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Sudoku for Beginners: How to Improve Your Problem-Solving Skills
Are you a beginner when it comes to solving Sudoku puzzles? Do you find yourself frustrated and unsure of where to start? Fear not, as we have compiled a comprehensive guide on how to improve your problem-solving skills through Sudoku.
Understanding the Basics of Sudoku
Before we dive into the strategies and techniques, let’s first understand the basics of Sudoku. A Sudoku puzzle is a 9×9 grid that is divided into nine smaller 3×3 grids. The objective is to fill in each row, column, and smaller grid with numbers 1-9 without repeating any numbers.
Starting Strategies for Beginners
As a beginner, it can be overwhelming to look at an empty Sudoku grid. But don’t worry. There are simple starting strategies that can help you get started. First, look for any rows or columns that only have one missing number. Fill in that number and move on to the next row or column with only one missing number. Another strategy is looking for any smaller grids with only one missing number and filling in that number.
Advanced Strategies for Beginner/Intermediate Level
Once you’ve mastered the starting strategies, it’s time to move on to more advanced techniques. One technique is called “pencil marking.” This involves writing down all possible numbers in each empty square before making any moves. Then use logic and elimination techniques to cross off impossible numbers until you are left with the correct answer.
Another advanced technique is “hidden pairs.” Look for two squares within a row or column that only have two possible numbers left. If those two possible numbers exist in both squares, then those two squares must contain those specific numbers.
Benefits of Solving Sudoku Puzzles
Not only is solving Sudoku puzzles fun and challenging, but it also has many benefits for your brain health. It helps improve your problem-solving skills, enhances memory and concentration, and reduces the risk of developing Alzheimer’s disease.
In conclusion, Sudoku is a great way to improve your problem-solving skills while also providing entertainment. With these starting and advanced strategies, you’ll be able to solve even the toughest Sudoku puzzles. So grab a pencil and paper and start sharpening those brain muscles.
This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.
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How to develop your problem-solving skills at university
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.
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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By developing strong problem-solving skills, you'll be able to find solutions even when they aren't obvious.
During your studies, you'll encounter many different problems you need to solve. Sometimes you may be unsure how to solve a problem or you may not fully understand what the problem is — which makes it hard to find the right solution.
When solving problems, it can help to start by identifying any barriers that may stop you finding a solution. Once you've identified any barriers, you can apply strategies to help overcome these and strengthen your problem-solving skills.
Some common barriers include:
- a lack of experience or confidence in how to solve problems
- trouble identifying the knowledge required to solve the problem
- believing that if you don't know how to solve the problem you shouldn't bother trying
- waiting until you know what to do before starting to write down ideas
- going with the first solution you think of instead of coming up with different options
- trying to force a solution to work when it's clear that it won't.
Once you know what barriers you're facing, apply the following problem-solving strategies to identify and work through possible solutions:
Identify relevant knowledge
Review the concepts or theories discussed in your lectures and tutorials to see if any of the information is relevant to the problem. It can be helpful to build up a summary sheet of information you learn over the semester so you have a reference guide ready.
Try multiple solutions
There may be multiple solutions to a problem, and some may work better than others.
If you find the solution you're trying doesn't fit, you'll to need to re-evaluate the problem and try other options. Remember if you make a mistake it doesn't mean you've failed — mistakes can help guide you to the correct answer.
- identify the most important points in the question you're trying to solve and any factors that may influence the solution
- make a list of possible solutions
- use a process of elimination to select potential solutions.
Try reviewing the knowledge you have prior to problem-solving and organising it into a table, flowchart or diagram. This can help you to:
- compare and analyse information
- identify any information gaps
- avoid being overloaded by irrelevant information.
Download a guide to organising information (PDF, 3.8 MB)
Reframe the problem
Sometimes when thinking about a problem, you can make assumptions that stop you from finding a solution.
If you become stuck trying to solve a problem, it can help to approach the problem from a different perspective.
Some ways to help you reframe a problem include:
- questioning what the 'actual' problem is
- thinking about the cause of the problem
- identifying your assumptions
- creating a list of all possible solutions.
- Help with how to study
- Critical reading and analysis
Our advisers can help undergraduate and postgraduate students in all programs clarify ideas from workshops, help you develop skills and give feedback on assignments.
How a Learning Adviser can help
Download tips to help your problem-solving (PDF, 159 KB) Watch an example of a common problem-solving process
- Student Life
Problem solving and decision making
"This has shown increasing demand as employers are acknowledging that graduates are expected to think for themselves and perhaps find different ways of working and thinking creatively"
Carl Gilleard, Former Chief Executive, Association of Graduate Recruiters
How to be an effective problem solver
We all use our initiative and creativity to solve problems every day. For example, you might have to change your route due to traffic congestion, solve an IT issue, or work out what to make for dinner with the ingredients left in the fridge. The challenges you may face in your professional career are likely to be a bit more complicated than these examples, however the skills and processes you use to come up with solutions are largely the same, as they rely on your ability to analyse a situation and decide on a course of action.
Problem solving and decision making are likely to be essential aspects of a graduate-level job, so it is important to show a recruiter that you have the personal resilience and the right skills to see problems as challenges, make the right choices and learn and develop from your experiences.
You are likely to have to apply techniques of problem solving on a daily basis in a range of working situations, for example:
- using your degree subject knowledge to resolve technical or practical issues
- diagnosing and rectifying obstacles relating to processes or systems
- thinking of new or different ways of doing your job
- dealing with emergencies involving systems or people.
You may have to use a logical, methodical approach in some circumstances, or be prepared to use creativity or lateral thinking in others; you will need to be able to draw on your academic or subject knowledge to identify solutions of a practical or technical nature; you will need to use other skills such as communication and planning and organising to influence change.
Whatever issue you are faced with, some steps are fundamental:
I - Identify the problem
D - Define the problem
E - Examine alternatives
A - Act on a plan
L - Look at the consequences
This is the IDEAL model of problem-solving. There are other, more complex methods, but the steps are broadly similar.
What do recruiters want?
Problem solving, decision making and initiative can be asked for in a variety of ways. Many adverts will simply ask for candidates who can “ take the initiative to get a job done " or " have the ability to resolve problems "; others, however, may not make it so obvious. Phrases such as those below also indicate that initiative and problem solving are key requirements of the role:
- “We need people who can set goals and surpass them; people who have ideas, flexibility, imagination and resilience…”
- “Take responsibility and like to use their initiative; Have the confidence and the credibility to challenge and come up with new ways of working…”
- “An enquiring mind and the ability to understand and solve complex challenges are necessary…”
- “We are looking for fresh, innovative minds and creative spirits...”
- “Ambitious graduates who can respond with pace and energy to every issue they face…”
These quotations are all taken from graduate job adverts and they are all asking for more or less the same two things:
- The ability to use your own initiative, to think for yourself, to be creative and pro-active.
- The ability to resolve problems, to think logically or laterally, to use ingenuity to overcome difficulties and to research and implement solutions.
These are important skills which recruiters look for. They want staff who will take the personal responsibility to make sure targets are met; who can see that there might be a better way of doing something and are prepared to research and implement change; who react positively, not negatively, when things go wrong.
Gaining and developing problem solving and decision making skills
Below are some examples of how you may already have gained decision making and problem solving skills at the University of Bradford and beyond. There may also be some useful suggestions here if you are looking to develop your skills further:
- dissertation - researching and analysing a specific issue and providing recommendations
- group projects - overcoming challenges e.g. a change of circumstances, technical problems, etc.
- part-time jobs, internships and work experience* - dealing with challenging customers, identifying and solving issues in your role, completing projects, etc.
- organising events - deciding on date, venue, marketing; solving logistical issues, etc.
- travel - organising trips, planning and reacting to change, etc.
- enter competitions - to provide a solution to a challenge.
*Using your initiative in a work context is about spotting opportunities to develop the business. This can, for example, include learning new technology to make your work more productive and efficient; being willing to look at processes and systems to see if there are things you can suggest to improve workflow; recognising opportunities that will improve the business and being prepared to follow them through; volunteering to learn new tasks so you can be adaptable and help out in emergencies or at peak periods.
How can you prove to a recruiter that you have these skills?
Think of examples of when you have used these skills. See the above section for suggestions, and then to provide a full and satisfying answer you can structure it using the STAR technique:
- S - Define the Situation
- T - Identify the Task
- A - Describe your Action
- R - Explain the Result
Here is a detailed example:
Define the SITUATION: (where were you? what was your role? what was the context?)
I work shifts at a call centre which manages orders for several online companies. One evening I had to deal with a very irate customer who had been promised a delivery a week ago and had still not received it.
Identify the TASK: (what was the problem? what was your aim? what had to be achieved?)
Whilst listening to the customer, I accessed his record. This was no help in solving the problem as it simply reiterated what the customer was saying and did not give any more up-to-date information. I promised the customer that I would do my best to help but I would need to do some research and phone him back. He reluctantly accepted this.
Describe the ACTION you took: (be clear about what you did)
I could not check with the office as they were closed and my supervisor had already left for the evening, so I searched for the same product code to see if I could find updated information on other records. This confirmed that the product was now back in stock and that several deliveries were actually scheduled for the following day. There seemed to have been an error which had resulted in my customer’s record not being updated, so I reserved the item for this customer and then persuaded the Logistics Manager to include him in the schedule.
Highlight the RESULT you achieved: (what was the outcome? Be specific and, if possible, quantify the benefits)
My shift was over but I telephoned him back and explained what I had done and hoped very much that it was convenient for him to accept delivery the following day. He was delighted with the initiative I had taken and thanked me. Two days later my supervisor told me that I had received excellent feedback from a customer and I would be nominated for Employee of the Month.
To use the STAR technique effectively, remember:
- You are the STAR of the story, so focus on your own actions.
- Tell a story and capture the interest of the reader. Include relevant details but don’t waffle.
- Move from the situation, to the task, to your actions, and finally to the result with a consistent, conversational approach.
A detailed statement like this can be used in online applications, or used at interview. It is also easy to adapt it for use in your CV, for example:
- My work experience at the call centre required me to develop good problem solving skills when dealing with difficult customers with stock and delivery issues.
- I have good customer service skills developed through resolving problems relating to stock and deliveries whilst working for a call centre.
Adapting your examples
The example above, for instance, could easily be altered to prove your communication skills , show that you can adapt and be flexible , and that you have great customer service skills . It is worthwhile spending time writing statements like this about all your experiences and then adapting them to match each recruiters’ specific requirements.
Related key words / skills
- Analytical and logical thinking
- Creative thinking
- Adaptability and flexibility
- Time management
- Applying knowledge
We run regular workshops on employability skills , and you can book an appointment with one of our advisers to discuss how to improve your employability in relation to your career choices.
- Problem Solving defined on Skills You Need
- Mind Tools on Problem Solving Techniques
- Problem solving: the mark of an independent employee (via TARGETjobs)
- Problem Solving and Decision Making processes via businessballs.com
You can also check out our Assessement Centre and Psychometric Tests pages for details of the problem-solving exercises recruiters use in their selection processes.
Other relevant websites with general information on skills are:
- Prospects – features articles on skills and how to evidence them.
- TARGETjobs – has details on essential skills and competencies.
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Problem-Solving Skills for University Success
This course is part of Academic Skills for University Success Specialization
Taught in English
Some content may not be translated
Instructors: Katherine Olston +1 more
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There are 6 modules in this course
In this course, you will learn how to develop your Problem Solving and Creativity Skills to help you achieve success in your university studies. After completing this course, you will be able to:
1. Recognise the importance and function of problem solving and creative thought within academic study and the role of critical thought in creative ideation. 2. Develop a toolkit to be able to identify real problems and goals within ill-defined problems 3. Recognize and apply analytical problem solving techniques 4. Recognise and apply creative problem solving techniques 5. Identify the use of creativity within and types of problems most common to your field 6. Apply learnt problem solving and creative ideation skills to a real-life context and reflect on personal learning processes
Introduction to Problem-Solving Skills for University Success
After this module, you will be able to 1. Understand the structure & expectations of the course 2. Understand expectations about Problem-Solving within academic culture 3. Articulate the skills & dispositions needed for Problem-Solving 4. Demonstrate awareness of ethical issues related to academic integrity surrounding Problem-Solving
6 videos 8 readings 6 quizzes 3 discussion prompts
6 videos • Total 42 minutes
- Welcome to the Academic Skills for University Success Specialization! • 1 minute • Preview module
- 1.1a Introduction to the Course • 4 minutes
- 1.2a Introduction to Academic Culture • 10 minutes
- 1.2b Introduction to Problem Solving • 8 minutes
- 1.3a Survival Skills for University • 8 minutes
- 1.4 Academic Integrity • 9 minutes
8 readings • Total 52 minutes
- Overview of Weekly Topics & Learning Outcomes • 10 minutes
- Problem-Solving Skills Assessment Overview • 10 minutes
- Glossary of Terms • 10 minutes
- Acknowledgements • 10 minutes
- Learning Outcomes • 3 minutes
6 quizzes • Total 150 minutes
- Summative Quiz - Module 1 • 20 minutes
- Discussion Board Self-Assessment - Module 1 • 10 minutes
- 1.1. Review • 30 minutes
- 1.2 Review • 30 minutes
- 1.3 Review • 30 minutes
- 1.4 Review • 30 minutes
3 discussion prompts • Total 35 minutes
- Brain Teaser: "The Deadly Lion" • 10 minutes
- 1.1 Introduction Forum • 10 minutes
- 1.4 Academic Integrity • 15 minutes
Categorise Problems & The Problem-Solving Process
After this module, you will be able to 1. Categorize different problems based on their type 2. Identify the different problem types most common at university 3. Recognise language associated with descriptive & analytical problem types 4. Recognise & apply the four-step problem solving process
9 videos 4 readings 6 quizzes 3 discussion prompts
9 videos • Total 54 minutes
- 2.1a Defining Problems • 3 minutes • Preview module
- 2.1b Categorizing Problems 1 • 7 minutes
- 2.1c Categorizing Problems 2 • 5 minutes
- 2.1d Problems in Different Fields • 7 minutes
- 2.2a Descriptive Tasks and Problems • 7 minutes
- 2.3a Analytical Tasks • 4 minutes
- 2.3b Analytical Problems • 7 minutes
- 2.4a The Problem Solving Process • 7 minutes
- 2.4b The Problem Solving Process • 4 minutes
4 readings • Total 12 minutes
- Summative Quiz - Module 2 • 20 minutes
- Discussion Board Self-Assessment - Module 2 • 10 minutes
- 2.1 Review • 30 minutes
- 2.2 Review • 30 minutes
- 2.3 Review • 30 minutes
- 2.4 Review • 30 minutes
- Brain Teaser: Coloured Hats • 10 minutes
- Types of Problems • 10 minutes
- The Problem-Solving Process • 15 minutes
Understanding Problems, Generating Solutions & Solution Paths
After this module, you will be able to 1. Apply strategies to help you better understand a problem & identify the goal of a problem 2. Generate ideas or approaches for solving a problem 3. Apply strategies to help you find alternative solutions 4. Recognise the place of research & evidence in problem solving 5. Identify & justify formulas, theories or outside tools required for problem solving.
8 videos 6 readings 6 quizzes 3 discussion prompts
8 videos • Total 43 minutes
- 3.1a Understanding the Problem • 6 minutes • Preview module
- 3.1b Strategies for Understanding and Beginning the Problem • 5 minutes
- 3.1c Check your Marking Criteria! • 5 minutes
- 3.2a Starting with What you Know • 5 minutes
- 3.3a Using Specialized Knowledge • 6 minutes
- 3.4a Problem-Solving with Special Cases • 4 minutes
- 3.4b Strategies for Problem-Solving with Specialized Knowledge & Special Cases • 5 minutes
- 3.4c Using Special Cases to Solve Problems • 4 minutes
6 readings • Total 32 minutes
- 3.1d Strategies for Understanding the Problem • 10 minutes
- 3.2b Brainstorms & Mind-Maps explained • 10 minutes
- Summative Quiz - Module 3 • 20 minutes
- Discussion Board Self-Assessment - Module 3 • 10 minutes
- 3.1 Review • 30 minutes
- 3.2 Review • 30 minutes
- 3.3 Review • 30 minutes
- 3.4 Review • 30 minutes
3 discussion prompts • Total 30 minutes
- Brain Teaser: Prince's Dilemma • 10 minutes
- Starting with What you Know • 10 minutes
- Understanding the Problem • 10 minutes
Taking Creative & Critical Approaches to Solving Problems, & Evaluating Solutions
After this module, you will be able to 1. Change analogies & viewpoints to solve problems. 2. Apply a variety of forms of reasoning & thinking. 3. Employ creative techniques to the solution of problems. 4. Evaluate a number of solutions to a problem to determine the best one.
9 videos 5 readings 6 quizzes 3 discussion prompts
9 videos • Total 47 minutes
- 4.1a Seeking Different Perspectives • 5 minutes • Preview module
- 4.1b Learning from Other People • 4 minutes
- 4.2a Applying Forms of Reasoning and Thinking • 6 minutes
- 4.2b Questioning Assumptions & Considering Alternatives • 4 minutes
- Questioning Assumptions: The 9 Dot Problem • 3 minutes
- 4.3a Using Creative Strategies • 5 minutes
- 4.3b The Importance of Creativity • 4 minutes
- 4.4a Evaluating Solutions • 6 minutes
- 4.4b Strategies for Evaluating Solutions • 6 minutes
5 readings • Total 22 minutes
- 4.3c Creative Ideation Strategies • 10 minutes
- Summative Quiz - Module 4 • 20 minutes
- Discussion Board Self-Assessment - Module 4 • 10 minutes
- 4.1 Review • 30 minutes
- 4.2 Review • 30 minutes
- 4.3 Review • 30 minutes
- 4.4 Review • 30 minutes
- Brain Teaser: 9 Dot Problem • 10 minutes
- Traffic Control Insight • 15 minutes
- Evaluating Solutions • 10 minutes
Communicating Solutions & Solving Problems in Academic Life
After this module, you will be able to 1. Communicate your solutions to problems to your audience. 2. Study for university exams, & communicate your solutions to problems in exams. 3. Deal with competing priorities at university. 4. Find solutions to problems that can occur at university.
10 videos 6 readings 6 quizzes 3 discussion prompts
10 videos • Total 54 minutes
- 5.1a Communicating Solutions • 5 minutes • Preview module
- 5.1b Communicating Solutions in Written & Oral Form • 3 minutes
- 5.2a Communicating Solutions in Exams • 6 minutes
- 5.3a Group Problem Solving • 6 minutes
- 5.3b Solving Group Problems • 5 minutes
- 5.3c Group Work at University • 5 minutes
- 5.4a Problems, Problems, Problems • 4 minutes
- 5.4b Organisation & Time Management • 5 minutes
- 5.4c Learning to De-Stress & Let Things Go • 8 minutes
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- Summative Quiz - Module 5 • 20 minutes
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- 5.4 Review • 30 minutes
- Brain Teaser: The Trolley Problem • 10 minutes
- Exam Strategies • 10 minutes
- Spy Game • 10 minutes
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Problem solving is an incredibly important skill and used by students to navigate challenges throughout the curriculum (1). Research shows that problem solving helps pupils develop their resilience, ability to think for themselves and persevere (1). It not only underpins all curricular areas by improving their cognitive skills but also helps with their social development (2).
At the end of the summer break, teachers across the country are thinking about the new academic year. The main focus of the first few weeks is on settling students back into the school or college environment. During this time learners can face both social and cognitive challenges, negotiating new classes or beginning to learn new topics.
Whilst also considering the academic content needed in that first term it’s important to think about how you will support your students to start building their problem solving skill to navigate these challenges. Here are four simple ways that students can develop this skill in school or college, that can be seamlessly added into your lessons and teaching resources .
Completing tasks by following instructions
The first step in the problem solving skill is being able to follow instructions to complete tasks. Students encounter multiple different forms of instructions in each lesson, such as behaviour expectations, preparing for learning or completing tasks. Here they will need to follow the order of the instructions otherwise the task will not be completed accurately and they will encounter problems.
Supporting your students to follow instructions
There are a few strategies that you can teach your students to help them follow instructions:
- Know what the goal is : It is helpful for students to know what the end goal is. If they can imagine what they are trying to achieve then they can see whether or not they are on track to do so.
- Have the space to focus : Following instructions takes focus and concentration. Students need to be in a space where they don’t have any initial distractions so they can make the best start.
- Look over the instructions before starting : This is always good practice and students should have a good look at all of the instructions before they begin. This helps them to understand how they fit together.
- Work through them in orde r: Encourage your students to work through the instructions one at a time and follow them carefully. They could use strategies such as repeating them, rereading them or saying them to someone else.
- Check them as they go : Remind students to check their work as they complete each instruction and only move on if they are happy to do so.
Reinforcing the learning
By building chances to encounter and follow a variety of instructions into lessons and teaching resources , students will increase in their confidence and ability to complete them accurately.
Finding someone to help with any problems
Students will undoubtedly encounter situations where tasks are too difficult to do themselves. They might not understand, they might not have done that task before, they might not have learnt the necessary information to complete it or they might be in a new place. This is particularly relevant at the beginning of an academic year when there are lots of firsts for students as they settle into a new year group.
Encouraging learners to be able to ask for help
When facing these situations students need to feel comfortable in asking for help . However, before they do,they should be encouraged to think about the issue: are there any instructions they could follow?; do they remember doing something like this before?; are there ways of solving it themselves?
How to ask for help
Once they have been through these steps and are at the point of asking for help, students need to consider who the best person to ask is, based on the situation. You can support them with this by sharing these handy questions to help them identify the most suitable individual:
- Why do I think this person might be able to help me?
- Who else could I ask if they are not the right person?
- How will I explain to them what the problem is, so that they can help me?
No matter who they ask, the key takeaway for your students is to keep asking others if the first person cannot help them.
Modelling and practising the step
One example of how you could develop this aspect of the problem solving skill with your students is by taking through examples of problems they might encounter. Model identifying who they would need to talk through and encourage them to share their own examples and experiences.
Explaining problems to ask for advice
When encountering any type of problem, your students will need to explain what that issue is . Depending on the complexity of the situation, this is sometimes an area that they might struggle with.
You can teach and develop your students’ ability to explain a situation as part of your wider lessons. The below structure is something they can use to guide their explanations.
- Start with the goal - what are you trying to do, and why? Whoever is helping the student needs to know what they are trying to achieve so that they can see whether their suggestions can help.
- The challenge - where have you got stuck? Students then need to explain what is currently stopping them from achieving their goal.
- Attempts already - what have you tried so far? By letting the person assisting know what has already been tried they know not to suggest similar solutions.
Learners need to be open to receiving advice but they also need to ensure it makes sense before acting on it. They should always think fully about any guidance, either following it if it seems logical and sensible, or thinking of their own solution by using it as a starting point.
Applying the structure
As with the above steps, this is also one that can also be practised in the classroom.
Your students could provide examples of problems they have found difficult to solve and can be supported to gather advice from their peers. You could then model the next part of thinking about the advice and deciding whether to follow it or not.
Finding the information needed to solve the problem
Information is another word for knowledge and usually focuses on facts or things we know to be true, particularly when used in the context of education.
Sometimes students may encounter problems because they don’t have enough information to complete tasks. For example they might not know what maths formula to use to solve a question, or may not have read the chapter of the book being referred to in English lessons so they don’t know what happens.
In this situation it’s important for students to have the confidence and ability to find the information they are missing. This is often something that happens naturally in schools, with learners being encouraged to gain that knowledge then allows them to solve the issue or question. However, this is about really making that process explicit and demonstrating how it also helps to build their ability to problem solve .
Supporting learners to find information
For learners who are unsure how to find the relevant information, you could help them think about where they need to look; different types of information can be found in different places. For example, if they were after dates or facts about an event they could look in an encyclopaedia or online. If they are looking for instructions on how to do something they might want to look in a manual. In some cases the information they need may not be written down so they need to think about who to ask to get it.
Practising retrieving information
Getting students to practise this is a beneficial and straightforward activity. You could provide them with different problems where they only have parts of the information and encourage them to talk through how they would find the missing information. This could be applied to different situations in subjects or wider school or college events.
Further resources to build essential skills
Developing this skill early means students will be equipped with strategies to use across their education when problems arise in different subjects. It will also help set them up to deal with and navigate problems they encounter in all aspects of life.
The Skills Builder Partnership has developed a range of teaching resources on Skills Builder Hub for schools and colleges to use to develop pupils’ essential skills. The short lessons for the problem solving skill, focusing on each skill step, are a great place to start in September with key information and engaging activities for students to practise the skill. You can sign up for free as an individual teacher or join us as a school or college on an Education programme .
1) Wood, I. (2017). ‘Want to develop your pupils’ problem solving skills? Here’s the solution’ [Blog] TES Magazine . Available at: https://www.tes.com/magazine/sponsored/smart-technologies/want-develop-your-pupils-problem-solving-skills-heres (Accessed: 28th July 2023).
2) Admin, O. (2021). ‘5 Ways to Encourage Problem-Solving in your Classroom’ [Blog] Osiris Educational . Available at: https://osiriseducational.co.uk/blog/2021/08/25/5-ways-to-encourage-problem-solving/ (Accessed: 28th July 2023).
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Being skilled in problem solving draws on several other skill areas, including analysis, flexibility and research. These can allow you to deconstruct the problem, making it easier to think laterally and develop informed solutions. A balance of logic, creativity and perseverance can sometimes be required to demonstrate your versatility in this area.
Problem solving appears frequently in job descriptions as an essential skill. No matter which professional area you are considering, a strong ability to demonstrate your problem solving skills will be a valuable offering to a future employer, especially if you can show you have acted swiftly.
Activities where you could develop your problem solving skills
Problem solving skills can be a key learning outcome of many degree courses, but you cannot assume that everyone who reads your CV will recognise this. Take care to provide evidence of the problems encountered, their complexity and the means by which you solved them. Project or business case-based activities can form excellent examples.
- University hall Residence Association The challenges and rewards of helping to run a hall of residence will put your problem solving to the test.
- Student representation Fielding questions from both your fellow students and the responses of your academic staff can require a creative approach to problem solving.
- Peer Mentoring Develop problem solving skills by supporting others through their studies and wider university life.
- Nightline Lateral thinking, compassion and good listening will help you develop your skills while supporting others.
- Competitions and prizes Look great on your CV, even if you don't win you will have experience to talk about.
How is problem solving tested in recruitment?
Written applications may start testing your problem solving skills directly by asking for examples of problems you have solved in the past. This can be probed further by psychometric tests , particularly Situational Judgement. At interview, you can expect questions which re-examine this skill:
- Tell me about a complex problem you have faced – what were the critical issues, and the steps that you took to solve the problem?
- Describe a time when you demonstrated creativity in solving a difficult problem.
- Give me an example of when you used good judgment and logic in solving a problem.
If you are unsure how to structure an answer for either application or interview questions, visit the application and interviews section of our website and find out about the CAR (context, action, result) and STAR (situation, task, action, result) models. Our recommendations are based on feedback from employers.
During an assessment centre , real life business problems will be presented to you, either individually or as part of a group task. You will need to deploy a mix of sector knowledge and analytical skills to develop proposals to solve the problem. You will be assessed on your problem solving strategy and your creativity. You may need to think on your feet, and be able to cope well under pressure in order to succeed.
Sometimes you may be asked to complete practical problem solving activities, such as building a tower from Lego, paper or other materials. This will test other skills such as clear communication and team working skills.
Critical thinking and problem solving are the skills that go hand in hand. At Compaira, we look for someone who takes initiative and thinks laterally to challenge accepted ways of approaching or solving a problem. CEO & Founder, Compaira
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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.
Now let’s practice problem solving by working through the following activity.
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Teaching Problem-Solving Skills
Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision making skills whereas the latter requires only the application of previously learned procedures.
Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.
Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.
Principles for teaching problem solving
- Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
- Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
- Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
- Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
- Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
- Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.
Woods’ problem-solving model
Define the problem.
- The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
- Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
- Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
- Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
- Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
- Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.
Think about it
- “Let it simmer”. Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
- Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
- Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.
Plan a solution
- Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
- Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.
Carry out the plan
- Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
- Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.
Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:
- Does the answer make sense?
- Does it fit with the criteria established in step 1?
- Did I answer the question(s)?
- What did I learn by doing this?
- Could I have done the problem another way?
If you would like support applying these tips to your own teaching, CTE staff members are here to help. View the CTE Support page to find the most relevant staff member to contact.
- Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
- Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN. (PDF) Principles for Teaching Problem Solving (researchgate.net)
- Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
- Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.
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