Problem solving

After a decade of tutoring math, I’ve realised the power of a problem-solving mindset. It extends beyond exams, aiding in everything from basic calculations to complex and often undefined business issues. At its core, this mindset revolves around a systematic, unemotional approach to problem-solving -a kinship with the scientific method. It’s about asking the right questions and developing an understanding of the issue and exploring the relevant paths.

In this post, we will explore how one develops a problem-solving mindset. Readers can expect to gain insights into the principles of problem-solving, practical strategies, and how to navigate ambiguity and uncertainty with confidence.

The Basics

As we embark on exploring the process of problem-solving, mastering foundational elements is crucial. These basics serve as the building blocks upon which our understanding is constructed, much like grammar and vocabulary in language.

Let’s take a moment to delve into the significance of mastering these basics. In high school math, for instance, these basics encompass concepts like fractions, algebra, and basic geometry.

Here’s why they’re essential:

• It allows for clear articulation of thought processes. Just as grammar aids clear writing, understanding basics helps break down problems and communicate solutions effectively.
• Facilitates the development of technical language. It equips us with the vocabulary and terminology necessary for deeper discussions and exploration of more complex ideas.
• The basics provide precision and confidence when tackling problems.

By mastering the basics, we allow for success in our problem-solving endeavours.

Tackling Problems

As you become proficient in the basics and gain independence in learning, you’ll naturally move towards more complex problems. These challenges often intertwine various layers of fundamental concepts, requiring you to unravel them in order to present a clear and concise solution.

It is essential to note that problem-solving isn’t always linear; it frequently entails revisiting earlier stages. Perseverance and resilience is necessary for such tasks. Remember it is essential to embrace these difficulties in order to grow.

Now, let’s explore the typical stages of problem-solving that I’ve observed through tutoring. First lets discuss getting started as it can be daunting, so here are my suggestions:

• Initiate with the “If in doubt, draw it out” approach to visualise the problem thoroughly. This aids in exploring all components of the problem effectively.
• Similar to writing an essay, problem-solving benefits from a structured approach involving separate drafting and editing phases. Begin with drafting to freely explore ideas before refining them in the editing phase.
• Consider the tools at your disposal. Even the faintest idea, when explored appropriately, can lead to success.

Next determining the next steps within a problem-solving question can be challenging. Here are some guiding questions:

• Trust your instincts and follow your nose. Where does the provided information lead you? Practice with similar problems can help refine your intuition in guiding your problem-solving process.
• Consider asking, “What is the stupidest thing I can currently do?” and “So what?” I suggest this, as often progress is made incrementally.
• Reflect on whether you have considered all aspects of the question and how the new information relates to what you already know.

Finally providing a solution which is clear and easy to follow is the aim. Here are some thoughts on the matter:

• Be precise and avoid ambiguity in your steps. Clarity in your presentation aids in externalising your thoughts and guiding the reader through your logical process. If your solution is difficult to comprehend, don’t hesitate to start afresh.
• Unlike the drafting stage, aim to eliminate redundancies and resist the urge to explore tangents while presenting your solution.
• Tailor your presentation according to the context of the question and the level of depth required. Ask yourself, “What is enough?” to ensure clarity and relevance for your audience.

Going Beyond

Once you’ve mastered the basics and practiced your problem-solving skills, you’ll encounter a different breed of challenges – research-style questions that mirror real-world problems. These types of problems often arise in business contexts and are characterised by opacity, human dynamics, and unpredictability, very unlike the straightforward problems encountered in examinations and school work.

For example, imagine being tasked with deploying a machine learning model to provide insights into customer retention. This type of problem requires more than just textbook knowledge. It demands creativity and adaptability, as there’s often no predetermined solution or formula to follow.

In real-world problem-solving, it’s important to consider various factors:

• These problems involve various stakeholders, each with their own interests and constraints. Understanding and navigating these constraints is essential to ensure that solutions are feasible and acceptable to all relevant parties. Remember to ask yourself, “What is enough?”
• Real-world problems often necessitate an iterative, non-linear approach. Unlike the linear problem-solving process common in academic settings, this approach involves being open to feedback and continually refining solutions. Embracing this process can alleviate the pressure of finding a definitive answer and help you focus on what is feasible within given constraints.

By actively practicing your creativity and adaptability in tackling these challenges, you can navigate through ambiguity and uncertainty with confidence and effectiveness. Remember, problem-solving is a skill that can be refined through its application.

Conclusion

In summary, we’ve explored the significance of problem-solving skills across different domains, from academia to the business world. We’ve highlighted the essential principles of problem-solving, in particular the importance of mastering the basics, and discussed strategies for tackling complex challenges, and how to handle the uncertainties of more real life problems.

Remember that problem-solving is not just a skill; it’s a mindset - a continuous journey of learning and growth. Armed with the right practical tools, you can confidently navigate through the ambiguity and uncertainty of real-world problems.

Now, I leave you to embrace your own challenges with confidence.