Computation & Problem Solving: Links from School, to Life, to the Future

Attention math phobes and nerds! If you’re in the first group like me, you dreaded math class for its confusions, tediousness, and darn right scary exams. You might have done everything possible (as I did) to avoid the math requirements in college and settled comfortably in English and social science courses. Or, perhaps you were like my “nerdy” friends and found math problems interesting, intriguing, and even fun. All those symbols led you to seek out math, physical science, engineering, and computing courses later on.

It turns out what we learned about computing thinking goes way beyond the 3rd R in Reading, wRiting, and aRithmatic. That foundation set us up with attitudes and preferences that followed us into our futures. And more than ever, both avenues and all of those skills are needed in the 21st century, AI future world that we can’t even imagine!

Computing, calculating, problem solving – they’re no small matter! They’re all decision making activities, and it’s estimated that we make some 35,000 decisions a day! Of course, that includes small choices like rolling or jumping out of bed or coffee, cereal, eggs, or skipping breakfast, as well as high impact decisions like “should I ask for a raise?” or “how can we improve our company’s customer service?” Nevertheless, we are all mega problem solvers!

That doesn’t mean it’s easy. Computing and problem solving are often high stakes activities with confusing and complex processes that we’d rather not take on. But that’s not the way it has to be. Let’s tease it all apart and see how to improve the thinking that takes so much. Here’s a mini-training that covers

• The Computation – Problem Solving Links
• The Problem with Problems
• Frameworks for Great Solution Finding

The Computation – Problem Solving Links

Computation thinking is not about becoming a human calculator! And it goes way beyond math class assignments. It’s where calculating, logic, decision making, and evaluation converge. Overall, traditional approaches can be summed up in 3 stages:

1. Analyze the Problem:

Use thinking skills such as breaking the whole into parts, pattern recognition, and simplifying to clarify the problem and the goal.

2. Identify the Procedures:

Often called algorithmic thinking, this phase includes identifying step-by-step procedures, useful resources, and helpful tools.

3. Implement and Evaluate:

Use logical thinking. This includes data analysis, decision making, and evaluating the results. 

When we think about problem solving, the terms change but the stages are very similar:

1. Define the Problem:

Analyze the issue for subproblems, causes, and effects. State the goal.

2. Identify Solutions:

Brainstorm possible ways to “fix” the issue. Evaluate and select the optimum solution.

3. Implement and Monitor:

Apply the solution and evaluate the results. Adjust as needed.

But there are some important differences between the two. In computation thinking, the solution is THE goal. There’s just one right answer or best decision. In problem solving, we talk about “solutions” which are the steps to the desired result. Here, we agree that there’s more than one way to get there.

These thinking differences match the kinds of problems we face. 

1. Issues with several solutions call for divergent thinking.

Think of trying to decide where to go on a vacation — the beach, the mountains, an untried place, or an old standby. Or how should a company advertise a new product? In social media, ads, blog posts, emails etc.? This is creative, “think outside the box” time.

2. Problems with a correct answer require convergent thinking. 

Here’s where logic, analysis, and calculating shine. For example, once you’ve chosen the beach destination, there’s a best place to stay based on budget and the activities you want to pursue. Or, when a business opts for a social media campaign, there are logical steps to get the biggest return on the time and money costs. Here’s where research into best practices and the saying “don’t recreate the wheel” come in.

What happens when we mix up the two? Mislabel a problem and you’ll misthink the solution! Ever have a “discussion” with someone who was sure their way was the one “right” way? Or try to follow a set of directions with someone who wants to do it “their own” way? It’s not only frustrating, the results are likely to be way less than stellar! So, knowing which issue is which is critical. 

But this is not an either-or situation. We’re faced with both types of problems and both types of thinking are needed. In fact, most complex problems – like that vacation or advertising a new product – require both. The best thinkers aren’t wedded to one thought pattern. They flow between the two. And they also avoid the other common problems that issues bring.

The Problem with Problems

The problem with problems is that problems come with problems! Obviously, there’s always something missing. Confusion is common.

And facing, fathoming, finding, and fixing that demands effort and risks failure. Dread for the time it’ll take and drudgery are common. Fear of mistakes is common.

Many problems have numerous solutions. Overwhelm is common!

Worry thoughts of “I could choose the wrong one,” or “I could make things worse,” or “others won’t like …” are common.

Where do all these everyday reactions come from? Kid training sticks with us long after we get to adult age. If we struggled with math, our inner, student chatter tends to face problems with dread and worry about finding the right answer or facing undesirable consequences. If we were the “brainy” ones, life and work problems can be frustrating because we have a deep, inner teacher voice telling us there IS a right answer.

In short, early school experiences can become models of what the word “problem” means. For many, they set us up with problems we bring to the problems we face!

It’s time for a new attitude and a better approach!

Frameworks for Great Solution Finding

Computation and problem-solving thinking are mental pathways. And that makes them learnable, improvable, and organizable. It all starts with using the best frameworks for the “problem.”

Think of building a house. There’s a framework or outer system of walls that defines the overall style, size, and shape of the building. Then, there are interior frameworks that define different spaces. Similarly, great solution finding involves 3 frameworks.

The Set Up Framework

Coming up with a solution or solutions demands focused thinking. And that requires a shift from other activities. It doesn’t take a lot of time. It does take a conscious redirection. Use these 3 tactics and any or all of the suggestions to turn your mind towards solution finding.

1. Make Time and Quiet Happen

• • The two greatest destroyers for both computation and problem solving thinking are distractions and rushing. 
  • Work where you are undisturbed. 
  • Allow time for your mind to access all you know, think clearly, be accurate, get creative. 
  • Solution finding takes – and deserves – time.

2. Lower Your Stress and Anxiety

• • Past training and current needs can make the issue a high stakes matter. 
  • Big, complex problems can overwhelm. 
  • Cut tasks down to very small, success-oriented steps that initiate actions. 
  • Cut out the worry with positive self-talk. Remind yourself of past success.
  • Seek out the support of those who believe in you.

3. Persist

• • Problems don’t unravel easily, because they’re not our usual way of doing things. 
  • Effort and repeated trial and error are frequently needed. 
  • Put things aside – temporarily – when nothing new comes to you or obstacles become frustrating. 
  • Read and research new ideas to prime your creative pump.
  • Seek outside input and advice. 
  • Don’t give up!

The Divergent Framework

Freedom to choose and finding great possibilities are the benefits of divergent thinking. All that depends on tapping into your creativity, inferring what’s missing, and getting insights. To create something new, you need uncluttered thinking. Here’s 5 steps and some suggestions for how to create that kind of SPACE.

Self-motivate

• All problem solving begins with the belief that better is possible. 
• Visualize and/or put words to the positive outcome you desire.
• Psych yourself up not just with “I want this …” but with “I can do this” thoughts. 
• Be open minded. 
• See problems as opportunities, as signals that an issue has risen to the “fix me” level. 
• Embrace the effort of finding a better way, a better place. 
• Research and learn from others knowledge, choices, and ideas. 

Preview

• Define the problem. Exactly what is the issue? 
• State the consequences. Why is this a problem?
• Think of results as making things better.
• Identify progress points and improvement milestones.
• Remind yourself that small successes lead to big wins!
• Imagine good, better, and best outcomes.
• Identify your values: what will be your personal criteria for success?

Analyze

• Break complex problems into parts. Tease apart the contributing factors.
• Break big issues into stages or phases.
• List the causes and effects of the factors or stages.
• Link the issue to other areas that you know or that work well. How is this similar? Different?

Create 

• Brainstorm possible solutions. Don’t judge or eliminate any. Go for quantity. Hint: The best ideas often come at the end of a string of poor ones.
• Ask not just what “should be” but “what could be.”  Imagine the best!
• List what could be deleted and what could be added to improve the situation.
• Dream up how the outcome could be multiplied into something extraordinary.
• Work with others, ask for help, seek advice, research. More ideas are the road to better ideas!

Evaluate

• Run a trial test with the best of your solutions.
• Monitor each step. Identify what works well and what doesn’t.
• Ask: Does this create progress? An improvement?
• Apply your good, better, best criteria. How do the results measure up?
• Check everything against your values. Are they supported by what you’ve done?
• Modify parts and pieces as needed. 

Convergent Framework

Getting the mind to a “right” answer or the best decision takes a process of mentally working through things. It also requires doing or applying procedures and processes accurately. This 5-step process leads the way to both. For better math driven work and problem solving, follow the PDQ2R steps and suggested tactics.

Preview

• Overview and get a big picture view of the problem. Skim it if it’s a print problem; record your own brief, outline sketch if it’s not written out.
• Identify the problem type or the context where it’s found.
• State the goal. Exactly what will the right or best answer look like?

Divide

• Break long or complex problems into parts.
• List the givens.
• Identify and list the unknowns.
• Define the terms and symbols that are not in your “common knowledge.”

Question

• Ask “How can I do this? What operations or steps should I use?
• If it’s a decision, list the best information gathering steps and resources. Collect them up.
• If options are possible, brainstorm possible solutions.
• If there’s only one right answer, identify the best procedure, equation, or method to use to find it.
• Find processes, models, or examples if you’re unsure of how to proceed.

Reason

• Analyze any data or resources.
• Apply the steps or processes you identified above.
• Check each step for clerical errors.

Review

• Evaluate the answer. Ask: “Is this logical?”
• Check your answer against the goal you initially set. Is it a match?

In the End …

In a world where so many problems have risen to the “fix it” level and where technology is literally outstripping our ability to forecast the future, computation and problem-solving thinking are required! 

Some key ideas in the computing and problem-solving arena that we face every day are:

1. Two kinds problems require two different types of thinking. 

• • They are called divergent and convergent.
  • Divergent thinking creates multiple solutions. 
  • Convergent thinking is used where there is one right answer or a best decision is needed.

2. Problems come with problems or automatic, negative reactions.

• • We need to recognize and counteract each one.

3. Three mental frameworks can effectively improve our solution finding abilities. They are:

• • The Set Up Framework
  • The Divergent Framework
  • The Convergent Framework

Those who perfect these skills and strategies will be the innovators, leaders, and shapers of tomorrow!