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Problem solving is central to success in any college course. Throughout their academic careers and their lives, students will encounter problems that need to be solved. These problems may range from the personal (how to pay for college) to the interpersonal (how to work with a partner on a project) to the occupational (how to solve an issue relating to school or work). Although every course requires students to engage in problem-solving, mathematics is a course that students readily associate with the task—the questions written on a whiteboard or on a page are more often than not math problems that need to be solved.  

Although problem solving is a task that students engage in throughout their academic careers, they frequently have little experience in the metacognitive process of problem solving. Traditionally, students are taught subject-specific tools to apply to a subject-specific problem (example: how to add or how to use a dictionary) rather than problem solving strategies. This results in students who do not understand the process behind problem solving and has a direct impact on student success. Research indicates students who are successful problem solvers are those who are taught how to use and develop metacognitive problem-solving techniques and who engage in the deliberate and reflective process of problem solving (Mason et al.) Problem solving is a multi-step process that students must be taught and must have practice engaging in. Although multiple problem-solving processes exist, some more complex than others, most of them include variations of Polya’s four-stepped approach:  

  • understanding--What is the problem? What is the purpose? What is known/ unknown?  
  • planning--How does this connect to prior knowledge? Where are there gaps in knowledge? How to proceed?  
  • solving--How to carry out the plan? Where to stop and check progress along the way?  
  • reflection--Is the solution correct? What have I learned?  

Students who are not college-ready in math struggle with problem-solving as a process. Often, they try to answer problems by using subject-specific tools like formulas or equations without stopping to understand the problem and engage in problem-solving. This results in students who frequently fail to arrive at a solution and end feeling defeated and demoralized about their success in math (Yuan 99). Students who are not college-ready in math benefit from being taught stepped problem-solving techniques and strategies, practicing those steps, and reflecting on their learning. Engaging in this process results in students who are able to make connections and understand the material that they otherwise would not (Yuan 99-104). Students in Soar Towards Success will be taught problem-solving strategies and engage in this metacognitive process. This practice will benefit students in all their courses and will help them develop the necessary readiness skills for their college-level math courses.  

Module 5: Thinking and Analysis

Problem-solving, learning objectives.

  • Describe how critical thinking skills can be used to problem-solve

For most people, a typical day is filled with critical thinking and problem-solving challenges. In fact, critical thinking and problem-solving go hand-in-hand. They both refer to using knowledge, facts, and data to solve problems effectively. But with problem-solving, you are specifically identifying, selecting, and defending your solution. Below are some examples of using critical thinking to problem-solve:

  • Your roommate was upset and said some unkind words to you, which put a crimp in the relationship. You try to see through the angry behaviors to determine how you might best support the roommate and help bring the relationship back to a comfortable spot.
  • Your campus club has been languishing on account of lack of participation and funds. The new club president, though, is a marketing major and has identified some strategies to interest students in joining and supporting the club. Implementation is forthcoming.
  • Your final art class project challenges you to conceptualize form in new ways. On the last day of class when students present their projects, you describe the techniques you used to fulfill the assignment. You explain why and how you selected that approach.
  • Your math teacher sees that the class is not quite grasping a concept. She uses clever questioning to dispel anxiety and guide you to new understanding of the concept.
  • You have a job interview for a position that you feel you are only partially qualified for, although you really want the job and you are excited about the prospects. You analyze how you will explain your skills and experiences in a way to show that you are a good match for the prospective employer.
  • You are doing well in college, and most of your college and living expenses are covered. But there are some gaps between what you want and what you feel you can afford. You analyze your income, savings, and budget to better calculate what you will need to stay in college and maintain your desired level of spending.

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Problem-Solving Activity

Now let’s practice problem solving by working through the following activity.


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Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

  • Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
  • If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
  • In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
  • When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

  • Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
  • Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
  • Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

  • Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

  • Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

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How to develop your problem-solving skills at university

James davis.

Developing problem-solving skills can be a problem unto itself for the uninformed. Fortunately, it doesn’t have to be a mystery. We’ll highlight some methods for improving your ability to think laterally, vertically and push beyond your comfort zone. Bear in mind all of these will require continuous practice and effort, but as long as you’re mindful, they won’t be as challenging as you might initially think. Even if they are, the more you solve problems, the easier they’ll become. 

But first, what exactly is problem-solving?

In a university context, it can mean just about any necessary activity or idea for overcoming… well, problems! It’s here types of problems (and consequently the sort of solutions required) start to diverge. There are several ways to categorise problems, but for the sake of argument we’ll be using the following:

Urgent problems. These are issues for which there’s only limited time to ponder and require an immediate response, but that response is both known and simple. For instance, an exam question. 

Linear problems. These are complicated and solvable through methodology, be it predefined or created for the purpose. A mathematical proof is an example. 

Nonlinear problems. Although just as complicated, their solutions are ambiguous and have no defined methodology for arriving at them. An example would be a loosely defined research paper.

The method you use for categorising is subjective. All that matters is you’re able to identify the problem to the best of your ability so you’ve got the best shot at using the most effective tool for the job. For instance, what if you’re assigned a research paper with a recommended structure and type of content already laid out? It’s far more linear at that point. What if you’re a masochist working on a famed paradox or mathematical dilemma without a solution? Maybe you’ve got a nightmare combination of these problems demanding usage of multiple methods, imagination and haste. If you can label it, you’ve got a better shot at applying the right methods. 

So what can you actually do with this knowledge? It’s pretty unhelpful just slapping all kinds of labels onto problems. What you need to do is understand the two major methods of innovative thinking, which we’ve got an entire article on here. If you’re not ready to click off just yet, here’s the run-down. 

Lateral thinking is what people refer to when they’re ‘thinking outside the box’. It’s about weighing up problems creatively to come up with multiple potential solutions and make an educated guess at which is best. 

Vertical thinking is methodical, logical and strict. It’s about driving home the solution to a problem, working through the steps until you’ve got an answer. 

At a glance, you may not see something like “vertical thinking” as particularly innovative, but adhering to formula or rulesets often requires more than just reading an instruction manual. It can involve creating those methods in the first place, perhaps even in combination with lateral thinking too. In fact, you’ll find many problems that could benefit from both. We’d definitely recommend reading our article if you’re interested in the specifics of what each entails. 

So how on earth does one go about improving these skills? Well, there are several every-day exercises and activities just about any university student in Australia can undergo. The natural progress of your degree will kind of ‘force’ you to refine them as you blast through your assignments, but it doesn’t hurt to know the tricks. 

Spend more time reflecting

If you’ve got a commute into work or uni, it pays to just turn off your podcasts, put your phone back into your pocket (especially if you’re driving), put on some quiet music and use the trip to work through problems nagging at you, be they academic or personal. This is your chance to practice whichever method of thinking is required. If you’ve got an essay you’ve yet to start, now’s the time to work through different potential structures and the research each may require. If you’ve got some basic tute questions, try to recall the method for solving them in as much detail as possible. 

Reflecting is also valuable for reviewing how you performed. What worked? What didn’t? Where do I think I need to improve regarding my problem-solving methods? Was the execution flawed? Even with something like group assignments, it pays to consider what you could have done better rather than fall to the temptation of shifting blame. This is such a simple, yet easy to overlook practice. We’re absolutely inundated with distractions after all. If you can find plenty of moments to just disconnect and think, you’ll give yourself a significant chance to truly develop as a problem-solver. 

Be inquisitive

Just asking how your mate tackled their assignment, answered their exam or thought through their issues and why can make a lot of difference. It’s a chance to expose yourself to potentially new methods of thinking, which is in-turn a chance to evaluate your current methods. Are theirs better? If they are, why not adopt them? Did they go wrong in their reasoning? Perhaps you misunderstood how they went about it. No matter the outcome, the skill development should always be positive. Whether you adopt a new method for future problems of a similar nature or stick to your guns, you’ll have tested yourself, which is what becoming a better problem-solver is all about. 

You can also ask mentors for examples of when they overcame problems, be it your parents, professors, former teachers or just about anyone whose judgement you trust. The most important thing is being exposed to different methods of thinking. To this end, your questions can be oriented toward vertical or lateral examples depending on your current focus or interest. 

Discussing methods for coming to true conclusions is valuable for both lateral and vertical thinking. A perfectly memorised method for doing something doesn’t equate to perfect execution, after all! Perhaps there’s some refinement to your process or execution you hadn’t considered. Computer science is often like this; while there are many ways to write code and make it work, for most languages, solutions are often not created equal! In this example at least, reviewing your friend’s code or asking why they wrote it as they did can be an immense help. For something more open-ended like bedside manner if you’re learning to become a nurse, you may learn new ways to express sentiments to patients in a more comforting manner. If you’re always being inquisitive and seeking better ways to do things, you’ll really advance by leaps and bounds as a problem-solver. 

Find more responsibilities

Naturally, exposing yourself to new problems carries the benefit of practice in finding solutions. You’ll likely doing all the right things just through building your resume anyway. New internships, part-time work, volunteering and getting on the committees of student clubs are all valuable ways to expose yourself to new problems. It doesn’t matter how big they are; every one is a chance to get out of your comfort zone and exercise multiple methods of thinking. 

You’ll probably be surprised at just how many new responsibilities you can take on and still have time for study. Near the end of each semester, you’ll have to dial the notch back of course, but during semester breaks and the first four or five weeks of your first and middle years, you’ll be able to find prime opportunities for these activities. No shame in keeping third-year clear, provided you’ve done all you can in previous years! 

We’d highly recommend doing all these things, even if they weren’t useful for developing your problem-solving skills. Yet, they do! Here are just a few examples of what each can do:

Internships give you an insight into what could be your first graduate job. Your work will likely involve a combination of urgent, linear and nonlinear problems. As an intern, you’ll be able to see how professionals tackle these problems sequentially, calmly and what methods they use to arrive at sound conclusions. This is an opportunity to exercise the previous steps too; asking plenty of questions and reflecting on the answers are things you absolutely should be doing to maximise value from an internship. 

Volunteering is similar. Even something simple like serving soup at a homeless shelter can carry with it the obligation to listen to an understand struggling people. Am I listening effectively? Am I communicating effectively? How can I better hear and understand the people I’m speaking with? Am I cooperating with my fellow volunteers to the greatest extent I can? With a bit of imagination, many optimisations and questions can be come mini problem-solving exercises and chances to improve. Outside these internal exercises are the real-world opportunities that logistical hurdles can present. If you’re called upon to advertise for a dinner, book a lecture or find catering for an event, these are all problems that may not have defined solutions or a single correct answer. It’s a chance to sift through your options. 

Student clubs can offer a similar experience. If you’re part of a club’s organisational committee, you may be called upon to spread the word about an event, help organise a ball, figure out how to delegate appropriately or any number of problems that again, may not have clear-cut solutions. 

Seek additional problem solving exercises

This is for those of you wanting to go the extra mile! While other activities in this article specify the utilisation of things you should already be doing anyway, or just making use of downtime, this will take a bit of concerted effort. 

There are plenty of books on critical thinking, innovation and general problem-solving you can use to bolster your efforts. Why not pick up one or two of the classics, like Edward de Bono’s Six Thinking Hats or Decision Making and Problem Solving by John Adair? If books aren’t your thing, there are all kinds of activities and problems online. Lateral thinking puzzles are a fairly popular activity among those wanting to improve their lateral thinking skills, for instance. As for vertical thinking, just undergoing math problems appropriate to your current knowledge level are a great way to develop. This might seem wildly counterintuitive if you’re an aspiring artist or historian, but what better way to develop your adherence to strict methods than with math? Hey, even just doing increasingly difficult sudoku puzzles can suffice. If you keep at it, you may develop a real taste for this sort of thing and will find it easier to tackle problems throughout academia and work. 

You should now have a much better idea of all the ways problem-solving skills can be developed at university. Honestly, the biggest takeaway is to just be creative with all the activities you’re already doing. Reading books and putting effort exclusively into this can be effective, but it’s also time consuming. Some of the most practical things you can do include simply working problem-finding and solutions into your current schedule, which is totally doable. No matter what you’re doing, there’s likely a way to get better at solving problems while doing it. Even if you’re in a repetitive part-time job, there are bound to be opportunities for self-improvement just by treating each perceived inefficiency or opportunity as a problem that can be solved. With keen reflection, asking good questions regularly and taking on more responsibilities, you’ll be well on your way to becoming a formidable problem-solver. 

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Decision-making and Problem-solving

Appreciate the complexities involved in decision-making & problem solving.

Develop evidence to support views

Analyze situations carefully

Discuss subjects in an organized way

Predict the consequences of actions

Weigh alternatives

Generate and organize ideas

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Design systematic plans of action

A 5-Step Problem-Solving Strategy

Specify the problem – a first step to solving a problem is to identify it as specifically as possible.  It involves evaluating the present state and determining how it differs from the goal state.

Analyze the problem – analyzing the problem involves learning as much as you can about it.  It may be necessary to look beyond the obvious, surface situation, to stretch your imagination and reach for more creative options.

seek other perspectives

be flexible in your analysis

consider various strands of impact

brainstorm about all possibilities and implications

research problems for which you lack complete information. Get help.

Formulate possible solutions – identify a wide range of possible solutions.

try to think of all possible solutions

be creative

consider similar problems and how you have solved them

Evaluate possible solutions – weigh the advantages and disadvantages of each solution.  Think through each solution and consider how, when, and where you could accomplish each.  Consider both immediate and long-term results.  Mapping your solutions can be helpful at this stage.

Choose a solution – consider 3 factors:

compatibility with your priorities

amount of risk


Keys to Problem Solving

Think aloud – problem solving is a cognitive, mental process.  Thinking aloud or talking yourself through the steps of problem solving is useful.  Hearing yourself think can facilitate the process.

Allow time for ideas to "gel" or consolidate.  If time permits, give yourself time for solutions to develop.  Distance from a problem can allow you to clear your mind and get a new perspective.

Talk about the problem – describing the problem to someone else and talking about it can often make a problem become more clear and defined so that a new solution will surface.

Decision Making Strategies

Decision making is a process of identifying and evaluating choices.  We make numerous decisions every day and our decisions may range from routine, every-day types of decisions to those decisions which will have far reaching impacts.  The types of decisions we make are routine, impulsive, and reasoned.  Deciding what to eat for breakfast is a routine decision; deciding to do or buy something at the last minute is considered an impulsive decision; and choosing your college major is, hopefully, a reasoned decision.  College coursework often requires you to make the latter, or reasoned decisions.

Decision making has much in common with problem solving.  In problem solving you identify and evaluate solution paths; in decision making you make a similar discovery and evaluation of alternatives.  The crux of decision making, then, is the careful identification and evaluation of alternatives.  As you weigh alternatives, use the following suggestions:

Consider the outcome each is likely to produce, in both the short term and the long term.

Compare alternatives based on how easily you can accomplish each.

Evaluate possible negative side effects each may produce.

Consider the risk involved in each.

Be creative, original; don't eliminate alternatives because you have not heard or used them before.

An important part of decision making is to predict both short-term and long-term outcomes for each alternative.  You may find that while an alternative seems most desirable at the present, it may pose problems or complications over a longer time period.

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6 strategies to instill problem-solving skills in students.

Critical Thinking In Students: 6 Top Strategies

Why Developing Problem-Solving Skills Is Important

Problem-solving is defined as the ability to quickly solve any given problem with ease. This requires convergent and divergent thinking skills. Convergent thinking is a process aimed to deduce a concrete solution to a problem. And, the process of exploring all the possible solutions to analyze and generate creative ideas is called divergent thinking.

People with good problem-solving skills are indeed an asset to society. Problem-solving also plays a vital role in child development. These skillsets are much sought-after in this competitive world and are therefore imperative for general life and workplace success .

Problem-solving is an important 21st-century skill because it determines one’s personal development, employment prospects, and overall contribution to society.

6 Practical Ways To Foster Critical Thinking In Students

1. promote skill building through self-directed learning .

Research [1] proved that self-directed learning promotes critical thinking in students as it allows them to fully explore their creative and imaginative sides. It fosters the ability of independent thinking in students and eventually promotes a sense of self-actualization in them. Today, the principle of autonomous learning is applied in most visionary schooling platforms because it is the most credible way to inculcate this new-age skill in young learners.

This methodology perfectly suits middle and high school students because they enjoy the process of discovery learning and are capable of drawing conclusions in the light of facts.

As a parent, you need to be a facilitator in this process and understand the importance of problem-solving skills in kids. The simplest way to do this is to allow some independent thinking time after the instructional delivery and encourage multiple original ideas by promoting divergent thinking. All this fosters advanced reasoning abilities in students and promotes critical thinking for advanced problem-solving.

Top educators from great-quality accredited online schools make use of these strategies, along with several other eLearning skills , and guide the learners throughout the process of gathering, prioritizing, interpreting, and concluding information.

2. Encourage Brainstorming In A Non-Judgmental Environment

Problem-solving in child development is a game-changer for success later in life. So, try to create the right atmosphere for kids at home to nurture this core competency.

A non-judgmental environment is always free from negative criticism and sarcasm. Allow children to voice opinions freely and make sure there is enough positive reinforcement for all genuine attempts.

Individual brainstorming is the best to craft creative solutions for less complex issues because it allows individuals to break free from regular, conventional ideas while interacting in a more positive environment.

Support your kid for more and more lateral/parallel thinking and appreciate all out-of-box/innovative responses.

3. Strengthen The Components Of Problem-Solving 

Another way to foster problem-solving skills in learners is by strengthening the decision-making component of the problem-solving process. Decision-making skills are imperative to solve problems because they help to weigh the advantages and disadvantages before reaching a conclusion.

Encourage kids to make choices between possible alternatives and make this fun by trying out everyday basic choices like food, books, movies, sports, etc. Make sure you allow kids to take charge of these decisions and intervene with your logical and valid inputs. Remember that it is essential to understand the importance of problem-solving skills in kids. So, try to create enough such opportunities for young learners.

These practices will develop habits of analyzing situations from multiple dimensions and eventually, children will learn to research and preempt the repercussions of their individual choices.

4. Use The Best Techniques Of Some Researched Theories

Some great psychological theories can be easily applied in real-life situations. As a parent, you can foster these relevant problem-solving skills in the child by incorporating some components of popular theories.

Let me explain this through some examples:

Use the theory of "psychological distancing" [2] to disconnect children from their emotions while solving the problem. It will help them see the bigger picture of the issue by viewing it from a wider perspective. This strategy eliminates the chances of biases and selective understanding based on personal preferences and therefore, helps in viewing issues through multiple perspectives.

Another helpful strategy can be the "heuristic framework" [3], which can help foster advanced thinking abilities by breaking information into smaller and more comprehensive parts. With middle and high schoolers, you can try its component of backward planning effectively. This strategy can be mindfully implemented in any day-to-day situation, like planning for a get-together or estimating monthly expenses for budget planning. Encourage responses in a way that starts from the most distant challenges like month-end crunch/emergency funds, etc., and look for these solutions before planning the immediate requirements.

5. Be A Positive Role Model

As parents, we can also foster problem-solving skills through numerous informal interactions and behaviors. Our own approach toward solving problems largely influences our children's abilities because there is a powerful impact on the family atmosphere and parenting in the critical habit formation stages.

Look for opportunities to involve children in problematic situations and create some hypothetical ones if you do not have real ones. Involve children in discussions that need deep thinking; for example, preparations for extreme weather change or changing some business strategies (like hoarding raw material) to bring down the investments of a family business.

Be a structured and organized problem solver yourself and present your thoughts in the most logical and sequential manner. Support children's efforts throughout and share your input about their dilemmas. The importance of problem-solving skills in kids is evident. So, try to be an ideal role model for kids all the time.

6. Observe, Facilitate, And Share Feedback

Last but not least, be a guide and mentor for your students at all times. Observe them and be ready to intervene as and when it is required. Avoid interrupting and criticizing directly at any point in time because these competencies are best developed in a positive learning environment .

So, make sure you share enough positive feedback and facilitate this process throughout. However, do not give any direct answers to make the task easy for children. Instead, guide them through the pathway that can lead to possible and relevant solutions. Encourage multiple solutions and prejudice-free opinions and allow enough time for kids to derive conclusions. Re-explain the steps of the process (identifying, analyzing, solving, and reviewing, etc.) repeatedly, and motivate children for more and more divergent thinking.

Problem-solving skills are an asset for our kids in all stages of life. So, put your best foot forward and support your child in and out to acquire these 21st-century relevant skillsets for a tremendously successful and happy life ahead!


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[2] Construal-Level Theory of Psychological Distance

[3] 7.3 Problem-Solving

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  2. 5 Steps To Teaching Problem Solving

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  3. Here is my handout on teaching children problem-solving skills, based on this post…

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  4. How to Improve your Students' Confidence with Problem Solving Skills in Math

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  5. Problem Solving Strategies in 2021

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  8. Teaching Problem Solving to College Students John M. Malouff

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    Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the

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