reasoning technology introduced today. “There are two paradigms,” Murati says. “The scaling paradigm and this new paradigm. We expect that we will bring them together.”
LLMs typically conjure their answers from huge neural networks fed vast quantities of training data. They can exhibit remarkable linguistic and logical abilities, but traditionally struggle with surprisingly simple problems such as rudimentary math questions that involve reasoning.
Murati says OpenAI o1 uses reinforcement learning, which involves giving a model positive feedback when it gets answers right and negative feedback when it does not, in order to improve its reasoning process. “The model sharpens its thinking and fine tunes the strategies that it uses to get to the answer,” she says. Reinforcement learning has enabled computers to play games with superhuman skill and do useful tasks like designing computer chips . The technique is also a key ingredient for turning an LLM into a useful and well-behaved chatbot.
Mark Chen, vice president of research at OpenAI, demonstrated the new model to WIRED, using it to solve several problems that its prior model, GPT-4o, cannot. These included an advanced chemistry question and the following mind-bending mathematical puzzle: “A princess is as old as the prince will be when the princess is twice as old as the prince was when the princess’s age was half the sum of their present age. What is the age of the prince and princess?” (The correct answer is that the prince is 30, and the princess is 40).
“The [new] model is learning to think for itself, rather than kind of trying to imitate the way humans would think,” as a conventional LLM does, Chen says.
OpenAI says its new model performs markedly better on a number of problem sets, including ones focused on coding, math, physics, biology, and chemistry. On the American Invitational Mathematics Examination (AIME), a test for math students, GPT-4o solved on average 12 percent of the problems while o1 got 83 percent right, according to the company.
The new model is slower than GPT-4o, and OpenAI says it does not always perform better—in part because, unlike GPT-4o, it cannot search the web and it is not multimodal, meaning it cannot parse images or audio.
Improving the reasoning capabilities of LLMs has been a hot topic in research circles for some time. Indeed, rivals are pursuing similar research lines. In July, Google announced AlphaProof , a project that combines language models with reinforcement learning for solving difficult math problems.
AlphaProof was able to learn how to reason over math problems by looking at correct answers. A key challenge with broadening this kind of learning is that there are not correct answers for everything a model might encounter. Chen says OpenAI has succeeded in building a reasoning system that is much more general. “I do think we have made some breakthroughs there; I think it is part of our edge,” Chen says. “It’s actually fairly good at reasoning across all domains.”
Noah Goodman , a professor at Stanford who has published work on improving the reasoning abilities of LLMs, says the key to more generalized training may involve using a “carefully prompted language model and handcrafted data” for training. He adds that being able to consistently trade the speed of results for greater accuracy would be a “nice advance.”
Yoon Kim , an assistant professor at MIT, says how LLMs solve problems currently remains somewhat mysterious, and even if they perform step-by-step reasoning there may be key differences from human intelligence. This could be crucial as the technology becomes more widely used. “These are systems that would be potentially making decisions that affect many, many people,” he says. “The larger question is, do we need to be confident about how a computational model is arriving at the decisions?”
The technique introduced by OpenAI today also may help ensure that AI models behave well. Murati says the new model has shown itself to be better at avoiding producing unpleasant or potentially harmful output by reasoning about the outcome of its actions. “If you think about teaching children, they learn much better to align to certain norms, behaviors, and values once they can reason about why they’re doing a certain thing,” she says.
Oren Etzioni , a professor emeritus at the University of Washington and a prominent AI expert, says it’s “essential to enable LLMs to engage in multi-step problem solving, use tools, and solve complex problems.” He adds, “Pure scale up will not deliver this.” Etzioni says, however, that there are further challenges ahead. “Even if reasoning were solved, we would still have the challenge of hallucination and factuality.”
OpenAI’s Chen says that the new reasoning approach developed by the company shows that advancing AI need not cost ungodly amounts of compute power. “One of the exciting things about the paradigm is we believe that it’ll allow us to ship intelligence cheaper,” he says, “and I think that really is the core mission of our company.”
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Smart Church Management
Helping Churches Manage Their People, Time And Money
September 11, 2024 by Patricia Lotich, MBA
Anyone in church leadership understands that a big part of their role is to help solve problems.
Problems. Sometimes, it seems as if we solve one problem, and another one pops up right behind it.
Why? Because fixing a problem creates new problems!
Think about these examples:
Problem : A church of 1000
Church leadership creates strategies and sets goals to increase membership by 50 percent.
They’ve been successful in their endeavors, but now they have a new problem: there is not enough seating for the new members and not enough children’s ministry space for the increased number of kids.
New problem : We need more space.
The team recommends adding another service to relieve the stress of one weekly service. A second service begins.
Problem solved.
New problem : We need more volunteers to operate the second service.
As you can see, those who manage any organization are paid to solve problems. The tools they use can vary from gut instincts to structured problem-solving tools.
Skilled managers are good problem-solvers and use problem-solving tools to help them find the best solutions.
“Quality is never an accident; it is always the result of high intention, sincere effort, intelligent direction, and skillful execution; it represents the wise choice of many alternatives.” William Foster
Any growing organization constantly solves one problem, which creates a new problem that needs solving.
Having problems to solve is not necessarily a bad thing, but solutions are best when they’re part of an established problem-solving process.
The secret is having a structured problem-solving process called total quality management.
Quality concepts provide problem-solving tools that can help identify problems and provide ways to solve problems.
Organizations use quality tools to solve problems and monitor and manage improvement initiatives.
Several tools are used, but we’ll discuss the most common ones here. Different problems call for different tools, many of which have multiple uses.
The trick is to become familiar with and comfortable with all the quality management tools so you can pull the appropriate one out of your toolbox when a problem arises.
One quality problem-solving tool is called the “5 Whys.”
This exercise can quickly drill down to the root cause of a problem.
It’s tempting to jump to the first conclusion when trying to solve a problem, so it’s essential to make sure that what you think is the root of the problem truly is.
Let’s look at this example.
Problem: Children’s ministry has to turn away children because there aren’t enough workers to comply with teacher-to-student ratios.
Let’s look at this problem and ask the question why five times.
Now, if you look at the answer to the first “why” and stop there, you may tend to blame the workers and conclude that they are irresponsible and unreliable.
However, examining the fourth and fifth reasons will give you a clearer picture of the issue.
If you put good people in bad processes, the outcomes don’t improve.
When problems arise, it’s human nature to try to find the culprit and lay blame on someone, but more often than not, the person is working in a broken process that limits his or her ability to perform well.
Let’s look at another example.
Imagine you have a receptionist, and you’re constantly getting complaints about her not knowing the answers to callers’ questions and continuing to transfer them to the wrong person or department.
You can discipline that employee or try to learn what is not working in the process.
Problem : Complaints about the receptionist not knowing the answer to questions asked.
As you can see from this example, the problem is a training issue, but not with the receptionist, which would not have been identified without asking the question at least 5 times.
Once you separate the person from the problem, you can drill down on the causes and fix the process that will ultimately help the person perform their job duties.
Most of us are familiar with flowcharts. You’ve seen flowcharts showing relationships within organizational structures.
Flowcharts also show how a document process flows. Use this tool to identify bottlenecks or breakdowns in current processes.
Flowcharting the steps of a process gives a picture of what it looks like and can illuminate issues within it.
Flowcharts also show process changes when improvements or a new workflow process occur.
A check sheet is a basic quality tool used to collect data.
It can track the number of times a certain incident occurs.
For example, a large church that schedules hundreds of volunteers to serve at every church service may track the number of times volunteers don’t show up for scheduled shifts.
This check sheet would total the number of times a volunteer doesn’t report as scheduled compared to the reasons for the volunteer’s absence.
a | ||
A Pareto chart is a bar graph of data showing the most frequent occurrences through the least.
When viewed from the most to the least number of occurrences, it’s easy to see how to prioritize improvement efforts.
This chart shows volunteers not showing up to work their schedule. The most significant problems stand out, and you can target those first.
Control or run charts plot data points on a line over time and show data movement.
They demonstrate when data is consistent or when there are high or low outliers in occurrences.
A histogram is a bar chart picture showing data patterns within typical process conditions.
Changes in a process should trigger a new collection of data.
For example, the histogram below shows the highest volume of phone calls about contribution statements.
This is a seasonal high number that should be redistributed over time.
An adequate number of data points will require a minimum of 50 to 75 data points. This could mean collecting data on phone calls over several weeks or months.
The patterns demonstrate an analysis that helps understand variation and provides information to improve an internal communication process.
Scatter diagrams are graphs that show the relationship between variables. Variables often represent possible causes and effects.
A cause and effect diagram, also known as a fishbone diagram, shows the different causes of a problem. The problem is identified and written in the box (head of the fish) to the right.
Then, there’s the fish’s spine, and problems caused by things off the spine are major.
Causes typically fall into the categories of people, processes, materials, and equipment.
Brainstorming with a group familiar with the problem identifies the causes.
Once you identify all the causes, you can use them to develop an improvement plan to help resolve the identified problem.
Now, remember that these are common categories, but depending on the problem you’re trying to solve, the categories may be very different from these natural groupings.
The goal is to identify and put a list of issues in their own natural category.
This tool can help us identify some of the driving issues of the problem we’re trying to solve.
Every problem has a root cause, something driving it. We want to find that cause and eliminate it.
Let’s consider some easy problems we can all relate to and identify the root causes.
For example, debt. We know that the typical root cause of debt is spending more money than we earn (even though there are times when debt is out of someone’s control – job loss, medical care, etc.).
Another example is weight gain. The typical root cause is consuming more calories than we burn (unless there’s an uncontrolled medical condition, certain drugs, etc.).
We know that the root cause of being late for work is often sleeping in that extra 15 minutes (however, sometimes it’s weather, traffic, or car problems).
The point is that every problem has a root cause, and the goal is to take a hard look and try to determine the root cause so you can put a plan in place to eliminate it.
If we can identify the real (not perceived) issue, we can address it at its root and eliminate or greatly reduce the problem.
For example, there might be a perception that the root cause of debt is not earning enough money, but the real issue is spending more than is earned.
Separating the perception from the real issue is essential to get to the root cause.
Most problems fit into natural categories. From there, you can figure out how to address the issues. For example,
These are all questions you must consider when trying to drill down on a problem.
Each tool has advantages for certain situations, and not all are for all problem-solving. Once a tool is learned, you can adapt it for different problem-solving opportunities.
As with anything else, using tools properly takes time, practice, and experience.
What problems are you trying to solve today?
Learn other tips for hiring and managing your employees by enrolling in our course, Fundamentals of Church Administration .
Patricia Lotich is a Certified Manager of Quality and Organizational Excellence through the American Society for Quality and is the author of Smart Church Management: A Quality Approach to Church Administration . She helps churches fulfill their mission by managing their resources of - people, time and money.
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Computational Thinking is argued to be an essential skill for the workforce of the 21st century. As a skill, Computational Thinking should be taught in all schools, employing computational ideas integrated into other disciplines. Up until now, questions ...
The number of undergraduates entering computer science has declined in recent years. This is paralleled by a drop in the number of high school students taking the CS AP exam and the number of high schools offering computer science courses. The declines ...
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As business owners and leaders, we often encounter a variety of problems in our organizations, but not all problems are created equal.
I've found that most issues fall into one of three layers, each requiring a different approach to solve. Below, I'll break down the three layers so you can tailor your business's solutions to the right problem type.
Related: 2 Steps to Determine the Best Possible Solution to Any Problem
For Layer 1 problems, a process is in place, and the person involved knows exactly what they should be doing. The issue here is that they simply made a mistake . It happens to the best of us — sometimes, we just slip up.
When a Layer 1 problem pops up, your first move should be to remind the person of the correct process. A quick, gentle nudge is often all that's needed to get things back on track. These are the kinds of problems that can be fixed with a brief conversation or a simple reminder.
If this kind of mistake starts happening regularly, it's time to dig a little deeper. There may be something else going on — stress, disengagement or even burnout. In these cases, it's important to address the root cause rather than just the symptom. Consistent Layer 1 problems could signal that the employee needs support, whether that's through better time management, more frequent breaks or addressing any personal issues that might be affecting their work.
No matter what the specifics entail, it's best to address a Layer 1 problem quickly, ideally providing feedback within 24 hours. The sooner you address it, the easier it is to course-correct and prevent the mistake from becoming a recurring issue.
The second layer of problems is a bit more complex. For Layer 2 problems, a process is in place, but the person doesn't fully understand it. This could happen for several reasons — maybe they're new and still learning, or maybe their training wasn't as thorough as it should have been. Either way, the root of the problem is a lack of understanding, not just a simple mistake.
The solution for a Layer 2 problem is straightforward: training. Whether that involves a refresher course or sitting down one-on-one to go over the process again, the goal is to ensure the person fully understands what's expected of them. Training helps close the knowledge gap and equips the employee with the tools they need to succeed.
If a Layer 2 problem keeps happening, it's a sign that your training materials — or your training methods — might need an update. Take a look at what you're teaching compared to the outcomes you're seeing. Are there gaps in the training? Are there certain parts of the process that employees consistently struggle with? If so, it might be time to update your training to better meet the needs of your team.
When you're addressing a Level 2 problem, aim to share feedback within a week. This gives you enough time to reassess and retrain while keeping the issue fresh in the employee's mind. Also, consider including others who might also benefit from the refresher. This proactive approach can help prevent similar problems from arising with other team members.
Related: 5 Steps to Creatively Solving Business Problems
Finally, we have the third layer of problems, which occurs when there's no process in place at all. If there's no process, you can't expect your team to know what to do. Layer 3 problems often happen when your business has grown or changed, and you're facing new challenges that existing processes just don't cover. They're a great sign that it's time to create or overhaul some new processes.
Layer 3 problems are the most complex because they require you to build something from scratch. The first step is to assess the situation and define what needs to be done. Once you have a clear understanding of the problem, you can begin creating a process that addresses the issue. This might involve mapping out the steps, assigning responsibilities and ensuring that the process aligns with the overall goals of the organization.
Once the process is in place, it's also essential to train your team so they know how to execute it. You may need to hold workshops, provide ongoing support and be available to answer any questions as they arise.
If a Layer 3 problem keeps happening, it could mean that the process you created isn't quite right for the team's needs. In this case, you may need to tweak or update the process or create supplemental processes to cover other parts of the business.
Typically, it takes 2-4 weeks to properly assess a Layer 3 problem, define and document the solution and then train (and retrain) the relevant teams. This might seem like a long time, but it's worth it to ensure that the process is solid and that your team is prepared to follow it long-term.
Understanding the three layers of problems is crucial for effective problem-solving in any organization. You don't want your managers to overthink or waste too much time solving Layer 1 problems — these should be quick fixes. On the other hand, you don't want them to rush through solving Layer 3 problems, as these require more careful planning and execution.
It's also important to look for trends. For example, if you have a lot of Layer 2 problems, it might be a sign that your training methods need improvement. If you're seeing a lot of Layer 1 problems, it could be time to review your hiring practices or provide more support to your team.
Related: Facing a Tough Problem? Try These Hacks to Find the Solution You Need
By identifying the layer of the problem, you can set the right expectations around the amount of time and effort needed to find a solution. Next time you face a challenge, ask yourself: Which layer does this problem belong to? Approaching it with this framework will save you time, effort and maybe even a few headaches along the way.
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Instructor: Madecraft
All organizations have problems and the tools to solve those problems. In this course, inclusive leadership expert Amani Edwards guides you through a people-centered approach to problem solving across an organization. Amani emphasizes the importance of understanding the people and culture. She gives actionable insights to help you better understand your organization, so you can begin solving problems equitably and efficiently. Amani dives into identifying the underlying issues and shows you how to identify all players involved in the problem at hand. Next, she explores how to create problem-solving goals and act on those goals. Finally, Amani describes how to evaluate the success of the problem-solving and determine your next steps. After completing this course, you will be equipped with an effective problem-solving strategy that alleviates issues in the short-term, while setting up your organization for long-term success.
This course was created by Madecraft . We are pleased to host this training in our library.
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Spending the majority of their time modeling problems and making sense of relationships in math can help students move beyond a surface-level grasp.
At every grade level, math teachers in the Success Academy Charter Schools Network in New York City ask students to spend the lion’s share of their time during math lessons deeply examining the question they are being asked to solve. Students start by asking themselves questions like, “What are the mathematical relationships in the problem?” “What is this problem asking me to do?” and “How can I model my thinking?” Every classroom even has a formula—a problem-solving plan for math, printed out and displayed on the wall—called the “Plan of Attack,” which includes three parts: using 80 percent of the allotted time to conceptualize the question by reading the problem multiple times, then modeling the relationships and actions in the problems; 10 percent to answer the question by determining a strategy they will use to solve it and then computing; and finally double-checking in the last 10 percent of their time—by rereading the problem, evaluating their own reasoning, and checking computations for accuracy.
First-grade teacher Evelyn Gonzales and eighth-grade teacher Fei Liu both reinforce this strategy during precious class time by working through the problem as a whole with their students first, emphasizing the importance of this step before rushing in to solve. As a result, their students develop a much stronger understanding of the mathematical concepts at hand. “In my classroom, I don’t really care for the answer,” says Liu. “They can double-check once they have the answer. What we really need to focus on is why we set the things up, so that when they see a problem, they have an idea of where to start to think.”
The network led the state for math test scores in the 2023–2024 school year, with with 49 percent of Black and 55 percent of Hispanic students earning fours, the highest possible mark.
See all of Edutopia’s coverage of Success Academy Charter Schools to learn more about the network.
1st Edition
In their new book Solving Managerial Problems Systematically , Hans Heerkens and Arnold van Winden teach students how to identify and efficiently deal with problems. The book uses the Managerial Problem-Solving Method, which deals with problems step by step. Solving Managerial Problems Systematically describes the seven phases of the Managerial Problem-Solving Method, a roadmap on how to identify, conduct thorough research into, and lastly solve a core problem. This textbook treats the concept of a ‘problem’ as an analytical one; a concept that can be found in any department in any organisation. Creative techniques are used to help find a solution for the problems encountered, which makes the method an ideal tool that is applicable in nearly any situation. Solving Managerial Problems Systematically is intended for Bachelor studies (professional education and university) where students engage in problems and problem-solving in individual courses, projects, or graduation. It is a valuable aid for consultants and advisors to help identify and analyse managerial problems, and to advise companies on possible solutions.
Hans Heerkens is assistant professor at the University of Twente, and associate professor of Methodology at the Business School Netherlands in Buren. Arnold van Winden teaches Communication Management at the Amsterdam University of Applied Sciences, and is the owner of Van Winden Communicatie.
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IMAGES
VIDEO
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Conclusion. To sum up, the foundation of AI problem-solving is comprised of the ideas of problems, problem spaces, and search. In AI issue solving, efficient search algorithms are crucial for efficiently navigating vast and intricate problem spaces and locating ideal or nearly ideal answers. They offer an organized method for defining ...
Introduction. In computer science, problem-solving refers to synthetic intelligence techniques, which include forming green algorithms, heuristics, and acting root reason analysis to locate suited solutions. Search algorithms are fundamental tools for fixing a big range of issues in computer science. They provide a systematic technique to ...
Chapter 3 Solving Problems by Searching . When the correct action to take is not immediately obvious, an agent may need to plan ahead: to consider a sequence of actions that form a path to a goal state. Such an agent is called a problem-solving agent, and the computational process it undertakes is called search.. Problem-solving agents use atomic representations, that is, states of the world ...
Problem formulation: define a representation for states define legal actions and transition functions. Search: find a solution by means of a search process. solutions are sequences of actions. Execution: given the solution, perform the actions. =) Problem-solving agents are (a kind of) goal-based agents.
Problem-solving agents decide what to do by finding sequences of actions that lead to desir-able states. We start by defining precisely the elements that constitute a "problem" and its "solution," and give several examples to illustrate these definitions. We then describe sev-eral general-purpose search algorithms that can be used to ...
Problem Solving and Search Problem Solving • Agent knows world dynamics • World state is finite, small enough to enumerate • World is deterministic • Utility for a sequence of states is a sum over path The utility for sequences of states is a sum over the path of the utilities of the individual states.
Toy problems (but sometimes useful) Illustrate or exercise various problem-solving methods Concise, exact description Can be used to compare performance Examples: 8-puzzle, 8-queens problem, Cryptarithmetic, Vacuum world, Missionaries and cannibals, simple route finding. Real-world problem. More difficult No single, agreed-upon description ...
7. Solution evaluation. 1. Problem identification. The first stage of any problem solving process is to identify the problem (s) you need to solve. This often looks like using group discussions and activities to help a group surface and effectively articulate the challenges they're facing and wish to resolve.
The Solution to a search problem is a sequence of actions, ... It is used for solving real-life problems using data mining techniques. The tool was developed using the Java programming language so that it is platform-independent. 3 min read. ML - Convergence of Genetic Algorithms.
Problem Solving as Search •Search is a central topic in AI -Originated with Newell and Simon's work on problem solving. -Famous book: "Human Problem Solving" (1972) •Automated reasoning is a natural search task •More recently: Smarter algorithms -Given that almost all AI formalisms (planning,
The problem-solving process typically includes the following steps: Identify the issue: Recognize the problem that needs to be solved. Analyze the situation: Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present. Generate potential solutions: Brainstorm a list of possible ...
There are basically three types of problem in artificial intelligence: 1. Ignorable: In which solution steps can be ignored. 2. Recoverable: In which solution steps can be undone. 3. Irrecoverable: Solution steps cannot be undo. Steps problem-solving in AI: The problem of AI is directly associated with the nature of humans and their activities.
Several mental processes are at work during problem-solving. Among them are: Perceptually recognizing the problem. Representing the problem in memory. Considering relevant information that applies to the problem. Identifying different aspects of the problem. Labeling and describing the problem.
The McKinsey guide to problem solving. Become a better problem solver with insights and advice from leaders around the world on topics including developing a problem-solving mindset, solving problems in uncertain times, problem solving with AI, and much more.
Balance divergent and convergent thinking. Ask problems as questions. Defer or suspend judgement. Focus on "Yes, and…" rather than "No, but…". According to Carella, "Creative problem solving is the mental process used for generating innovative and imaginative ideas as a solution to a problem or a challenge.
Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to ...
Infrastructure for search algorithms I A problem is de ned by ve components: I initial state e.g., \In(Arad)" I actions, Actions(s) returns the actions applicable in s. e.g, In Arad, the applicable actions are fGo(Sibiu), Go(Timisoara), Go(Zerind)g I transition model, Result(s;a) returns the state that results from executing action a in state s
Problem solving, and the techniques used to gain clarity, are most effective if the solution remains in place and is updated to respond to future changes. Problem Solving Resources. You can also search articles, case studies, and publications for problem solving resources. Books. Innovative Business Management Using TRIZ
In this episode of the McKinsey Podcast, Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.. Podcast transcript. Simon London: Hello, and welcome to this episode of the McKinsey Podcast, with me, Simon London.
This page continues from Problem Solving an Introduction that introduces problem solving as a concept and outlines the stages used to successfully solve problems.. This page covers the first two stages in the problem solving process: Identifying the Problem and Structuring the Problem. Stage One: Identifying the Problem. Before being able to confront a problem its existence needs to be identified.
The new model, dubbed OpenAI o1, can solve problems that stump existing AI models, including OpenAI's most powerful existing model, GPT-4o. Rather than summon up an answer in one step, as a ...
Frameworks for Mathematical Problem Solving. One widely accepted and useful definition of a mathematical problem is that a problem exists when the procedure for solving the task is unknown to the solver, the number of solutions is uncertain, and the task requires critical thinking (Schoenfeld, Citation 2011).Word problems are a type of problem that are frequently found in classroom instruction.
Having problems to solve is not necessarily a bad thing, but solutions are best when they're part of an established problem-solving process. The secret is having a structured problem-solving process called total quality management. Quality concepts provide problem-solving tools that can help identify problems and provide ways to solve problems.
This study aims to investigate current trends and key elements of computational thinking in problem-solving within mathematics education. A systematic literature review was conducted using the 2013-2013 Scopus database, focusing on the keyword "computational thinking in mathematics education" for document collection.
Related: 5 Steps to Creatively Solving Business Problems. Layer 3: Lack of process. Finally, we have the third layer of problems, which occurs when there's no process in place at all. If there's ...
Finally, Amani describes how to evaluate the success of the problem-solving and determine your next steps. After completing this course, you will be equipped with an effective problem-solving strategy that alleviates issues in the short-term, while setting up your organization for long-term success. This course was created by Madecraft. We are ...
Search. George Lucas Educational Foundation. Using a Plan of Attack for Math Problem-Solving ... Every classroom even has a formula—a problem-solving plan for math, printed out and displayed on the wall—called the "Plan of Attack," which includes three parts: using 80 percent of the allotted time to conceptualize the question by reading ...
Solving Managerial Problems Systematically is intended for Bachelor studies (professional education and university) where students engage in problems and problem-solving in individual courses, projects, or graduation. It is a valuable aid for consultants and advisors to help identify and analyse managerial problems, and to advise companies on ...