problem solving maps

Problem Solution Mapping — Everything You Need to Know!

Edraw content team, do you want to make your problem solution mapping.

EdrawMax specializes in diagramming and visualizing. Learn from this article to know everything about what is a problem solution map, problem-solving process, how to make your problem solution map. Just try it free now!

When facing a problem, you have two options. You can either continue untangling the problem in your mind. Or, you can put it all out in a problem-solution map and save time and energy. A problem-solution map helps you find the root cause of the problem. Then, when you know the reasons, you can also find your ultimate solution.

So, let's explore more about problem and solution maps and elements of the problem-solving process in the following guide. We'll also learn about EdrawMax - a free online software to fulfill all your diagramming needs!

So, let's dive into it!

1. What is a Problem Solution Map

A problem solution map represents a logical analysis of available data leading towards a solution. In other words, a problem solution map uses the given data to provide a solution to the problem. A straightforward solution map can have various elements. Typically, it has the following structure:

• a problem statement
• problem definition
• possible causes and effects
• an effective solution

You can change the structure of a solution map according to the problem. However, it should include all the possible laws and principles at all stages to find a practical solution. Solution mapping is crucial and better than thinking about a solution. It's because solution mapping makes you visualize your problem and simplify it.

You consider all the possible reasons behind the problem and milestones to achieve to solve it. As a result, your thoughts become organized and clearer in a visual representation. It also saves your time and effort and increases your productivity.

2. Problem-Solving Process

Practical problem-solving is more than just visualizing and figuring out the solution. It is a process with several steps to guide you to the optimal solution. It includes:

• Problem definition
• Problem analysis
• Possible solutions
• Analysis of the solutions
• Select the best solution
• Execute the solution

Let's explore these!

Problem Definition

Before you start working on your problem solution map, you should define your problem. It might surprise you but defining a problem is more challenging than just writing it on paper. It's because the main problem is often a vague idea merged with unnecessary, distracting conflicts. So, please understand the problem and clear up its confusion.

Problem Analysis

After defining the problem, the next step is to analyze it. When deciding if a solution will truly work, it is vital to recognize where the problem begins, how it fits with the latest advancements, and what the present environment is.

For instance, the following is a problem solution map example. It is a problem tree designed on EdrawMax displaying the causes behind poor health conditions among Gapachi Vileans. You can tell a problem's roots from its consequences (branches) by comparing them to a tree (trunk).

Possible Solutions

In this step, you should focus on solutions. However, it is essential to come up with as many solutions as possible without evaluating them. You should consider it a solution, even if it seems vague. So, think for some time and list all the ideas that come to mind as solutions to the problem.

Analysis of the Solutions

Here, you will go back to all the solutions you wrote in the previous step. Then, you will consider each idea individually and investigate it. When analyzing an argument, assess its positive and negative aspects and whether it addresses the problem entirely. You can also write unique benefits of each idea to differentiate it from others.

For example, consider this Graphic Organizer: Problem Solution diagram by EdrawMax. It simplifies finding a solution as you can write all the possible choices and their pros and cons. Then, you can select the most effective solution as the final one.

Select the Best Solution

After writing the pros and cons of all the ideas side by side, you need to filter the best solutions from the list. You can also improve it by revising the ideas and refining their individual traits. In the end, you might have one or more solutions (the best ones!). If not, consider reevaluating the problem statement or repeating the 3rd and 4rth steps.

Execute the Solution

Once you have come up with the solution, the final step is to execute it. Then, consider what you should do next to follow that particular solution. In other words, you need to plan your solution to solve the problem.

3. Visualize Your Problem Solution Map Process

The best thing about a solution map is that it is open-ended. However, it also means no hard and fast rule or rocket science behind creating a solution map .

Still, creating a problem and solution map from scratch takes a lot of work. The good thing is that you can always take advantage of powerful software like EdrawMax . It is an incredibly powerful online service to tackle all your diagramming needs.

EdrawMax has all the features you need to visualize your problem-solution map. For instance:

• You can insert tables, charts, timelines - anything that can help define and analyze the problem and/or solutions.
• You can add, remove, replace, and do much more with symbols and shapes through Predefine Libraries in EdrawMax.
• You can use the Connector feature and drag it to draw a line (arrows) to a connection point on the shape you want to connect to.
• You can edit color, line weight, dash style, and arrow style using the Line or Line Style feature to customize your solution map.

What else? You can also find hundreds of ready-made solution map templates on the EdrawMax community. These editable templates make everything easy, as you can edit them according to your preference. Creating a solution map from scratch takes less time and effort.

4. Conclusion

Every problem has a solution, but finding that solution can be challenging. The road map to finding the ultimate solution is often chaotic and messy. With a problem and solution map , you can visualize your problem, its root causes, and possible solutions. A problem solution map is a way to analyze the available data and find the perfect solution to solve the problem. With EdrawMax , you can easily create your problem solution map. Or you can also save time by editing an already published template on the EdrawMax community!

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Oxford University Press's Academic Insights for the Thinking World

How to use maps to solve complex problems

Strategic Thinking in Complex Problem Solving

• By Arnaud Chevallier
• February 9 th 2020

Imagine that you’ve just been appointed the head of operations for a five-star hotel in Manhattan. Your boss calls you in her office on your first day and says: “Our biggest problem is how slow elevators are. Everyone complains about it, and we can’t have that. Speed them up.”

How would you do it?

Most people intuitively focus on speeding up the elevators: installing stronger motors, modifying the dispatch algorithm, getting the doors to shut faster, or even installing additional elevators. But there is also a whole set of options that consists of giving the impression that the elevators are faster, for instance by distracting the users with windows or, on the cheaper side, with mirrors, TVs, or newspapers.

Facing a complex challenge, it’s tempting to pursue whichever option we first identify and start implementing it quickly. But  relying on this kind of intuitive thinking, particularly   in  unpredictable   environments ,  might result in poor outcomes — even when we have a high degree of confidence .

Instead, we should first identify the range of solutions that are available to us, which is challenging, because we don’t know what we don’t know. It’s like being an explorer a few hundred years ago who would land on an uncharted piece of land having to decide how to explore it. Well, there is a time-tested approach: map it.

Facing that complex challenge, your first task should be to frame your problem in the form of an overarching question that, once answered, will lay out your proposed plan of action. A good way to frame your problem is to summarize that key question and its context in  a situation- complication-question sequence .  Once you’ve framed your problem, you should then think of alternative ways—or options—to solve it before deciding which one is on balance the best.

A question map   helps you explore that universe of potential options. Question maps are similar to other knowledge cartography tools, such as mind maps, decision trees, and the issue trees that management consultants use. But question maps are also different from these tools in that they obey their own rules, four rules that actively drive structure into your problem-solving process.

• 1. Good question maps answer a single type of question The first rule of good question maps is that they answer a single type of question. Facing a complex problem, we face two types of questions: why and how. A why question is problem centric; it helps you to diagnose your problem, uncovering its root causes and, ultimately, enabling you to summarize your problem in a more insightful key question. In contrast, a how question is solution centric: It enables you to consider all the possible solutions to your problem.One type of question isn’t consistently better than the other. Both are useful and, in general, you want to ask why before you ask how.
•  Good question maps have a mutually exclusive and collectively exhaustive structure Next, consider all the possible answers to your question exactly once. That is, give your map branches that are  mutually exclusive and collectively exhaustive  (or MECE ). Giving your map this structure is a critical element of the process, and in most cases, it isn’t easy to do, as it requires you to think both creatively and critically. So, expect to spend some effort here—and by “expect to spend some effort,” I mean that if you don’t feel some frustration, you’re not doing it well!
• Good question maps are insightful The final rule of good maps is that they should have an insightful structure. That is, the structure should be both logically valid and useful. Concretely, this means finding a way to structure the map that helps bring some new, useful light into your question. This is especially important for the first cut, the top-most node of the map.

Striving to be insightful also means that you need to keep developing your map until you identify concrete answers. Don’t stay at a philosophical level (e.g., by just writing “by creating the impression that the elevators are faster”) but identify concrete ways to answer your question (“by installing mirrors in the elevators”).

Question maps only have four rules, and those are simple enough to understand. Following them when solving a complex problem, however, can be, let’s say, challenging. But realize that the complexity isn’t in the map; the complexity is in the problem, all that the map does is expose that complexity so that you can better address it. So, embrace the challenge, and happy mapping!

Feature image by Daan Stevens via  Unsplash

Arnaud Chevallier is a professor of strategy at IMD Business School. He researches tools to help people solve complex, ill-defined problems. He is particularly interested in common denominators: the knowledge and skills that, irrespective of disciplines, can benefit people confronted with a challenging problem. He is the author of Strategic Thinking in Complex Problem Solving published by Oxford University Press.

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• EXPLORE Random Article

How to Solve Problems Using Mind Maps

Last Updated: August 4, 2021

This article was co-authored by Jeff Siegel . Jeff Siegel is a Holistic Life Coach and the Founder of Jeff Siegel Wellness. With nearly 10 years of experience, he specializes in mind-body medicine, life coaching, health and wellness coaching, mindfulness, corporate training, and transformational public speaking. He received a Master of Education from Harvard Graduate School of Education, a Master of Buddhist Studies from The University of Hong Kong, and a BSc in Neuroscience & Biology from Emory University. He’s also a certified personal trainer, a certified Eating Psychology Coach, and a certified Koru Mindfulness Teacher. This article has been viewed 88,558 times.

If you want to solve a problem, it's a good idea to combine

• mind mapping and
• problem solving tools (like brainstorming, asking questions, drawing a diagram...).

This way, you can profit from the benefits of each approach. (If you are not yet familiar with mind mapping, have a look at the wikiHow article How to Make a Mind Map)

• Avoid a description of your problem that is too narrow.

• I = identify problems and opportunities
• D = define alternative goals
• E = explore possible strategies
• A = anticipate and act
• L = look and learn.

• Develop your ideas in subbranches.
• Use problem solving tools for each stage.
• You find a collection of problem solving tools in the "Tips" section below.

• See the video below for an example.

Expert Q&A

• For each of the IDEAL stages, you can assemble a number of useful tools.
• Understand the problem
• Devise a plan
• Carry out the plan
• Review/extend
• For more detailed information, see https://en.wikipedia.org/wiki/George_P%C3%B3lya

Things You'll Need

• blank paper, size A4 or larger
• pens, preferably in different colours
• optional: text markers
• this is great for keeping your tool map up to date
• Freeplane (download at http://freeplane.sourceforge.net/wiki/index.php/Main_Page ) or
• FreeMind (download at http://freemind.sourceforge.net/wiki/index.php/Main_Page ).

You Might Also Like

• Bransford, J.D.; Stein, B.S.: The IDEAL Problem Solver. W.H. Freeman and Company, New York 1993 (Source for the IDEAL strategy)

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Nine essential problem solving tools: The ultimate guide to finding a solution

October 26, 2023 by MindManager Blog

Problem solving may unfold differently depending on the industry, or even the department you work in. However, most agree that before you can fix any issue, you need to be clear on what it is, why it’s happening, and what your ideal long-term solution will achieve.

Understanding both the nature and the cause of a problem is the only way to figure out which actions will help you resolve it.

Given that most problem-solving processes are part inspiration and part perspiration, you’ll be more successful if you can reach for a problem solving tool that facilitates collaboration, encourages creative thinking, and makes it easier to implement the fix you devise.

The problem solving tools include three unique categories: problem solving diagrams, problem solving mind maps, and problem solving software solutions.

They include:

• Fishbone diagrams
• Strategy maps
• Mental maps
• Concept maps
• Layered process audit software
• Charting software
• MindManager

In this article, we’ve put together a roundup of versatile problem solving tools and software to help you and your team map out and repair workplace issues as efficiently as possible.

Let’s get started!

Problem solving diagrams

Mapping your way out of a problem is the simplest way to see where you are, and where you need to end up.

Not only do visual problem maps let you plot the most efficient route from Point A (dysfunctional situation) to Point B (flawless process), problem mapping diagrams make it easier to see:

• The root cause of a dilemma.
• The steps, resources, and personnel associated with each possible solution.
• The least time-consuming, most cost-effective options.

A visual problem solving process help to solidify understanding. Furthermore, it’s a great way for you and your team to transform abstract ideas into a practical, reconstructive plan.

Here are three examples of common problem mapping diagrams you can try with your team:

1. Fishbone diagrams

Fishbone diagrams are a common problem solving tool so-named because, once complete, they resemble the skeleton of a fish.

With the possible root causes of an issue (the ribs) branching off from either side of a spine line attached to the head (the problem), dynamic fishbone diagrams let you:

• Lay out a related set of possible reasons for an existing problem
• Investigate each possibility by breaking it out into sub-causes
• See how contributing factors relate to one another

Fishbone diagrams are also known as cause and effect or Ishikawa diagrams.

2. Flowcharts

A flowchart is an easy-to-understand diagram with a variety of applications. But you can use it to outline and examine how the steps of a flawed process connect.

Made up of a few simple symbols linked with arrows indicating workflow direction, flowcharts clearly illustrate what happens at each stage of a process – and how each event impacts other events and decisions.

3. Strategy maps

Frequently used as a strategic planning tool, strategy maps also work well as problem mapping diagrams. Based on a hierarchal system, thoughts and ideas can be arranged on a single page to flesh out a potential resolution.

Once you’ve got a few tactics you feel are worth exploring as possible ways to overcome a challenge, a strategy map will help you establish the best route to your problem-solving goal.

Problem solving mind maps

Problem solving mind maps are especially valuable in visualization. Because they facilitate the brainstorming process that plays a key role in both root cause analysis and the identification of potential solutions, they help make problems more solvable.

Mind maps are diagrams that represent your thinking. Since many people struggle taking or working with hand-written or typed notes, mind maps were designed to let you lay out and structure your thoughts visually so you can play with ideas, concepts, and solutions the same way your brain does.

By starting with a single notion that branches out into greater detail, problem solving mind maps make it easy to:

• Explain unfamiliar problems or processes in less time
• Share and elaborate on novel ideas
• Achieve better group comprehension that can lead to more effective solutions

Mind maps are a valuable problem solving tool because they’re geared toward bringing out the flexible thinking that creative solutions require. Here are three types of problem solving mind maps you can use to facilitate the brainstorming process.

4. Mental maps

A mental map helps you get your thoughts about what might be causing a workplace issue out of your head and onto a shared digital space.

Because mental maps mirror the way our brains take in and analyze new information, using them to describe your theories visually will help you and your team work through and test those thought models.

5. Idea maps

Idea maps let you take advantage of a wide assortment of colors and images to lay down and organize your scattered thought process. Idea maps are ideal brainstorming tools because they allow you to present and explore ideas about the best way to solve a problem collaboratively, and with a shared sense of enthusiasm for outside-the-box thinking.

6. Concept maps

Concept maps are one of the best ways to shape your thoughts around a potential solution because they let you create interlinked, visual representations of intricate concepts.

By laying out your suggested problem-solving process digitally – and using lines to form and define relationship connections – your group will be able to see how each piece of the solution puzzle connects with another.

Problem solving software solutions

Problem solving software is the best way to take advantage of multiple problem solving tools in one platform. While some software programs are geared toward specific industries or processes – like manufacturing or customer relationship management, for example – others, like MindManager , are purpose-built to work across multiple trades, departments, and teams.

Here are three problem-solving software examples.

7. Layered process audit software

Layered process audits (LPAs) help companies oversee production processes and keep an eye on the cost and quality of the goods they create. Dedicated LPA software makes problem solving easier for manufacturers because it helps them see where costly leaks are occurring and allows all levels of management to get involved in repairing those leaks.

8. Charting software

Charting software comes in all shapes and sizes to fit a variety of business sectors. Pareto charts, for example, combine bar charts with line graphs so companies can compare different problems or contributing factors to determine their frequency, cost, and significance. Charting software is often used in marketing, where a variety of bar charts and X-Y axis diagrams make it possible to display and examine competitor profiles, customer segmentation, and sales trends.

9. MindManager

No matter where you work, or what your problem-solving role looks like, MindManager is a problem solving software that will make your team more productive in figuring out why a process, plan, or project isn’t working the way it should.

Once you know why an obstruction, shortfall, or difficulty exists, you can use MindManager’s wide range of brainstorming and problem mapping diagrams to:

• Find the most promising way to correct the situation
• Activate your chosen solution, and
• Conduct regular checks to make sure your repair work is sustainable

MindManager is the ultimate problem solving software.

Not only is it versatile enough to use as your go-to system for puzzling out all types of workplace problems, MindManager’s built-in forecasting tools, timeline charts, and warning indicators let you plan, implement, and monitor your solutions.

By allowing your group to work together more effectively to break down problems, uncover solutions, and rebuild processes and workflows, MindManager’s versatile collection of problem solving tools will help make everyone on your team a more efficient problem solver.

Download a free trial today to get started!

Ready to take the next step?

MindManager helps boost collaboration and productivity among remote and hybrid teams to achieve better results, faster.

Why choose MindManager?

MindManager® helps individuals, teams, and enterprises bring greater clarity and structure to plans, projects, and processes. It provides visual productivity tools and mind mapping software to help take you and your organization to where you want to be.

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Motivation and Problem Solving (MAPS): Motivationally Based Skills Training for Treating Substance Use

Jennifer irvin vidrine.

University of Texas MD Anderson Cancer Center

Lorraine R. Reitzel

Patricia y. figueroa, mary m. velasquez.

The University of Texas–Austin

Carlos A. Mazas

Paul m. cinciripini, david w. wetter.

Over 10 years ago, Baer and colleagues proposed the integration of skills training and motivational strategies for the treatment of substance abuse. Since that time, several studies evaluating the efficacy of such hybrid approaches have been published, but few have been efficacious. Motivation and Problem Solving (MAPS) is a comprehensive, dynamic, and holistic intervention that incorporates empirically supported cognitive behavioral and social cognitive theory–based treatment strategies within an overarching motivational framework, and has been demonstrated to be effective in a randomized clinical trial focused on the prevention of postpartum smoking relapse. MAPS was designed to be applicable to not only relapse prevention but also the cessation of substance use, and is relevant for individuals regardless of their motivation to change. MAPS views motivation as dynamically fluctuating from moment to moment throughout the behavior change process, and comprehensively addresses multiple issues important to the individual and relevant to change through the creation of a wellness program. As a result, we believe that MAPS enhances the likelihood that individuals will successfully achieve and maintain abstinence from substance use, and that its comprehensive focus on addressing diverse and salient issues enhances both engagement in treatment and its applicability in modifying other health risk behaviors. The current paper introduces MAPS, distinguishes it from other hybrid and stage-based substance use treatments, and provides detailed information and clinical text regarding how MAPS is specifically and uniquely implemented to address key mechanisms relevant to quitting smoking and maintaining abstinence.

Overview and Rationale for Motivation and Problem Solving

O ver 10 years ago, Baer and colleagues ( Baer, Kivlahan, & Donovan, 1999 ) described how treatments for substance abuse could be enhanced by drawing from and integrating skills training and motivational strategies. Despite their call for the integration of two well-defined and empirically supported treatments, relatively little research on the efficacy of such hybrid approaches has been published to date. A notable exception to this is the combined behavioral intervention (CBI) tested in the COMBINE study, which was focused on the treatment of alcohol dependence ( Anton et al., 2006 ). Also, Arkowitz and Westra (2004) have described how therapists may shift into Motivational Interviewing (MI) during the course of another treatment, such as cognitive behavioral therapy (CBT), when ambivalence or resistance emerges ( Constantino, DeGeorge, Dadlani, & Overtree, 2009 ). To our knowledge, however, this specific treatment approach has not yet been empirically tested for substance abuse disorders. Other researchers have evaluated treatments that combine skills training and motivational strategies using a stepped approach. That is, one or more initial sessions typically focus solely on increasing motivation whereas subsequent sessions focus exclusively on skills training ( Budney, Higgins, Radonovich, & Novy, 2000 ; Haddock et al., 2003 ; Kertes, Westra, Angus, & Marcus, 2010 ; McKee et al., 2007 ; Westra, Arkowitz, & Dozois, 2009 ). Others have evaluated somewhat more flexible approaches that integrate CBT-based skills training within the context of MI-based treatment ( Lloyd-Richardson et al., 2009 ) or that shift from MI to CBT and back to MI again if individuals fail to change their behavior or relapse ( Stein, Hagerty, Herman, Phipps, & Anderson, 2011 ; Stein et al., 2006 ). However, none of these approaches dynamically shift therapeutic strategies on a moment-to-moment basis within a single treatment session, and none are anchored by a formal wellness program intended to guide the course of treatment.

The purpose of the current paper is to describe a new treatment for substance use based on the fluid integration of skills training and motivational enhancement, which follows from and extends previous treatments that have combined skills training with motivational strategies. This hybrid approach, entitled Motivation and Problem Solving (MAPS), focuses heavily on rapid and dynamic shifts between skills training and motivational strategies. Much of the current research on MAPS focuses on tobacco use and dependence. Therefore, tobacco use and dependence is utilized as the target behavior throughout the paper. The paper opens with a broad description of and rationale for MAPS, and then elucidates how MAPS differs conceptually from other prominent hybrid and stage-based treatment approaches. Next, the theoretical basis for MAPS is described, and detailed information is provided regarding how MAPS is specifically and uniquely implemented to addresses three key mechanisms relevant to quitting smoking and maintaining abstinence: motivation, stress and negative affect, and social cognitive constructs (self-efficacy, coping behavior). Each section includes a clinical text scenario intended to illustrate how a counselor trained in MAPS would typically interact with a client to address issues surrounding each mechanism (i.e., motivation, stress and negative affect, and self-efficacy/agency). Finally, a brief overview of the general content of each treatment session is presented. The paper concludes with an overall summary.

Broad Description of MAPS

A comprehensive, dynamic, and holistic approach to facilitating behavior change, MAPS, consistent with the Baer et al. (1999) model, incorporates empirically validated cognitive behavioral and social cognitive theory-based treatment strategies such as coping skills training and practical problem-solving techniques ( Fiore et al., 2008 ) within an overarching motivational framework ( Marlatt & Donovan, 2005 ; Miller & Rollnick, 2002 ) that addresses multiple issues relevant to considering, initiating, and maintaining behavior change. The motivational framework for MAPS is derived from MI, a goal-oriented and client-centered therapeutic approach designed to minimize resistance, enhance motivation for change, and increase self-efficacy in a nonconfrontational manner ( Miller, Zweben, DiClemente, & Rychtarik, 1995 ; Rollnick & Miller, 1995 ). In sum, MAPS utilizes an innovative combination of motivational enhancement and cognitive-behavioral treatment techniques, is built around a structure derived from effective approaches to chronic care management and patient navigation, is designed for all individuals regardless of their readiness to change, and specifically targets cardinal mechanisms underlying substance use, including motivation, agency/self-efficacy, and stress/negative affect.

MAPS is a unique treatment approach for several reasons. For example, although other conceptualizations of behavior change also emphasize both motivation and skills training, motivational shifts are conceptualized as relatively stable changes in “stage” ( Prochaska, DiClemente, & Norcross, 1992 ). Similarly, MI ( Miller & Rollnick, 2009 ) has two distinct phases of treatment: building motivation (Phase 1) and strengthening commitment (Phase 2; Miller & Rollnick, 2002 ). The transition to Phase 2 is prompted by participant cues of readiness to change, and the initiation of Phase 2 is a process entailing recapitulation, asking key questions, developing a change plan, etc. ( Miller & Rollnick, 2002 ). In contrast to an emphasis on stages and phases, MAPS is unique in that it conceptualizes motivation as a fluid construct that can fluctuate on a moment-to-moment basis depending on context. Counselors carefully assess and attend to changes in motivation so that treatment strategies are appropriately matched to motivation in the moment.

MAPS counselors follow a treatment manual and are trained to carefully attend to language used by their clients to help determine when to shift—on a moment-to-moment basis—from a discussion focused on CBT-based skills development to motivational enhancement and back again. Specifically, “change” and “sustain” talk expressed by the client serve as triggers intended to facilitate a shift from one approach to the other and back again. Change talk refers to language that indicates that an individual is moving toward or even just thinking about change (expressed desire, ability, reasons, or need for change). Examples of change talk are provided below.

“I really want to quit.” “I think I could start cutting back if I tried. I’ve done it before.” “I don’t want my kids to see me smoking.” “I need to do this before I get cancer or some other terrible disease.”

When counselors consistently hear the client voicing change talk, it serves as a signal that it is time to transition from motivational enhancement to a more CBT-based skills training approach, while maintaining the integrity of the MI framework.

Sustain talk refers to language that clients use to resist change. Examples of sustain talk are provided below.

“I really don’t think I want to quit anymore.” “I’ve tried so many times, and I just don’t have the willpower to do it.” “Smoking is the only thing that eases my anxiety.” “I need to smoke in order to relax.”

When counselors begin to hear this type of language, it serves as a signal to move out of or stay away from a problem-solving, skills-building-based approach. Shifts from motivational enhancement to CBT-based skills training can occur at any time, during any session, and even from one target behavior/goal to another.

The use of client language to help guide the course of treatment on a moment-to-moment basis is consistent with research by Amrhein and colleagues ( Amrhein, Miller, Yahne, Palmer, & Fulcher, 2003 ), who evaluated the role of client commitment language during MI treatment in predicting substance use outcomes. They found that the strength of commitment language expressed by clients uniquely predicted substance use outcomes such that stronger commitment language was associated with significantly more days abstinent following treatment, particularly when stronger commitment language was expressed toward the end of the treatment sessions. By attending to client language carefully and adapting the course of treatment to appropriately match the client’s degree of motivation and commitment in the moment, MAPS should enhance treatment outcomes compared to other more static treatment approaches that incorporate components of MI and CBT.

Given the emphasis in MAPS on shifting back and forth between MI and CBT based on client language, it is critical that MAPS be implemented in a consistent way across therapists. Therefore, the degree to which MAPS counselors are effectively delivering the treatment is regularly evaluated by listening to and coding a random sample of recorded sessions each month. A modified version of the Motivational Interviewing Treatment Integrity Code 3.1.1 (MITI) is used to measure therapists’ adherence to MAPS. We have added a global scale, Desirable Shifting, to the MITI. This scale rates each counselor’s skill at shifting back and forth between MI and CBT on a 1–5 scale (1 = a complete absence of shifting appropriately in response to client language and 5 = an ability to always shift appropriately from one modality to another based on client language ). If counselors begin to consistently score below minimum coding standards, more intense supervision is provided.

MAPS utilizes motivationally based techniques to enhance commitment and intrinsic motivation for change, and cognitive-behavioral techniques to target self-efficacy, coping, stress, and negative affect ( Fig. 1 ). Moreover, MAPS targets motivation and skills training within the context of a wellness program created in collaboration with each patient. Such a program includes not only goals related to behavior change, but also a plan for addressing other salient concerns such as anxiety, stress, depression, interpersonal issues, and family problems. MAPS also includes a focus on connecting participants with resources in the community to address their needs, such as vocational and educational training, and free or low-cost child care and medical treatment. Thus, in addition to directly targeting behavior change, the goal in MAPS is to assist individuals with general life stressors that are ultimately presumed to influence motivation, difficulty changing, and relapse ( Drobes, Meier, & Tiffany, 1994 ; Shiffman & Waters, 2004 ; Wetter, Fiore, et al., 1999 ). By addressing the larger context in which behavior change occurs, not only are many of the barriers for success addressed, but adherence may be increased because individuals perceive that the counselors care about them as whole people, and are not solely interested in their target behavior. Moreover, prioritizing and addressing substance users’ prominent concerns is also hypothesized to help individuals maintain their investment in the therapy process.

Proposed Treatment Mechanisms.

Our wellness program is similar to an approach recently described by Wagner and Ingersoll (2009) that uses MI to target multiple problematic behaviors simultaneously and facilitate broad lifestyle changes. Because MAPS is focused on both enhancing motivation and problem-solving/coping skills, this approach is appropriate for individuals who are not motivated to change, those who are ready to change, and those who have already initiated change. Most important, our previous research has demonstrated the efficacy of MAPS and its precursors for motivating a smoking quit attempt, increasing smoking cessation, and preventing relapse ( McClure, Westbrook, Curry, & Wetter, 2005a ; Reitzel et al., 2010 ; Wetter et al., 2007 ; Wetter et al., 2010 ).

Targeting Shifts in Motivation to Change

Applied to tobacco use and dependence, MAPS utilizes a motivational enhancement approach to develop discrepancy between the patient’s values, goals, and their smoking behaviors/history that is expected to have utility in treating all smokers regardless of their motivation to quit. This is important because a number of studies support that intention and motivation to quit smoking may vary over short periods of time. For example, one study found that intention to quit among smokers in the U.S. and Sweden changed rapidly and spontaneously over the course of a 4-week assessment period ( Hughes, Keely, Fagerstrom, & Callas, 2005 ). Similarly, Werner and colleagues found that 41% of smokers reported that their motivation to quit smoking changed daily ( Werner, Lovering, & Herzog, 2004 ). Larabie (2005) found that a majority of smokers and ex-smokers reported making unplanned quit attempts, suggesting that cessation may have been influenced by abrupt increases in motivation and/or intentions to quit. Finally, nearly half of smokers who responded to a household survey reported that their most recent quit attempt had been unplanned, and that unplanned (vs. planned) quit attempts were more likely to be successful ( West & Sohal, 2006 ). These findings are consistent with a new model of cessation based on catastrophe theory recently proposed by West (2006) . The model holds that smokers have varying levels of motivational “tension” to quit smoking, and that even rather small environmental “triggers” may lead to either (a) sudden cessation attempts, or (b) plans to quit at some later point in time. A plan to delay quitting (vs. attempting to quit immediately) may reflect a lower level of motivation or commitment to quitting ( West, 2006 ). Thus, measures of motivation or intentions to quit may only be valid for short periods of time, as motivation and intentions may fluctuate within the course of a single day.

Distinction Between MAPS and Other Prominent Hybrid Treatments

As described above, MAPS follows from and seeks to extend previously developed treatments that have combined skills training with motivational strategies. Several previous studies have evaluated hybrid treatment studies for substance abuse involving the combination of skills training with motivational enhancement strategies ( Anton et al., 2006 ; Babor et al., 2004 ; Budney et al., 2000 ; COMBINE Study Research Group, 2003 ; Lloyd-Richardson et al., 2009 ; McKee et al., 2007 ; Stein et al., 2011 ; Stein et al., 2006 ; Stephens, Babor, Kadden, & Miller, 2002 ). Consistent with these approaches, MAPS draws heavily upon and overlaps considerably with MI. Specifically, MAPS is grounded in MI in that all CBT-based treatment components are delivered within an MI framework. However, MAPS extends purely MI-based approaches in that the counselor shifts completely from motivational enhancement to CBT-based skills training and back again based on the degree to which the client expresses “sustain talk” versus “change talk.” Therefore, the degree to which MAPS counselors draw upon MI versus CBT is heavily guided by client language within sessions, and counselors may shift back and forth between MI and CBT multiple times during the course of a single treatment session. In contrast, previous hybrid treatments have generally emphasized motivational enhancement at the beginning of treatment and more a CBT-based approach later in treatment, with the caveat that the focus of counseling may shift back to motivational enhancement if a client lapses or relapses to substance use. Furthermore, although existing approaches that draw upon both MI and CBT are likely to address issues salient to the client that are broadly related to substance use such as general stress, depression, anxiety, and relationship and family issues, MAPS is unique in that it is built around a formal wellness program developed jointly by the client and therapist at the beginning of treatment that is used to guide the treatment. Because the wellness program is a central component of MAPS, it is revisited often throughout the course of treatment.

Distinction Between MAPS and Stage-Based Interventions

Interventions based on the transtheoretical model (TTM) are intended to address both motivation and skills training through matching the content of cessation treatment to an individual’s stage of readiness to change, which is intended to facilitate forward movement of the individual through the change process. The model posits that an individual’s stage of change should be reassessed often to ensure that the treatment content is optimally tailored. Thus, stage-based interventions are dynamic in that they are intended to evolve as individuals move through the stages of change ( Prochaska et al., 1992 ). For example, the treatment focus for individuals who are in earlier stages of change with regard to quitting smoking (i.e., precontemplation, contemplation) is generally on enhancing motivation to quit. For individuals who are in more advanced stages (i.e., action or maintenance), the focus of treatment is on training in the use of coping skills to achieve and/or maintain abstinence from smoking.

Thus far, interventions that target motivation based on stage of change have yielded equivocal results. Sutton (2001) conducted a review of TTM-based interventions for substance use and concluded that “current evidence for the model as applied to substance use is meager and inconsistent.” Similarly, Riemsma and colleagues (2003) systematically reviewed 23 randomized controlled stage-based counseling and self-help trials for smoking cessation and concluded that “The evidence suggests that stage-based interventions are no more effective than non-stage based interventions or no intervention in changing smoking behavior.” However, as acknowledged in the review ( Riemsma et al., 2003 ), the evidence base for smoking cessation interventions based on the TTM is limited because of weaknesses in study designs, lack of clarity about the algorithms used to assign participants to stage, and inconsistency in the interventions for a given stage (see Sutton, 2001 , for further elaboration). In fact, Sutton (2005) and others have noted that a number of these studies may not have been proper applications of the TTM (e.g., it is unclear whether some interventions were truly stage-matched). It is also important to note that two studies not included in the Riemsma et al. review (2003) have supported the efficacy of stage-matched self-help interventions for smoking cessation ( Dijkstra, De Vries, Roijackers, & van Breukelen, 1998 ; Prochaska, DiClemente, Velicer, & Rossi, 1993 ), and the Treating Tobacco Use and Dependence Clinical Practice Guideline concluded that such interventions are promising ( Fiore et al., 2000 ). Sutton (2001) has proposed that a motivational continuum (rather than distinct stages) underlies the change process. MAPS attempts to address this motivational continuum by being responsive to moment-to-moment changes in motivation, as well as by addressing multiple life issues influencing the motivation to attempt, achieve, and maintain abstinence.

MAPS is intended to build upon and extend previous hybrid interventions for substance abuse. MAPS is most similar to the CBI evaluated in the COMBINE trial ( Anton et al., 2006 ) and to integrative approaches described by Arkowitz and Westra (2004) and by Constantino and colleagues (2009) , in that skills training and motivational strategies are truly integrated throughout treatment. In contrast, the other approaches generally combined motivational techniques with skills training by delivering motivationally based treatment during the initial session or sessions, followed by subsequent sessions devoted to skills training ( Budney et al., 2000 ; Kertes et al., 2010 ; McKee et al., 2007 ; Westra et al., 2009 ). MAPS was designed to extend previous hybrid approaches through focusing heavily on fluid shifts between skills training and motivational strategies throughout treatment delivery.

MAPS was recently evaluated in an NCI-funded randomized clinical trial intended to prevent postpartum smoking relapse among underserved pregnant women who quit smoking because of their pregnancy ( Reitzel et al., 2010 ). Participants ( N =251) were very diverse (65% minority) and primarily low income (55% with total annual household incomes <$30,000). Importantly, MAPS significantly increased biochemically verified postpartum abstinence through 6 months postpartum (OR=1.60; p =.05). Further, each of the hypothesized motivational mechanisms was significant (stage of change, motivation, intrinsic motivation; all p’s <.05) and the other key mechanisms approached significance (self-efficacy for positive/social situations and negative affect situations, negative affect, all p’s <.10; Wetter et al., 2010 ). In sum, even in this small trial of largely unmotivated women, MAPS positively influenced the mechanisms of abstinence and key treatment mechanisms.

In addition, MAPS is currently being evaluated in a small randomized clinical trial to treat both tobacco dependence and at-risk alcohol use among smokers who are also at-risk alcohol users ( NIAAA, 1995 ; USDHHS & USDA, 1990 ), a large randomized clinical trial among low-income smokers who are not ready to quit, a randomized clinical trial among college students participating in a Quit and Win contest, and a church-based randomized clinical trial to promote positive changes in diet and physical activity among overweight/obese African American adults. Thus, MAPS is being evaluated for efficacy across the spectrum of tobacco cessation, as well as for multiple and other health risk behaviors. Although MAPS has demonstrated efficacy in one completed randomized clinical trial ( Reitzel et al., 2010 ) and is currently being evaluated in several other ongoing trials, a limitation of MAPS is that it has not yet been directly compared with stage-based treatment in a randomized clinical trial. This is an important direction for future research.

Theoretical Basis for MAPS

Social cognitive theory.

The overarching theoretical rationale for MAPS is the social cognitive or “relapse prevention” model of Marlatt and colleagues ( Marlatt & Donovan, 2005 ; Marlatt & Gordon, 1985 ; Witkiewitz & Marlatt, 2004 ). Based on cognitive social learning theory ( Bandura, 1977 , 1986 ), the model posits that both individual and contextual factors (e.g., affect, smoking cues, cigarette availability) increase drug use motivation and produce high-risk situations, thereby undermining motivation to quit, reducing the likelihood of cessation, and increasing the probability of relapse. Coping behaviors are posited to be instrumental in navigating high-risk situations without using drugs. Moreover, they have been demonstrated to be powerful determinants of success ( Davis & Glaros, 1986 ; Hall, Rugg, Tunstall, & Jones, 1984 ; Shiffman, 1984 ; Shiffman, Paty, Gnys, Kassel, & Hickcox, 1996 ; Zelman, Brandon, Jorenby, & Baker, 1992 ). Self-efficacy and outcome expectancies are hypothesized to be causal determinants of coping behaviors and they have been among the better predictors of smoking abstinence ( Businelle et al., 2010 ; Copeland, Brandon, & Quinn, 1995 ; DiClemente, Fairhurst, & Piotrowski, 1995 ; Juliano & Brandon, 2002 ; Wetter et al., 1994 ). The model has generated a tremendous amount of intervention research demonstrating that social cognitive/relapse prevention theory-based treatments for smoking cessation are effective ( Carroll, 1996 ; Fiore et al., 2000 ; Irvin, Bowers, Dunn, & Wang, 1999 ). Furthermore, these treatment components have become fairly standard components of substance use treatments. Nevertheless, such interventions have not yielded consistently superior results relative to other treatment approaches ( Carroll, 1996 ; Lichtenstein & Glasgow, 1992 ).

One attribution for the lack of superiority of social cognitive theory-based approaches is that the translation of theory into specific treatment components has been incomplete. Relapse prevention theory posits that “High levels of both motivation and self-efficacy are important ingredients … an individual may fail to engage in a specific behavior despite high levels of self-efficacy if the motivation for performance is low or absent” ( Marlatt & Gordon, 1985 ). That is, the performance of coping behaviors in high-risk situations during and after a quit attempt requires that individuals be sufficiently motivated to avoid lapse and relapse. As noted by Miller and colleagues (1995) , “the key element for lasting change is a motivational shift that instigates a decision and commitment to change. In the absence of such a shift, skill training is premature.” Although the conceptual model used to guide social cognitive theory–based interventions addresses motivation, the interventions themselves have generally focused on skills training with much less of an emphasis on motivation. Therefore, to address this gap, MAPS embeds practical problem-solving strategies drawn from social cognitive theory-based treatments within an overarching motivational enhancement framework drawn from MI ( Miller & Rollnick, 2002 ).

Motivational Interviewing

In contrast to social cognitive theory–based interventions, MI-based interventions have predominantly focused on enhancing motivation for change. There are four basic clinical principles underlying MI: (a) expressing empathy, (b) developing discrepancy, (c) rolling with resistance, and (d) supporting self-efficacy. MI avoids labeling, seeks to increase awareness, emphasizes individual responsibility for behavior, facilitates the development of dissonance between desired and problematic behavior, and utilizes goal setting to facilitate movement from behavioral intention to behavioral action within a client-oriented and nonconfrontational therapist perspective.

At least three meta-analyses of MI-based approaches to behavior change have been conducted, with the results unequivocally supporting the efficacy of the approach for alcohol use and other substance use ( Burke, Arkowitz, & Menchola, 2003 ; Hettema & Hendricks, 2010 ; Rubak, Sandbaek, Lauritze, & Christensen, 2005 ). However, only two smoking cessation studies met the inclusion criteria for the Burke et al. meta-analysis (2003) , and only one demonstrated a significant treatment effect. The treatment effect in this study ( Butler, 1999 ) was significant for 24-hour point prevalence abstinence, but not for 1-month abstinence. In the meta-analysis conducted by Rubak and colleagues (2005) , 12 smoking cessation studies were reviewed with 8 demonstrating significant treatment effects. However, only 3 of the 12 studies included adequate statistical data for inclusion in the meta-analysis. Although the overall effect size for these 3 studies only approached significance ( p <.10), the studies were plagued by substantial methodological problems, including very small sample sizes ( n ’s ranging from 29 to 121) and very minimal MI interventions (e.g., a single session with only short-term follow-up). Subsequent to these meta-analyses, McClure and colleagues ( McClure, Westbrook, Curry, & Wetter, 2005b ) found that a proactive, MI-based phone counseling intervention targeted at women with a recent abnormal Pap or colposcopy result produced greater treatment seeking and higher abstinence at the 6-month (but not 12-month) follow-up as compared with usual care. The results of a recent comprehensive meta-analysis of MI-based interventions for smoking cessation ( Hettema & Hendricks, 2010 ) indicated significant but very modest effects. The meta-analysis included 31 controlled trials with smoking abstinence as the outcome variable. The overall effect size for MI corresponded to only a 2.3% difference in abstinence rates between MI and comparison treatments. The authors concluded that the overall effect of MI on cessation was similar to the effects observed for other types of behavioral interventions for smoking cessation evaluated in the Treating Tobacco Use and Dependence Clinical Practice Guideline ( Fiore et al., 2008 ). Thus, MI-based interventions have demonstrated modest success in promoting abstinence from smoking, and there is clearly room for improvement.

How MAPS Addresses Key Mechanisms Relevant to Quitting and Maintaining Abstinence

Evidence suggests that mechanisms such as motivation, self-efficacy, coping behaviors, depression, negative affect, and stress may be crucial to successfully quitting smoking and maintaining abstinence ( Businelle et al., 2010 ; Cinciripini et al., 2003 ; Davis & Glaros, 1986 ; DiClemente et al., 1995 ; Hall et al., 1984 ; Piasecki, Fiore, McCarthy, & Baker, 2002 ; Shiffman et al., 1996 ; Wetter et al., 1994 ; Zelman et al., 1992 ). Moreover, theory suggests that there are reciprocal relations between stress/negative affect, social cognitive constructs such as coping, and motivation. That is, stress and negative affect can suppress motivation for behavior change and are likely to erode motivation for maintaining change over time, as well as reduce self-efficacy and inhibit the performance of coping behaviors ( Marlatt & Donovan, 2005 ; Piasecki et al., 2002 ).

Providing empirical support for these reciprocal relations, Crittenden, Manfredi, Cho, and Dolecek (2007) examined associations over time between general life stress and smoking outcomes among a large sample of low–socioeconomic-status women smokers and found that variations in perceived stress had negative effects on all smoking cessation outcomes examined (i.e., motivation to quit, action toward quitting, stage of readiness to quit, confidence, and abstinence). Conversely, ambivalence and a weak commitment to abstinence can increase stress and negative affect, particularly during high-risk situations ( Marlatt & Donovan, 2005 ). Therefore, addressing each of the mechanisms, in a manner consistent with participants’ preeminent needs and concerns, is an explicit goal of MAPS. For example, the focus of therapy in MAPS could flexibly switch from cognitive-behavioral methods to increase positive affect, to practical problem solving about time management, to strategies to enhance motivation to maintain smoking abstinence, based on the therapist’s attention to the client’s explicit statements about needs, wants, readiness, and importance, as well as their tone and nonverbal behaviors (for face-to-face therapy).

A substantial body of evidence demonstrates that motivation is a critical factor underlying both the decision to make a quit attempt, and the likelihood of cessation ( Prochaska et al., 1992 ; Sciamanna, Hoch, Duke, Fogle, & Ford, 2000 ). Motivation for the maintenance of behavior change has received relatively little attention in the literature despite the fact that relapse prevention theory posits that “The final and most important stage of the change process is the maintenance stage. It is during the maintenance stage (which begins the moment after the initiation of abstinence or control) that the individual must work the hardest to maintain the commitment to change over time” ( Marlatt & Gordon, 1985 ). Specifically, motivation for maintaining abstinence may weaken and ambivalence may increase as the individual is exposed to temptations and stressors ( Witkiewitz & Marlatt, 2004 ). The extant empirical data support the hypothesis that motivational deficits are important in determining the maintenance of abstinence ( Baker, Brandon, & Chassin, 2004 ; Heppner et al., 2011 ).

The importance of motivational deficits is also underscored by contextual analyses of relapse indicating that 24% of all relapse episodes are characterized by a prelapse plan to smoke ( Shiffman et al., 1996 ). Not surprisingly, this motivational deficit substantially reduces the likelihood of performing coping behaviors and lapses are often preceded by a lack of coping (Shiffman et al.). Taken together, the findings highlight that both motivation and intentions to quit and remain abstinent change rapidly and dynamically over time, indicating that a flexible and dynamic approach to targeting motivation is required. Thus, MAPS is designed to specifically address this issue.

MAPS attempts to address motivational deficits by having the therapist continually attend to subtle motivational cues, and to adjust therapeutic strategies in response to fluid changes in motivation; for example, from active problem solving to exploring and resolving ambivalence about a problem-solving strategy. That is, a person’s level of motivation determines the degree to which the therapist emphasizes problem-solving and coping skills training versus motivational enhancement. For example, a typical therapeutic exchange between a client and a therapist that addresses ambivalence about quitting smoking during a MAPS-based therapy session might play out as follows.

CLIENT: I’d like to quit because I know it’s supposed to be bad for you, but nothing bad has really happened to me from smoking. THERAPIST: Even though nothing bad has happened to you yet, you feel a little bit of pressure to do something about your smoking because of everything you hear about what it could do to your health. CLIENT: Well, I mean, sure it would probably be bad if I kept smoking for years or something … I mean, eventually something bad might happen. THERAPIST: Your health is important to you, but unless you feel that you are immediately at risk for health problems, you might not want to change your smoking behaviors. CLIENT: I guess so, but that doesn’t sound so good. You know, my grandmother found out she had emphysema from smoking and by then it was too late to really fix anything. She couldn’t even stop smoking after she found out her diagnosis! I don’t want to end up like that. She was miserable her last few years … THERAPIST: It’s scary to think that something like that could happen to you. You want to be healthy and smoking might not fit into the picture very well. CLIENT: Apparently not. Maybe I should give more thought to quitting. I haven’t thought of my grandmother and what she went through in a long time. I don’t see what it would hurt to at least try to quit.

From this point, the therapist might redirect the session to focus on enhancing the commitment and self-efficacy to quit.

THERAPIST: So you are willing to try to quit. CLIENT: Yes, I’m willing. THERAPIST: That’s great! One of the things we know from research is that quitting is often the best thing people can do for their health. If it’s okay with you, we can talk a bit about how you might go about quitting, and if you’re ready, after that we can set a quit date. CLIENT: Sure. THERAPIST: You mentioned that you tried quitting before, and that you were able to stay quit for almost two weeks last time. Tell me a little about what worked to keep you from smoking for those two weeks. CLIENT: Well, I stopped going to bars—that was a big one. THERAPIST: You stopped going to bars, and that helped you not to smoke. What else do you remember? CLIENT: I guess. … I talked with my wife about it and she was encouraging. I threw out all my ashtrays and cigarettes, and I stayed in my office at lunch rather than going to eat at the picnic tables outside. THERAPIST: Well, that’s a lot you did right last time. How do you think some of these things might work for you during your quit attempt this time? CLIENT: Yeah, I see what you’re saying. Maybe I’ve learned something during my previous attempts to quit that will be useful in helping me finally kick the habit.

This example illustrates how the therapist works in MAPS to help build self-efficacy. An example of a possible transition from increasing self-efficacy to identifying critical barriers to quitting follows.

THERAPIST: What we usually do next is to try to understand what situations or barriers have been problematic for you in the past. I know this might be a little difficult since we are talking about things that have kept you smoking. I’m not sure how you feel about this, but often people find that doing this is helpful because they can begin to anticipate difficult situations, which helps them better plan with respect to overcoming these barriers. What are some of the things that have tripped you up in the past? CLIENT: Well, I can usually make it a few days until something trips me up. Last time, I had a big argument with my wife and left the house to clear my head. On my way home, I bought a pack of cigarettes, and that was the end of that quit attempt! THERAPIST: It sounds like arguing with your wife has been really difficult for you to handle when you’ve tried to quit in the past. What specifically was difficult about this for you? CLIENT: I was just so mad that I really needed a cigarette to calm down.

From this point, the therapist might transition directly to coping skills training, and then back to enhancing motivation, as in the following example, but always interacting with the client in a manner consistent with MI.

THERAPIST: Okay, so it sounds like you made that connection between having an argument with your wife and going back to smoking. Tell me about how you think you might be able to get through arguments with your wife this time without smoking. CLIENT: I just don’t know how I’ll do it. We just argue constantly. THERAPIST: Would it be okay if I share something with you that other people have told me? Most smokers find it difficult to handle stress and anger—things like arguing with a spouse—when they are trying to stay abstinent. Many smokers try to avoid arguing at all, and even ask for extra support and understanding from their spouse when they are quitting smoking. How might that fit for you, if at all? CLIENT: I don’t think that really fits for me at all. When my wife and I get really angry at each other, we each become convinced that we’re right. It often takes us hours or even a day or two to get over it. And there is no way I can handle that time while we’re not speaking without smoking. I think I’m just one of those people who will never be able to quit. THERAPIST: When you think about the changes that might be needed to help you quit smoking, it seems overwhelming. so even though you really want to become a nonsmoker, it seems pointless to even try. It’s really difficult for you to imagine yourself living your life without cigarettes. CLIENT: Well, I really do want to quit. I can imagine myself being a nonsmoker down the road, but it’s hard for me to see myself actually getting there. THERAPIST: It’s difficult for you to see how you’ll actually make the transition from smoker to nonsmoker. CLIENT: Exactly. I guess it might help to talk about some of the situations that are going to be so difficult to get through without smoking.

Stress and Negative Affect

Stress and negative affect in smokers’ lives is likely to result from both the quit attempt itself (e.g., nicotine withdrawal, cue-induced craving), and from general life stressors that are completely independent of the quitting process. Several studies have indicated that such day-today experiences with stress and negative affect may impinge on successful quitting and abstinence maintenance. For example, most smokers experience elevated levels of postcessation negative affect that continue for relatively long periods of time, and these findings hold for smokers who receive nicotine replacement therapy as well as for those smokers who do not ( Piasecki, Fiore, & Baker, 1998 ). In addition, Shiffman and colleagues (1996) demonstrated a strong dose–response relation between smoking-related acute events and the severity of stress/negative affect. The magnitude and trajectory of stress/negative affect over time are also powerful predictors of cessation ( Burgess et al., 2002 ; Piasecki, Jorenby, Smith, Fiore, & Baker, 2003 ), as are individual differences in affective vulnerability ( Glassman et al., 1990 ; Wetter, Kenford, et al., 1999 ).

In addition, recent data indicate that financial stress is closely linked with smoking cessation success ( Kendzor et al., 2010 ; Siahpush & Carlin, 2006 ). Thus, life stressors that are unrelated to the acute quitting process may play a critical role in behavior change. Although MAPS often targets these general life stressors as a focus of counseling without explicitly linking them back to quitting or maintaining abstinence, it is important to note that many of these situations are likely to be ultimately related to successful cessation ( Siahpush et al., 2006 ).

A typical therapeutic exchange between a client and a MAPS counselor that addresses how stress and negative affect influence the success of an initial cessation attempt might occur as follows. In this scenario, the counselor may have begun the session with the mindset that the client was going to use CBT because the previous day was the client’s quit day. However, as soon as the session begins it becomes apparent from the amount of sustain talk used that the client has relapsed. Therefore, the counselor quickly switches to MI.

CLIENT: The past week has been a real struggle for me. I’ve just had so much going on in my life that it’s hard to even think about quitting smoking right now. I know yesterday was my quit day, but when I got home from work I couldn’t take it anymore and I smoked. Last that time we talked I felt like I might be ready to do this, but I just don’t know if I’m ready anymore. THERAPIST: Life is a little overwhelming lately, and you can’t imagine putting anything else on your plate right now. CLIENT: Exactly! I just have so much going on. Lately, it seems like the kids have been getting into so much trouble at school. I’m constantly having to deal with phone calls and notes from their teachers, and I’ve tried everything I can think of but nothing seems to be working. Plus, I’m under a lot of stress at work, and I have so many bills to pay! Sometimes I even feel like I’m smoking more than I usually do just to deal with this stress. THERAPIST: I’m sorry things have been stressful lately. It sounds like you’re working hard just to hold it all together. CLIENT: The fact that I haven’t quit still weighs heavily on me. I really wish I wasn’t smoking, because I know it’s bad for me and I hate spending money on it. But to be honest, I just can’t see myself doing it right now. THERAPIST: And that’s completely your choice. I’m not here to push you to do anything you’re not ready for. It sounds like you’re really torn. You can’t see yourself doing it right now, and at the same time it’s not a goal you’re willing to give up on. CLIENT: That’s true. I definitely know I have to do it, but I feel like it’s something I need to work towards. Maybe once I can get some other things in my life under control, it’ll be easier for me to try again. plus, I feel like there are a lot of things in my life that just add to the smoking. Maybe I could work on some of those first. THERAPIST: Tell me more about that. What sorts of things do you think are contributing to your smoking more? CLIENT: Well, we’ve kind of already talked about this before, and I don’t think I really saw it as a problem early on. Lately I’ve noticed that I smoke a lot more when I drink. My family has been getting together a lot on the weekends, and we always have a few drinks when we get together to barbeque. Plus, I have a couple of drinks every now and then to unwind after work. I don’t have a problem with drinking or anything, but it feels like I smoke a lot more when I drink. THERAPIST: You’ve started to notice that the two kind of go hand in hand, and you’re feeling like maybe it’s time to make some changes with the drinking so you won’t smoke so much. CLIENT: The smoking may be hard for me to manage, but I know the drinking is something I can control. I really think if I cut back, or even cut it out all together I won’t smoke as much, especially on the weekends. THERAPIST: I’m not sure if this is something you’d be interested in or not, but what are your thoughts about adding that as a goal on your wellness program? If you’d like, we can talk about how much you’d like to cut back, and when you’d like to start, and we can go from there. CLIENT: That sounds good to me! I’m willing to work on a plan. I think it would be a good place for me to start.

As illustrated within the scenario, the counselor continuously used an MI framework, and maintained the focus on MI when discussing the topic of smoking and setting a quit day. However, the client expressed more change talk than sustain talk with regard to drinking, which signaled the counselor to switch to a CBT-based problem-solving approach to address drinking behavior.

Social Cognitive Constructs

Because self-efficacy is a determinant of coping behavior ( Bandura, 1977 , 1986 ), standard social cognitive approaches to increasing self-efficacy are incorporated within MAPS. Thus, the therapist’s role is to help individuals learn to identify and verbalize issues of concern, recognize when difficult and high-risk situations or behaviors occur, learn to plan ahead for those situations, and acquire and perform coping strategies as appropriate. For example, to increase self-efficacy, the therapist will work to enhance individuals’ perceptions that they can be successful in making changes through identifying steps taken to change or reduce their smoking, providing positive reinforcement for those steps, reframing even small changes as positive steps toward reaching goals, and emphasizing the role of choice in making difficult behavior changes. The therapist’s first step in providing training in the use of coping skills is to help the individuals operationally define goals for change. The therapist then helps the individual to identify potentially difficult situations or barriers that might influence accomplishing the goal, and provides a menu of potential options for coping with difficult high-risk situations and overcoming barriers to change (e.g., avoiding high-risk situations such as bars, coping with urges to smoke and negative affect through positive self-talk, deep breathing, or distraction, and escaping situations that become too overwhelming to effectively cope with).

The following therapeutic exchange illustrates how a typical MAPS session might evolve for a client who has recently quit smoking and experiences a decline in motivation to maintain abstinence as he anticipates attending his birthday party at a bar where his friends will be drinking.

THERAPIST: So the first thing that we have on your wellness program, after your goal of quitting smoking, is to get back into exercising. The last time we spoke you mentioned that you wanted to start off by going to the park down the street a couple of times per week and walking at least 30 minutes. How’s that been going? CLIENT: It’s actually been going well. It’s been so long since I’ve been active. I was kind of worried that I would be too busy or that I just wouldn’t be very motivated when I got home from work, but I’ve actually stuck with it. I talked to my wife about it after our last session, and she’s been a big help on the days that I don’t feel like going. THERAPIST: She helps keep you motivated. CLIENT: She really does! She’s actually been going with me, which helps. But the best thing is that I’ve noticed that I can breathe so much better now that I’m not smoking. I think that’s one of the biggest reasons I stopped being active. It was just so much harder to breathe when I tried to be active before. THERAPIST: It’s a good feeling to actually know that your health is improving as a result of quitting smoking. CLIENT: It’s a great feeling! My main priority is to improve my health so I can be around for my family. THERAPIST: It’s an accomplishment you’ve worked really hard for! So tell me what you would like to do with your physical activity over the next couple of weeks. How would you like to modify what you’re doing, if at all? CLIENT: I think I’d like to keep it at two days a week for now. Every time I’ve tried to get back into exercising in the past, it seems like I always set such big goals that aren’t realistic. Then, when I’m not able to meet them, I get discouraged and give up. I want to make sure I stick with it this time. THERAPIST: Sounds great! You really know yourself well. We will keep it at twice per week. Are you still aiming for 30 minutes each time as well? CLIENT: For now, yes. THERAPIST: Alright. We will stick to 30 minutes, twice per week. Now the next thing we have on the wellness program is limiting yourself to 1 or 2 beers when you’re out with friends or at family gatherings on the weekends. How has that been for you? CLIENT: So far, so good—but I’m not sure how much longer I can keep going with that. I mean, I really don’t want anything to jeopardize everything I’ve done with the smoking, but it’s just so hard to not really be able to drink when you’re having a good time. Next weekend is my birthday party, so it may be even harder to stick to the 1- to 2-drink limit. THERAPIST: It’s hard to see yourself keeping up with this for the long term, and at the same time, you don’t want anything to get in the way of your staying away from smoking. CLIENT: Yeah, there have been so many times in the past where I’m able to quit smoking and I’m doing well, then I have a night out with friends and it all just goes out the window. It’s harder to say no to a cigarette when your inhibitions are lowered. Once I have that first cigarette, I’m back to full-blown smoking. Even then, I don’t know how realistic it is to not really drink on my birthday, at my own party. All my friends and my family are going to my favorite bar, and I just want to have a good time. THERAPIST: I can see how that would be an incredibly tempting situation. While you’d like to be able to control your drinking on your birthday, you’re not really confident that you’ll be able to. CLIENT: It’s just so hard when everyone around you is drinking and having a good time. Plus, it’s hard to say no when people keep offering you drinks. I’m just not sure how it’s going to go….

At this point in the session, because the client is engaging in much more sustain talk than change talk about drinking, the counselor should continue with MI. Next, the counselor uses the decisional balance exercise to help the client clarify his thoughts and feelings about a high-risk situation for drinking and smoking relapse.

THERAPIST: Now David, I know we had a similar discussion when you were thinking about smoking, but I’m just curious about what the good things about drinking might be for you? CLIENT: Well, there aren’t that many. I don’t feel like drinking is something I have to do, but it does help me to unwind. THERAPIST: It relaxes you. CLIENT: It does. Plus, it’s just something I do when I’m out with friends or at a get-together with family. THERAPIST: A part of your social life. CLIENT: There’s always a little bit of drinking at our social gatherings. People don’t usually get carried away or anything, but it’s just something that’s around when we get together. THERAPIST: Sure. It’s something you do in moderation, and usually have good control over. Now what do you think some of the not-so-good things about drinking are for you? CLIENT: Well, this usually doesn’t happen, but every once in a while I get a little carried away. It’s rare, though. It usually only happens on special occasions. THERAPIST: On holidays or birthdays. CLIENT: Exactly, that’s what worries me about this weekend. The aftermath isn’t very fun either. Usually when I get carried away, I feel terrible the next day. I kind of just lay around all day, trying to recover from the night before. My wife hates it, and has no problem pointing it out. THERAPIST: The consequences aren’t the best when you have too much to drink. You mentioned that you’re worried about getting carried away. What might happen if you did? CLIENT: Well the worst thing that could happen is that I would have a cigarette. That would be terrible! I’d be really upset with myself, and I think my wife would be disappointed. THERAPIST: You feel like you would be giving up everything you worked so hard for. CLIENT: It took a lot for me to be able to quit smoking. It wasn’t easy at all. I’ve tried so many times in the past, and this is the longest I’ve gone without smoking. The more I think about it, I don’t know that I want to do anything to risk giving up everything I’ve worked so hard for. It’s not like I have to go out and drink to celebrate my birthday. THERAPIST: Maintaining your abstinence is just too important to you. CLIENT: I’ve just come way too far to go back to smoking. THERAPIST: So if we go back to your wellness program, where does that leave you? What would you like to do with your goal of limiting the amount of alcohol you drink?

Now that the client is exhibiting a good amount of change talk (rather than sustain talk), the therapist shifts back into CBT-based skills training.

CLIENT: I guess I could try to stick to what I already planned, and try to keep it at one or two drinks. Maybe I should just have some friends over at my place instead of going out somewhere. It seems like I drink more when I’m out at a bar. Now I just have to find a way to not go overboard. THERAPIST: If you’re interested I can share some ideas that other people we’ve worked with sometimes use. I’m not sure if they would work for you, but you can let me know. CLIENT: Sure, I’m okay with that. THERAPIST: Often people that we work with try using some of the same skills that they used when they were trying to cut back or quit smoking. For example, they’ll avoid situations or people that they think may influence them to drink more. Some people will talk to their friends or family ahead of time and ask that they help encourage them or not pressure them to drink too much. I’ve even had some people say that they will just keep the same drink in their hand throughout the night or drink a lot of water in between drinks. What ideas come to mind for you? CLIENT: Well, I’ve actually done that last one before and it worked out okay. I drank several glasses of soda or water in between drinks, and people didn’t really push me to drink a whole lot because it always seemed as though I had a drink in my hand. THERAPIST: So you’re thinking that may work for you on your birthday. CLIENT: I’m going to give it a shot.

Presented below is a brief session-by-session overview intended to represent the general therapeutic content that should be addressed during a six-session MAPS-based treatment protocol.

Session-by-Session Overview of a Six-Session MAPS-Based Treatment Protocol

The goals for the first session include: (a) introduction of the agenda and establishing rapport; (b) review of confidentiality; (c) collection of information regarding smoking history, previous quit attempts, and current smoking; (d) administration of importance, confidence, and readiness rulers; (e) building motivation and completing the decisional balance exercise if the client is not ready to quit or preparing for the quit attempt if the client is ready to quit; (f) introduction of the wellness program; and (g) ending the session and scheduling the next session.

The introduction of the wellness program is a critical component of the first treatment session. To introduce the wellness program/plan, the counselor might use the following language: “ The final thing on today’s agenda is to talk with you about the wellness program. The wellness program is like a list of goals that can remind us of what you’d like to accomplish during the time we work together. May I have your permission to work on this plan with you? The first goal usually refers to something about your smoking. You’ve already indicated that you are/aren’t ready to make a quit attempt .”

For clients who are not ready to quit, the counselor might use the following language to talk about goal setting: “ You’re not yet ready to quit, but even deciding that you are willing to talk with me about smoking again in the future, or that you’d be interested in thinking about what things would be like if you were to quit would be reasonable goals? So, what should we write for yours?” For clients who are ready to quit, the counselor might says self the followingp: “ So, what should we write for your smoking goal?” The counselor then follows up by asking what else can be done to help the client prepare for the goal, and ensures that the goal is measurable.

For all clients (regardless of whether or not they are ready to quit smoking), the counselor then introduces the topic of expanding the wellness program using language similar to the following: “ Now, we’ll talk about this more fully the next time we speak, but the wellness program can contain a number of other goals. For example, people usually list other things that are important to them, things that have not been going well for them, or things that are connected with their smoking that they might also want to change, such as their stress level, feelings of depression, relationship issues, or their drinking. The wellness program gives us some specific things to touch base on during our next few sessions. What else should we list on your wellness program ?” At the end of the session, the counselor tells the client that the goals will be revisited during each session and that goals on the wellness program can change at any time. The counselor then summarizes the goals and checks in with the client to make sure nothing has been forgotten.

In the second session, in addition to introducing the agenda, the therapist’s goal is to continue building rapport. Therapist and client also review—and possibly revise—wellness program goals. If the client has not set a quit date, the counselor inquires about how things are going with smoking, and explores the client’s thoughts about quitting with the readiness rulers. If the client is ready to take action, the counselor draws from the “Preparing to Quit Smoking” module of the manual. If the client is not ready to take action, the counselor draws upon MI strategies to build motivation. At this stage, many smokers are ambivalent about their decision to quit and may lead themselves into negative self-talk. The counselor listens carefully and then reflects the client’s change talk statements in an effort to bolster motivation and enhance self-efficacy. The counselor also informs the client that wellness program goals can be set to “increase readiness to make a quit attempt.” If the client has quit, the counselor inquires about how things are going and listens carefully for ambivalence about maintaining abstinence. The counselor positively reflects change talk expressed by the client to help bolster motivation, enhance self-efficacy, and highlight small achievements in an effort to increase motivation to remain quit. If the client is at all willing to address smoking, the counselor begins to address high-risk situations for returning to smoking, and the remainder of the wellness program goals are reviewed, addressed, and revised if needed.

Values identification is another important element of Session 2. The therapist assists in identifying valiues that are important to the client. These values are linked to the goals listed in the wellness program to help the client move toward change. The counselor might say the following: “ If it’s okay with you, we can move on to exploring values that are most important to you and your family. Sometimes our goals, such as the ones you listed on your wellness program, are important to us because of the values that we have in life, and it may be helpful to see how that might or might not apply to the goals you listed, such as your [insert smoking goal here].”

The remainder of the session focuses on enhancement of self-efficacy and scheduling of the next session.

Sessions 3, 4, and 5

The goals for the third, fourth, and fifth sessions are as follows: (a) continuation of rapport building and introduction of the agenda; (b) review and possible revision of wellness program goals (review of progress with quitting; review of barriers to quitting; review of high-risk situations, CBT-based skills training strategies, and lapses); (c) check-in with importance, confidence, and readiness rulers; (d) repetition of decisional balance exercise as needed; (e) use of CBT-based treatment modules as needed; and (f) scheduling of next session.

The goals for the final session include (a) reconnection with the client; (b) review of progress made during treatment; (c) consideration of next steps; and (d) saying goodbye and providing referrals as necessary.

Summary and Conclusions

Despite strong theoretical and empirical bases for focusing on both motivational and social cognitive constructs, there are few evidence-based counseling interventions for substance use that encompass both motivational enhancement strategies and coping skills training, and to the best of our knowledge, even fewer that address motivation as a dynamic factor than can fluctuate rapidly and fluidly, or that include a strong emphasis on motivation following behavior change (i.e., it is generally assumed, whether explicitly or implicitly, that individuals in the action or maintenance stage are sufficiently and consistently motivated to maintain behavior changes ( Burke et al., 2003 ; Fiore et al., 2000 ; McClure et al., 2005b ). In response to these omissions, MAPS is a hybrid treatment for substance use based on the clinical integration of empirically supported coping skills training/problem-solving techniques derived from social cognitive theory ( Marlatt & Donovan, 2005 ; Witkiewitz & Marlatt, 2004 ) and motivational enhancement techniques derived from MI ( Miller & Rollnick, 2002 ). MAPS draws heavily from the model proposed by Baer and colleagues (1999) nearly 10 years ago, yet is unique in that it addresses substance use within the context of general life stressors and dynamically switches between skills training and motivational enhancement strategies based on motivation to attempt, achieve, and maintain abstinence. MAPS has demonstrated efficacy in the prevention of postpartum smoking relapse ( Reitzel et al., 2010 ) and we believe that it also has relevance for other health risk behaviors. Hybrid approaches, such as MAPS, for the treatment of substance use have the potential to profoundly affect public health. Therefore, we believe that the call for further research on hybrid approaches made by Baer over a decade ago remains salient today. In addition to describing MAPS, the current paper is intended to serve as a call for further research on hybrid approaches for the treatment of substance abuse and dependence.

Acknowledgments

This manuscript was supported by grants from the National Cancer Institute (R01CA89350; R01CA125413; R25TCA57730) and the Centers for Disease Control and Prevention (K01DP000086; K01DP001120).

Contributor Information

Jennifer Irvin Vidrine, University of Texas MD Anderson Cancer Center.

Lorraine R. Reitzel, University of Texas MD Anderson Cancer Center.

Patricia Y. Figueroa, University of Texas MD Anderson Cancer Center.

Mary M. Velasquez, The University of Texas–Austin.

Carlos A. Mazas, University of Texas MD Anderson Cancer Center.

Paul M. Cinciripini, University of Texas MD Anderson Cancer Center.

David W. Wetter, University of Texas MD Anderson Cancer Center.

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What does a problem-solving mind map look like?

So what does a problem-solving mind map refer to? Well, when we think of mind mapping, we think of generating ideas or brainstorming. When you brainstorm ideas, it’s not about possible solutions; it’s about all the possibilities. The focus of a mind map is more on where to explore and find strategies. Yet with a stable framework, it can help to find solutions for complex problems.

This is yet another one of many mind map examples out there and one of the most efficient problem-solving strategies you can use. Mind maps are already powerful idea-generating tools to consider. They help with the complexities and chaos to get to the most efficient path.

It can be a particular problem or several problems where you’re trying to process the big picture. It helps to organize solutions that are hiding in the brain, whether those problems come from life or business. The structure of a problem-solving mind map slightly shifts, but the technique of mind mapping stays the same. Of course, it helps to understand how to see the big picture of how to solve a problem first.

Is mind mapping an efficient tool for problem-solving?

Short and long answer, a mind map is excellent for problem-solving. This is because it’ll have all the elements that are different in one place. The central idea instead is the actual problem, and the connections branch out. We now brainstorm ideas that are really there to point out the possible solutions.

If the problem is too complex, creating multiple simpler mind maps will help the brain to process possible solutions easier. A recent study shows how the brain can handle the essentials first against complex problems. This puts less stress on the brain and gives a better chance to solve the problem.

A mind map helps with the rest of the components of the study as well. You’re able to divide up the ideas and content, such as images or even a reference article. The benefit of creating a mind map is that central concept and base for all the detailed information. It all depends on how you use mind maps , to begin with.

How is a problem-solving mind map structured?

It’s a good idea to have the key skills required to make a normal mind map. Even before we get there, take a moment to do an exercise on paper. Write the problem down and try to connect or implement solutions throughout. You’ll quickly see the need to organize, and here you can stop and head back to your mind map software. It’s more just to see that structure is essential, as well as data and information collection.

Key skills include knowing typical structures, what main branches are, and mapping out the flows. Getting these key skills mean using a graphic organizer on a constant basis. Whether you make business mind maps , creativity mind maps, or education mind maps , make sure to have the right level of experience. You want this before attempting mind mapping to find solutions to a simple or complex problem.

Once you get the key skills required, the structure of the problem-solving mind map starts out the same.

Here we begin with a hierarchical approach, where the main branches are the problems to address. The sub-branches are either ideas or solutions to the problems. It benefits from the creativity and brainstorming that comes with mapping a mind map.

You can also go with a radiant thinking approach, where you start with the problem in the center. As the central idea, the ideas and solutions will radiant from the center. It’s ok to put imaginative solutions as well as more practical ones as a mind-mapping technique.

Consider colors and symbols

It may be a good idea to color code the sub-branches and write down what each color means. Writing notes is a standard aspect of mind maps focused on solving a problem. Don’t be shy to use images in your mind maps. These images can be of an individual problem, such as a roadblock that represents an obstacle. You can use positive symbols for your mind mapping to show ideas or a solution.

Doing mind maps this way actually ends up making them much more fun to use. That means you’ll be more prone to map out everything that you need to solve.

Mind map templates for problem-solving

You can start creating your mind map from scratch and get inspiration from existing mind map examples, or you can use a predefined template. Here are the most used templates you can copy and edit anytime:

1. Problem solving mind map template

This mind mapping template helps you solve a problem following the 5 step strategy: describe the problem, set goals, identify possible solutions, make an action plan, and add conclusions.

2. Manage a problem

This mind map helps you identify all the information on how the elements of problem management interact with each other. It’s more suitable for complex problems.

3. 6 Thinking Hats

The 6 thinking hats template allows looking at a problem from multiple perspectives. This way, you get significantly higher chances of solving it more effectively.

4. 5-Whys Root Cause analysis

This template will help you find the reasons behind the obvious reasons and go back to the root of your problem.

5. Means-end analysis

This is suitable for simple problems and has a similar backward process as the template above.

6. Fishbone diagram

The fishbone diagram is a fantastic example of a mind map for kids , and adults can also use it.

7. Problem description toolbox

Before starting to solve a problem, it is essential to describe and analyze it constructively and comprehensively. That is exactly what this template will guide you to do.

Mind mapping a problem is not a one-time solution

Problem-solving is typically an iterative approach, and that means your mind map will be a dynamic tool. That’s why it’s always best to use mind mapping software when possible so as to be able to keep track of everything. Whether you’re using it for problem-solving on your business plan or for making life choices, you want it fresh. Even if a particular problem has been resolved, adding on a new creative problem keeps the brain working to find a solution.

Don’t forget to take time to get fresh air once in a while to clear your head. Your daily life problems you’re trying to resolve will still be there. A clear mind will help bring in more ideas and eventually the desired result you were looking for. Problem-solving isn’t always meant to be easy. Mind maps can only be effective at problem-solving when you’re fresh as well.

Use the right mind-mapping tools

When you are creating a mind map for problem-solving, you want to start with an example of an excellent mind map. Mindomo helps you not only with the right starter example but with one ready to handle a problem.

It comes with tools to help organize your thoughts , focus on the moment’s problem, and show all the possibilities. You can place problems on one end and solutions on the other. Or you can map out the whole end-to-end route from problem to solution. Either way, it will help you solve problems.

 Get your problem-solving hat out and be amazed at how mind-mapping software removes the difficulties of getting started. Feel free to try out our flexible tool and simple solution today. You’ll find the answer to your complex problems in no time.

Keep it smart, simple, and creative! The Mindomo Team

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Hand-drawn cadastral map parsing, stitching and assembly via jigsaw puzzles

• Original Paper
• Published: 14 May 2024

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• Tauseef Iftikhar 1 &
• Nazar Khan 1  

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We present a robust method for parsing the content of hand-drawn cadastral maps in order to obtain high-resolution, digitized assemblies of larger regions from individual maps. The parsing phase involves solving a challenging background grid detection plem. We exploit the geometry of detected grids for stitching overlapping map images. A novel method for computing geometric compatibilities between non-overlapping map pieces is also introduced. It is shown to be important since existing chromatic compatibility measures are not as useful for hand-drawn maps. Assembly of maps involves solving an arbitrary-boundary jigsaw puzzle problem with non-overlapping pieces of the same rectangular shape. It corresponds to finding a maximum spanning graph within a multigraph whose edge weights are the piece compatibilities. Since the problem is NP-hard, we develop a polynomial time approximation algorithm that involves two distinct greedy decisions at each iteration. In contrast to existing evaluation metrics for fixed-boundary jigsaw puzzles, we present an \(F_1\) -score based evaluation scheme for the arbitrary-boundary jigsaw problem that evaluates relative placements of pieces instead of absolute locations. On a testing set of 218 images of 109 cadastral maps comprising 15 different map assembly problems, we achieve a high average \(F_1\) -score of 0.88. Results validate our compatibility measure as well as the two-stage greedy nature of our method. An ablation study isolates the importance of individual modules of the developed pipeline.

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Acknowledgements

The authors are thankful to Sohaib Khan for providing access to the dataset [ 38 ] and for introducing this paper’s research problems to the corresponding author.

This work was supported by HEC-NRPU grant 8329 titled “DoCMap: Digitization of Cadastral Maps”.

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Creating a queens game map on linkedin.

N-queen Problem

Diagonal placement condition for the queens problem, the area condition in the queens problem.

LinkedIn is a recruitment and job search site with over 1 billion members worldwide, and its weekly active users (WAU) reach 65 million. 1 Although it is a social networking service, unlike Instagram or TikTok, it is a place where serious discussions about careers and work are prevalent. However, recently (as of May 1, 2024), three games were added to LinkedIn, which caused controversy as it didn’t seem to fit the atmosphere of the platform.

However, if we think about it, adding casually playable games is something that social networking sites like Facebook have been doing since ancient times, and even The New York Times has various games, including crossword puzzles. The acquisition of Wordle, which gained tremendous popularity after its launch in 2021, by The New York Times at a high price was a very famous event in the industry. 2

It seems that LinkedIn also recognized the importance of adding casually playable games, as the three games added this time all take only 5 to 10 minutes to play. Among them, two of the games are language-related, so algorithmically generating them seems not so simple (although it could be done quickly using LLM, we won’t delve into it here). Instead, in this blog, we will discuss how to generate maps for a game called Queens.

To understand the Queens game, you first need to know the N-queen problem. The N-queen problem, where N queens must be placed on an NxN board in positions where they do not attack each other, can be very time-consuming to solve indiscriminately, but it is a well-known algorithm problem that can be relatively easily solved by modifying the conditions for solving the problem.

In chess, queens can move to any square on the same row, same column, or diagonal from their current position. Therefore, to avoid attacking each other, the queens must be placed so that they do not overlap in rows, columns, or diagonals.

To simplify the problem slightly, let’s consider rooks instead of queens. Rooks can move only along rows and columns, not diagonally.

A common feature seen in the solutions for both N-queen and N-rook problems is that neither queens nor rooks can be placed more than once in the same row or column. When placing rooks one per row sequentially, as long as each rook is in a different column, it constitutes a solution to the N-rook problem.

Code 1. Code for finding the solution to the N-rook problem

The search(arr) function in the above code starts with an empty array and proceeds to find the column numbers of the rooks to be placed on each row. The termination condition of the search(arr) function, as seen in line 19, is when the length of arr is equal to N . Otherwise, if there is a number i from 0 to N-1 that is not already in the current arr , it finds it and calls a new search([...arr, i]) function. While not all results are displayed in the result pane on the right due to space constraints, you can verify that the number of solutions for N=4 is 24. By changing the N in line 30 to 5, 6, 8, and so on, you’ll notice that this number corresponds to the factorial function learned in mathematics. Hence, the number of solutions to the N-rook problem is \(N!\).

So, how would you solve the N-queen problem? You can slightly modify the search function in the above code to check for diagonal conditions. It involves checking if there are any queens already placed in diagonal positions with the new number i being added to the arr . Below is the code representation of this modification.

Code 2. Code for finding the solution to the N-queen problem.

  The additional condition added after the if statement on line 24 is arr.filter((c,idx) => Math.abs(i-c) == Math.abs(arr.length-idx)).length == 0 . This checks if there are no elements in the current arr where the difference in columns (Math.abs(i-c)) and the difference in rows (Math.abs(arr.length-idx)) for the queen to be placed in the arr.length -th row and the i -th column are equal. If there are no such elements, it means that the placement is possible, so the search([...arr, i]) function with i added to arr is called. The number of solutions reduces to 2 when N=4. Changing N to 8 in line 30 reveals that the answer is 92. The number of solutions has decreased significantly compared to the N-rook problem.

However, the diagonal placement condition in the Queens problem is slightly different from the N-queen problem. While the condition remains that only one queen should be placed in each row and column, in terms of diagonals, two queens can be adjacent to each other as long as they are not in the same diagonal. In other words, as long as they are one square apart diagonally, it is acceptable.

Code 3. Code for finding the solution to queen placement in the Queens game.

The condition in the if statement on line 24 has changed from checking the entire queens in arr to checking only the last queen ( arr[arr.length-1] ). Since queens are placed sequentially in each row, for example, if placing a queen in the 3rd row, there’s no need to consider the queen in the 1st row, only the queen in the 2nd row needs to be considered. With this change, the number of solutions for N=8 becomes 5,242. This is an increased quantity compared to the original N-queen problem.

However, the Queens problem goes one step further. In addition to the conditions mentioned earlier, each queen must be placed only one per area of the same color. For example, the arrangement of queens in the columns 02415736, as examined above, can be represented with the added area condition as follows:

An arrangement where an 8x8 chessboard is divided into 8 regions and only one queen is placed in each region. In this case, the regions must be connected to each other, each cell belongs to only one region, and all cells must belong to exactly one region, which seems to be implicitly applied. This scenario corresponds to the N=8 case in the Linkedin Queens game, and by using one of the 5,242 queen placements obtained earlier and randomly assigning regions, we can obtain a map that looks similar to the one offered in the Linkedin Queens game. However, whether it will be fun or not is a different issue, and this blog will not delve into that aspect.

To satisfy the region condition, we start with the queen placement state from Code 3. First, we designate each cell where a queen is placed as a different region.

Next, we designate as candidates the neighboring cells, vertically and horizontally, that have not yet been assigned a region.

Next, we randomly select one of these candidates and assign it to one of its adjacent regions. Then, we update the list of candidates.

By repeating this process, we can obtain a random region condition map based on the queen placements.

In this post, we explored how to create maps for the Queens game added to LinkedIn. We also have various articles in mind about generating game levels using PCG, so we appreciate your interest. Feel free to inquire about any further questions you may have. Thank you for reading this lengthy post.

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The Sudden Rise of Wordle , The acquisition price is said to be a seven-digit number, so it is a significant amount exceeding $1,000,000 or 1.3 billion Korean won.  ↩

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10 Best Math AI Solvers to Solve Math Problems Online

Tackling challenging math problems can be a time-consuming endeavor. Math AI solvers make learning math simple. These AI-powered tools use machine learning and advanced algorithms to rapidly analyze math problems at all grade levels. Whether you’re a high school student or at the college level, an AI math problem solver can help save you time, ensure accuracy, and boost your school success.

With 24/7 convenience, they can be used anytime to get instant help with confusing math problems. When curating our list of top 10 best math AI solvers, we looked at several important factors, such as pricing, features, strengths, and weaknesses. Let’s explore these tools and learn in which areas they excel:

Mathful – Best Overall Math AI Solver to Solve Math Problems

Mathful is a valuable AI math solver often used by students to get help with complicated math problems. It delivers step-by-step guidance that breaks down the problem to make it easier to digest. The tool also provides the final answer to allow students to verify their solutions and gain confidence in their math skills.

Mathful is available 24/7, making it a convenient tool for students to get instant help with their math homework. Mathful acts as the ultimate solution for boosting academic success at all math levels. 

• Helps students gain a deeper understanding of math concepts with step-by-step guidance.
• Serves as a verification tool where students can check their work without costing a dime. 
• Enables students to complete their math homework with just one click. 
• Cannot be used to supplement a real classroom education. 

Solve Math Problems Instantly with Mathful’s AI Math Solver >>>

AI Math – Best AI Math Solver for All Grade Levels

AI Math is an innovative math AI solver designed to solve a wide range of mathematical problems, ranging from basic math concepts to more challenging equations. 

The way this unique tool works is by analyzing the math problem, finding potential solutions, validating those solutions, and returning the best possible results for the given problem.

While some math AI tools are only capable of solving basic math problems, AI Math is more diverse. Use it to solve math problems at all grade levels, from elementary to university and beyond. AI Math is trained on an extensive database of mathematical information and can guarantee 98% accuracy.

• Generates solutions to math problems with a high rate of accuracy.
• Designed to provide almost instant results for efficiency. 
• Covers all types of math and homework at all grade levels. 
• Requires a subscription after the initial trial period.

HIX Tutor – Best AI Math Solver for High Accuracy

HIX Tutor provides students with the solutions they need to understand and solve their math problems. 

With this powerful math solver AI tool, users can type in a math question or upload a document or image of the question. Using this input, Math AI Solver uses machine learning technology to perform dynamic calculations and give users the correct answer. 

HIX Tutor can provide solutions for math homework problems at all levels with a 98% accuracy rate. However, the tool goes beyond mere problem-solving by offering comprehensive calculations on how to solve the problem from start to finish. 

• Provides step-by-step solutions to math problems.
• Is less expensive than hiring a math tutor.
• Can type in math questions or upload documents or images of the problem.
• May have difficulty recognizing documents with messy handwriting.

HomeworkAI – Best All-in-One Solution for Homework Help

HomeworkAI is the ultimate homework assistant that can be used to get answers to any homework question, from math and science to history and geography. Its math AI solver acts as your personal AI tutor by providing comprehensive solutions to math problems that help students better understand the material.

This unique AI tool is available 24/7, making it a convenient and accessible resource for students who need immediate help with their homework. As the tool is free to try, students can get started right away by asking a math question that they’re struggling with. HomeworkAI can also help students prepare for important tests or exams by providing step-by-step instructions on how to work through certain math questions.

• Covers all school subjects, including math.
• Provides step-by-step explanations for each math problem.
• Supports multiple math problem input methods. 
• Some math solutions may be difficult to understand. 

Question AI – Best Homework AI Tool for Greater Academic Success

Question AI is a leading homework helper that uses powerful AI technology to instantly help with any school subject. Question AI is often used for any math problems, covering algebra, geometry, calculus, arithmetic, and trigonometry. Students often waste hours struggling with challenging homework questions they simply don’t understand. Question AI simplifies the homework process by breaking down the question to make it easier to learn. The math AI solver also promises a 99% accurate answer to the math question, allowing students to verify their own work.

Question AI serves as an innovative all-in-one product for AI homework help. It is a highly effective tool for helping students reach greater academic achievement.

• Covers all homework subjects, including all branches of mathematics. 
• Boosts student grades.
• Supports many different languages.
• Accuracy may be limited beyond core math subjects.
• The mobile app is not yet available. 
• Costs money after the free trial. 

QuickMath – Best Math AI Solver for High School and College Students

QuickMath is designed to automatically answer common math problems in algebra, calculus, and equations. The tool offers several options for solving math problems, including solving an equation, inequality, or a system. It can also simplify an expression, factor an expression, or expand a product or power. The diverse AI math solver can also graph, find the greatest common factor, and the least common measure. Advanced math solvers are also available for more complex math problems.

QuickMath is geared toward high school and college-level students. The tool’s features and capabilities are always being improved to ensure that users have access to the most comprehensive AI math tools available. 

• Offers a wide range of standard and advanced math solvers.
• Available to download on the App Store and Google Play.
• Quick-solve tutorials are available to help users learn math concepts. 
• Math problems must be typed in and cannot be uploaded. 
• Not suitable for grade levels lower than high school.
• Some users may receive Timeout messages due to 15-second CPU time rules.

Smodin – Best AI Math Solver for Acing Math Exams

Smodin Math AI Homework Solver offers a fast and effective way to prepare for difficult math exams. The versatile homework helper uses machine learning and advanced algorithms to help students learn core math concepts and boost their grades in school. Simply input a question or assignment and Smodin instantly generates step-by-step solutions.  The math solver AI tool consists of a simple interface that allows students to enter a question to solve. At the click of a button, the tool starts working to analyze the problem and present the best answer based on the equation. 

While Smodin Math AI Homework Solver does lack advanced features and capabilities, it can be a useful tool for students who want to study before a big math test.

• Provides in-depth answers to math questions to help students ace math exams.
• Users are given 3 free credits a day to ask math questions. 
• The clean interface makes it easy to enter math questions to solve. 
• Offers no advanced math features or capabilities.
• Users must pay for a subscription after reaching the daily credit limit. 

StudyMonkey – Best AI Math Problem Solver for Personalized Learning

StudyMonkey is a diverse homework helper for students that uses complex machine learning capabilities to provide step-by-step guidance on many school subjects, including math.  The innovative math AI solver can be used by learners of all backgrounds and ages to improve their understanding of math concepts and enhance their academic success. With round-the-clock availability, this unique tool can save students significant time when completing homework assignments.

• Students can personalize their output based on the subject and grade level. 
• There is a free plan for users that only requires occasional homework help.
• Users can see a history of past questions and answers. 
• Users must purchase a paid plan to ask more than 3 questions daily.
• Answers to more complex math questions may not be as accurate. 
• Must upgrade to the $8 plan to use the Advanced AI Model. 

Interactive Mathematics – Best Math AI Tool for Solving Word Problems

Interactive Mathematics claims to be more accurate than ChatGPT, faster than a math tutor, and more powerful than a math calculator. The advanced AI math problem solver has been trained in a wide array of math subjects, such as basic algebra, advanced algebra, trigonometry, geometry, calculus, advanced calculus, physics, and more. It is also highly effective at solving math word problems with step-by-step solutions. 

With Interactive Mathematics, users can type in their math problems or copy and paste a photo. The tool then analyzes the problem and delivers near-instant results. 

• Efficient at solving math word problems.
• Optimized for mobile phones and tablet use.
• A subscription comes with additional discounts and bonuses. 
• Users can only ask 3 questions before having to upgrade to the paid version. 
• No app is yet available. 
• Pushes tutoring services when the tool is unable to give an accurate answer. 

SnapXam – Best AI Math Solver for On-the-Go

SnapXam is an AI-powered math tutor that can help students better understand different types of math, from calculus to trigonometry.  After entering the math problem, the tool quickly presents the final answer, as well as a step-by-step solution that shows how to work out the problem.

The unique AI math problem solver also provides access to informative YouTube videos that students can watch to learn more about different concepts in math. 

Upgrading to a Premium account can give students access to even more features and perks, including no ads, support for more than 100 math topics, and premium access to the iOS and Android apps.

• Students can get AI math help with only access to a smartphone. 
• Offers multiple solving methods.
• Covers more than 100 different math topics. 
• An ad-free environment is only available with the premium version.
• Geared toward older students. 
• Accuracy issues may occur with advanced math problems.

Completing math assignments can be a long and tedious process. Having access to the best math AI tools can help eliminate the stress and frustration that come with not understanding math problems. For convenience, efficiency, and unmatched accuracy, try some of the top math AI tools like Mathful for free today!

This is a guest post, created for informational purposes only, and should not be considered as professional advice. Readers are encouraged to conduct their own research and consult with relevant experts before making any financial or investment decisions.

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How to prepare for a sustainable future along the value chain

Our lives have changed radically as a result of the pandemic. But as dramatic as the impact of COVID-19 has been, it has by no means eclipsed another topical issue: the need to shape a more sustainable economy. In fact, this task has attracted heightened public attention following extreme weather events such as the devastating flooding all over Europe last summer. Last fall, decision makers from around the world met in Glasgow, Scotland, for the 26th United Nations Climate Change Conference  to discuss the challenges ahead. Although the debate primarily focused on major emitters, such as the energy, steel, and construction industries, the consumer-goods sector is equally called upon to take action.

About the authors

But what exactly do we mean by “sustainability”? In its broadest sense, the term covers three areas: environmental, social, and governance—or ESG for short. Specifically, ESG encompasses the degree of responsibility that companies assume—irrespective of what they are legally required to do—for sustainable development in the three areas mentioned.

80%: Share of consumer emissions that reside in supply chains. To meet the pathway to net zero, CPG companies need to work with their suppliers to secure green raw materials and supply

For many, sustainability is primarily about our use of natural resources and the climate impact of our actions. This is also highly relevant for consumer-goods manufacturers. As a rule, it is not enough to look only at one’s own value creation. After all, a typical consumer-goods company’s supply chain generates far greater environmental costs than in-house operations: for instance, it is responsible for more than 80 percent of greenhouse-gas emissions and more than 90 percent of the impact on air, land, water, biodiversity, and geological resources.

The consumer-goods industry is facing a huge environmental challenge: if it intends to meet the current EU climate targets, it will have to more than halve its greenhouse-gas emissions by 2030. Given that prosperity and consumption will continue to grow in the coming years, a fundamental change in thinking is required; new business models—especially those relating to the circular economy —will have to gain an increasingly firm footing.

Growing pressure and rising opportunities

Even beyond the climate targets that have been set, regulatory requirements for the economy are becoming more stringent—for example, through levies such as the “plastics tax.” The European Union’s Green Deal provides for all packaging in the EU area to be reused or recycled by 2030. The Circular Economy Action Plan also provides for products to have long life cycles and be repairable (“right to repair”).

But it’s not just from the regulatory side that pressure is growing. Other stakeholders are also demanding more sustainability from companies or setting their own new standards for sustainable business practices.

Consumers. Today’s consumers are another pressure point since they no longer see sustainable products as simply an alternative.

They are partly basing their purchasing decisions on the sustainability of products and companies. Granted, what some refer to as an “attitude–behavior gap” remains. In other words, consumers don’t always make purchasing decisions that are consistent with their sustainability preferences as expressed in surveys. That said, two-thirds of consumers now say they are changing their consumption habits in favor of a lower environmental impact 1 “A natural rise in sustainability around the world,” NielsenIQ, January 10, 2019. —and are staying true to their word: brands, such as oat-drink maker Oatly, that promote the ecological benefits of their products are recording above-average growth rates.

Employees. Sustainability is already a top criterion in choosing an employer for two-thirds of those under the age of 34. Across all age groups, three out of four employees would like their company to place a greater emphasis on environmental and social issues. 2 Sustainable working environment index 2021 , Epson, June 2020, epson.co.uk.

57% of all start-ups in the consumer-goods sector are ‘green’ start-ups

Investors. The financial sector is, to some extent, already ahead of the real economy when it comes to sustainability. A survey of decision makers from more than 40 investment firms (including BlackRock, Vanguard, and State Street) shows that an ESG-oriented mindset is already an integral element of investment decisions. 3 “The investor revolution,” Harvard Business Review , May 1, 2019.

Increasing demands for sustainability stem partly from investors’ risk management and partly from the increasing incidence of loans linked to sustainability criteria. Furthermore, sustainability-oriented funds are more resilient, as studies show: on average, 77 percent of ESG funds established ten years ago continue to exist today. Compare that to only 46 percent of traditional funds that have survived over the same period. 4 Siobhan Riding, “Majority of ESG funds outperform wider market over 10 years,” Financial Times , June 13, 2020, ft.com.

New market entrants. “Green” start-ups are increasingly gaining market share in consumer-goods segments—be it in the footwear market, where the Californian–New Zealand start-up Allbirds has made a successful entry, or in the food segment, where products made from plant proteins (among others) are increasingly gaining popularity. According to the Green Startup Monitor 2021, three-quarters of all newly founded companies in Germany view their environmental and social impact as relevant to their strategy. In the consumer-goods sector, for example, 57 percent of all newly founded companies are now green start-ups. 5 Klaus Fichter and Yasmin Olteanu, Green startup monitor 2021 , Borderstep Institute for Innovation and Sustainability, 2020, deutschestartups.org. Take, for instance, the marketplace Cirplus, which has set itself the goal of simplifying the currently complex and confusing global trade in recyclates and plastic waste.

In view of the growing pressure from all sides, for established consumer-goods companies, it is no longer a question of whether or not they need to operate sustainably—and most are also clear about what they need to do; however, there is still great uncertainty when it comes to how. What is needed is a sustainability strategy and, above all, a road map to implement the strategy in the context of a transformation.

Moving toward action

Where do companies currently stand in their efforts to make their operations more sustainable? Rating agencies such as S&P try to answer this question systematically by referencing an array of sustainability criteria. As the ESG score of leading consumer-goods suppliers shows, the industry performs well on average (Exhibit 1). In the social dimension in particular, the consumer-goods sector almost universally earns high scores (As and Bs). This means good to excellent ESG performance and an above-average level of transparency in the disclosure of ESG data. The analysis shows that 30 percent achieve a score of A or A+ in at least seven out of ten ESG dimensions, and 52 percent achieve the same in at least five out of ten. There are also champions in individual disciplines: the consumer-goods companies listed below demonstrate strengths in certain sustainability dimensions—typically in areas that are particularly important for their business.

Nestlé has launched the Creating Shared Value program, which assures 30 million farmers and people in rural areas stable agricultural incomes through 2030, as well as the creation of fair and inclusive jobs. By 2030, Danone wants to use solely renewable energy and lower its water consumption by one-quarter. The company was already a pioneer in discontinuing the use of genetically modified feed and supporting farmers worldwide.

Unilever aims to reduce the environmental impact of water, waste, and greenhouse gases per consumer use of product by 50 percent by 2030. The group has long been an advocate of sustainable palm oil.

Henkel aims to triple the value of its business in relation to its environmental footprint by 2030 and, among other things, is relying for certain brands entirely on “social plastic”—that is, old plastic packaging collected from people living in poverty for a fee. In addition, Henkel plans to make all product packaging recyclable, reusable, or compostable by 2025 and to make its operations climate-positive by 2040.

Adidas is already a global leader in sourcing more sustainable cotton (“better cotton”). In doing so, it maintains production levels with minimal environmental impact and supports the livelihood of local producers. In addition, Adidas plans to use only recycled polyester across its entire product range by 2024.

Patagonia is a pioneer when it comes to the circular economy and good working conditions. For many years now, the manufacturer of outdoor clothing has offered to repair older articles and return them to consumers. By 2025, it aims to make its entire business carbon-neutral—including the supply chain, which is responsible for 95 percent of Patagonia’s emissions.

Beyond Meat and Impossible Foods offer product portfolios that are based on sustainable alternatives and have created significant growth in the plant-based protein industry.

Explanation of Exhibit 2

Exhibit 2 shows which sustainability targets ten leading consumer-goods companies aim to achieve by what year. The target year is indicated by the color code (with the palest shade being 2050), the percentage of companies making commitments is shown within the rings, and the magnitude of the planned change is indicated outside the rings. “Committed” means that these companies have committed to making reductions but have not explicitly specified a percentage.

An example of how to read the “Sustainable procurement” chart is as follows: 20 percent of companies want to make their procurement 100 percent sustainable by 2025.

The Honest Company was founded by Jessica Alba for the purpose of promoting cleaner and more sustainable products in the baby space.

The initiatives show how seriously consumer-goods companies are now addressing sustainability. Almost all of them have set ambitious targets in a range of areas, from emissions mitigation and recycling to sustainable procurement and water use (Exhibit 2).

Implementing sustainability goals effectively

Effectively implementing the envisaged sustainability goals is an all-encompassing organizational challenge and often means change for both the product portfolio and the organization, including its culture. Given the scope involved, it is not enough to launch individual initiatives sporadically and hope for success. Instead, sustainability must be seen for what it is: a transformation of company operations spanning the entire supply chain. Four elements are crucial here:

Set the right target level. The first step begins with a realistic outside-in assessment: What are regulatory expectations? Where are competitors raising the bar? What are the expectations of customers and other stakeholders, including investors? It is usually strategically advisable to take the lead in a small number of relevant dimensions and determine what the future minimum requirements will be in all other dimensions. The level of the targets and the speed of their achievement should be based on realistic assumptions and plans. Knowledge of the levers and the technical possibilities to arrive at a realistic ambition is of particular importance.

Plan the transformation and set the framework. Once the target level has been set, senior management should make the transformation a visible priority for everyone and plan it in detail.

To this end, measures need to be developed and incorporated into an overall road map. Governance is also crucial for successful implementation at this point; thus, instituting a sustainability officer at the senior-management level is an important framework condition. This does not necessarily have to be the chief sustainability officer, as long as the organization ensures that the central team works effectively with the operational units and can not only create initiatives but also enforce them.

Secure and track implementation. For the implementation process, it is worth setting up a transformation office that regularly measures the degree of target achievement. This enables the prompt adoption or reprioritization of countermeasures. It is also imperative that adequate resources be made available. To change ways of thinking and behavior within the company, it also makes sense to recruit employees as change agents. In this context, the communication and anchoring of sustainability goals in the organization—for example, through incentive systems—should also be addressed.

Create transparency. Last, investments should be made in data and transparency because retailers, consumers, regulators, and investors are increasingly demanding it. In particular, traceability across supply chains poses a challenge. This makes it all the more important for companies to deal with the sustainability data of their own products right from the start and to develop the corresponding analytical skills.

No function is left untouched when changes of this magnitude are needed: everyone is involved and responsible for bringing sustainability to life in their area—from purchasing to production and logistics to marketing and sales (Exhibit 3). For successful implementation, the key actors in the individual divisions need to develop both function-specific and overarching measures.

In purchasing, for example, the focus may be placed on biologically derived ingredients, recycled plastic for packaging, biodegradable and certified materials, and regenerative agriculture.

To do this, it is first necessary to assess the volume of emissions caused by each purchasing category and what reductions are possible in each area. The procurement team is also responsible for ensuring suppliers adhere to social standards.

In logistics, it is key that companies consider alternative propulsion systems for their vehicle fleets or the use of more sustainable transport options. In the field of warehousing, organizations should review cooling technologies and use renewable sources to ensure energy supplies, employing their own solar panels if necessary.

Production should first optimize its energy efficiency. In addition, consideration needs to be given to the use of renewable and sustainable energy sources for electricity and heat at production sites. It is also necessary to investigate how water and other resources can be used more efficiently and how waste can be reduced.

Meanwhile, R&D teams can work on more sustainable designs and formulations (design to sustainability). This can involve sustainable packaging or formulas for new products that lead to greater sustainability in use—such as laundry detergents that clean textiles thoroughly even at low water temperatures. L’Oreal, for example, has developed the Sustainable Product Optimization Tool (SPOT), an evaluation tool focusing on ecological design on two levels. First, it simulates different design options, evaluates their impact on the environment and society, and identifies improvement measures. Second, SPOT quantifies the effects of sustainability on various product attributes, such as packaging; the environmental footprint of product compositions and chemical processes; and social implications.

The initiatives described above for illustration purposes show that sustainability is not an issue that can be left to a central unit; rather, it reaches deep into all functions of consumer-goods companies. Citizens, policy makers, investors, and new competitors are increasing the pressure to act. Above all, however, it is the companies’ own sustainability ambition that requires a structured and holistic approach if the goals set are to be achieved.

Jordan Bar Am is a partner in McKinsey’s New Jersey office; Nina Engels is a consultant in the Düsseldorf office; and Sebastian Gatzer is a partner in the Cologne office, where Jacqueline Lang is a consultant and Frank Sänger is a senior partner.

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Problem Solving Maps International Summit

Listen to 39 different presentations done by teachers using the Problem Solving Maps approach to teach mathematics

Free for teachers, parents, and educational consultants!

What is the problem solving maps method.

Problem Solving Maps (PSM) are graphical representations of critical thinking processes needed to solve math problems successfully. The maps are 1) Example-Conclusion Map, 2) the Multi-Rule Map and 3) the Math-Breaker Map.  The purpose of these maps is twofold: 1) to provide support in learning a specific topic and 2) to map out problem-solving strategies that are generic enough to be used on a large variety of math content.

• Instructors, tutors or parents can use PSM to teach a large variety of topics
• PSM do not take a long time to learn
• Students learn thinking and problems solving skills that are transferable from one math topic to the next
• PSM are very effective to diagnose where students are having trouble
• With PSM, students can have better notes to study
• With PSM, student can improve self confidence and performance

Listen to 39 presentations of teachers using Problem Solving Maps

  Extending and Completing a Pattern by Elisa T. Maramag

Visualizing, Representing, And Converting Liter And Milliliter From Larger To Smaller Unit And Vice-Versa by Jhoanna Marie T. Teru

Ordering Numbers with the Multi-Rule Map by Jamaica F. Lacson

Square Of A Binomial by Jean Aiko C. Domingo

Finding The Surface Area Of A Cylinder  by Darwin B. Lico, PhD Order Of Operations PEMDAS Rule Using The Multi Rule Map  by Myrna B. Mallanao Teaching Mathematics Using PSM Approach: Finding The Area Of A Composite Figure  by   Mary Jean A. Nalunat   The Effectivity Of Problem Solving Maps To Improve Academic Performance Of Grade 6 Learners In Mathematics  by   Rowena R. Yumul

Product Of Cube Of Binomial Multiplication Of Integers (Using Example Conclusion Map) by Arjon Paul D. Dela Paz Multiplication Of Integers (Using Example Conclusion Map) by Jonah M. Asuncion   Factoring Perfect Square Trinomials Teaching Complementary And Supplementary Angles Using The 3 Problem Solving Maps (PSM) by Novy H. Facun Teaching Complementary and Supplementary Angles Using the 3 Problem Solving Maps (PSM) by  Katherine A. Matarlo   Solving Problems Involving Sides And Angles Of A Polygon by Reina Ross Yumul Solomo   Measures Of Variability Of Ungroup Data by Fatima L. Tambago   Teaching Laws Of Exponents Using Example Conclusion Map by Anna Lisa T. Dela Rosa   Improving Mathematics Aptitude Of Grade 7 Students Of Sauyo High School Through Problem-Solving Maps by Grace D. Gutano

Solving Systems Of Linear Equations By Elimination Method Using Problem Solving Maps by Evelyn C. Torrefranca Fundamental Counting Principle by Aimee Rose A. Galicia Integrating Problem Solving Maps In A Video Lesson On Grade 8 Mathematics, Triangle Congruence Postulates by Joshua P. Salazar Proving The Congruence Of Triangles Using SAS Postulate by Mary Ann L. Abundo Proving Triangle Congruence Using Multi Rule Maps by Aileen D. Canonicato

Angle Of Elevation And Angle Of Depression by Lahlyn G. Unica Problem Solving Maps (PSM) A Problem Solving Strategy To Lessen The Mathematics Anxiety Level Of Grade 9 Students by John Richard L. Quiambao Transforming Standard Form Of Quadratic Function Into Vertex Form by Charnel D. Santos Enhancing Student's Performance In Variation With The Use Of Problem Solving Maps (PSM) On Selected Grade 9 Students by Elmer L. Cinco PSM Completing The Square by Sherrelle Francisco Mendoza Maxie And Minnie Application Of Maximum And Minimum Of Quadratic Functions by Sheryl F. Dullano Solving Problems Involving Trigonometric Ratios Using MRM And MBM by Queenie Pearl E. Domasig Law Of Sines by Ken-Ken A. Bormate Addition And Subtraction Of Radicals by Jonofre M. Borja

Synthetic Division by Karen T. Basada Math Breaker As A Tool In Solving Problems Involving Permutations by Randy Dela Vega Utilizing Math-Breaker Maps To Improve Performance In Mathematics And Self-Efficacy Of Students In Online Distance Learning by Joshua P. Salazar Investigating The Use Of Example-Conclusion Maps For Mathematics Enhancement Program by Benigno F. Baluyut The Use Of Math - Breaker Maps In Improving The Performance Of Grade 10 Mathematics Learners In Solving Problems Involving Probability by Zenaida W. Halili Geometric Mean by Charisma T. Banag Solving Problems Involving Probability Of Union Of Two Events And Joint Events by Jona M. Zapata Circle Theorems (Angles In A Circle) by Rhon C. Suliva

  Rational Inequalities by Rachelle Anne Marie S. Adriano

Praises for Problem Solving Maps

 "We are glad that we turned to the Problem Solving Maps (PSM) system as one of one of our strategies to improve students' quantitative thinking skills in the Philippines.  We have been able to positively impact thousands of students in our schools." 

Dr. Jeni Corpuz Superintendent, Department of Education - Philippines

 "I attribute much of the success of my Math students to the use of the Problem Solving Maps (PSM). This mathematical tool helped my students understand different concepts in Math, which are crucial to their success not only in school but in preparation for the Math portion of the ACT and SAT Tests as well". 

Felesia M. Harrel Johnson Founder, College Bound Academic Center - USA

 "We have observed that with Problem Solving Maps (PSM) students get a deeper and quicker understanding of math concepts for topics that are usually challenging.  PSM methods are without a doubt a cutting edge process to teach quantitative and logical reasoning skills." 

Maciej Winiarek Critical Thinking Specialist - Poland

 "The Problem Solving Maps are helping our students make concrete their thinking about abstract concepts. This process also allows teachers to clearly see where students are struggling so they can address these concerns easily and directly."

Vikki Wandmacher Principal, White Pine Middle School - USA

 "The [PSM] math tools enable us to organize our thought by a pattern. Learning a thinking pattern makes life much easier, not only in studying math but also in various aspects of everyday life." 

Motoi Tobita, Ph.D., Master Lead Facilitator, TOCFE - Japan

 "With the Problem Solving Map (PSM) system, it is very easy to find out the gaps students have in their knowledge.  I am glad I learned PSM so I can help my students being successful." 

Karyna Lopez Award Winning Math Teacher-Mexico

How the summit works

Fill out the registration form, you will be added automatically to the summit site and receive a welcome email, follow the email instructions to set your password, you will have access to the presentations, leave a comment for your fellow teachers who made the effort to create their presentations, you will have access to watch the presentations at any time, macatangay, ma. rossell b. macatangay.

Review of PSM

I would like to commend the preparation of different insightful presentation that will definitely be a big help to teachers. Congratulations!

Onuorich De Lara

Congratulations to all the presenters, I learned a lot from the presentation. Here I realized how lucky are the pupils if all the teachers learned this PSM.

Niña Resan Niña Resan

I would like to congratulate all the presenters for a job well done! Watching all the presentations made me want to use PSM in my lessons for better understanding of my students. Thank you for this free summit. Iearned a lot ?

Rosette S. Dela Cruz

Watching all the presentations inspired and motivates me to use PSM in my classes. After watching, the presentation, it made me realize that it is doable for me.

Congratulations to all. The first summit show how teachers apply the PSM in different lessons in Math. To make math enjoyable and easy to understand. (Sobrang gagaling nyo pong lahat ma'am and sir)

Ludivina A. Porcare

PSM review.

Congratulations to all presenters. The strategies presented will surely be a big help to teachers in teaching the subject. Kudos to all presenter and organizer of this summit.

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