2.02: Interpreting the Problem

What is a problem?

A problem is a situation, question, or new experience that requires a solution. They can range from simple tasks, like putting on your shoes for the first time, to complex global issues, such as solving world hunger. When solving a problem, it is helpful to break it down into smaller, manageable steps. For example, consider the process of putting on your shoes:

1. Find your shoes

2. Put on your socks

3. Put on your shoes

4. Tie the laces

5. Done!

We can further break down each step if needed. Let's take the first step, finding your shoes:

1. Walk to your closet

2. Look at your outfit

3. Examine your shoe options

4. Choose a pair of shoes that match your outfit

5. Grab the shoes

By breaking problems into smaller steps, we can approach them more systematically and effectively.

We need skills to solve problems:

Understand the problem that needs to be solved

What information do we have? What information do we need for this problem? Read the text, graphs, charts or tables provided and pull out necessary information. Decide which mathematical skills we need to use.

Process the information that is available to solve a problem

Read the text, graphs, charts or tables provided and pull out necessary information. Decide which mathematical skills we need to use.

Analysing data & representing it in different ways

Looking at problems from different perspectives and diverging multiple solutions.

Looking for a problem that we have had experience with and considering more complicated problems.

Have simpler versions of this problem occurred before? How can I use that information to solve this problem?

Interpreting the Problem

You may think that problems are like traps. They check whether you, the problem-solving pioneer, are sufficiently skilled and self-aware to locate the 'right answer' amidst the tempting wrong ones. They can appear to be deliberately obscure, designed to confuse the reader by their means of presentation. And, on top of it all, what are they good for, apart from making bright-eyed innocent teenagers, like you, feel stupid?

Real-life problems:

rarely have one answer

normally allow some scope for interaction (to check that the details mean what they appear to mean)

often involve a situation with which you have some familiarity (problems often arise from a context which you have partly created yourself).

Success in posing problems and finding efficient answers will inevitably lead to your success in life. (If you doubt this, then pose yourself the problem: 'How can I achieve success in life?' And then find an efficient solution to it!)

This first chapter will show you how the world of real-life problem solving and the world of the problem-solving exam paper are linked.

This will enable you to extract the information from a problem confidently, carefully and efficiently.

You may be tempted to omit some of the sections, since they seem too distant from the reality of problem solving. But beware: you don't become a performance musician by studying what a performance musician looks like. You need to cultivate the underlying disciplines and attitudes as well as the surface-level skills. The foundational work on how a problem is created and presented will ensure you are genuinely prepared for new problems, both in your everyday life and when tackling an exam paper.

This is because, in order to successfully solve problems in both situations, you need to:

have a feeling for the context of the problem

have confidence to interact with and probe the problem

be familiar with the difficulties of modelling and articulating the problem.

This will enable you to extract the information from a problem confidently, carefully and efficiently.

When you heard the word problem, you may have thought about maths. In this class, some of the problems we will come across will involve mathematical calculations, charts and graphs.

Before solving a problem, we need to consider what strategy we want to use. We can use an algorithmic technique, which involves going step by step, or we can use a heuristic technique which involves using past shortcuts and past experience to solve the problem.

How to interrogate the question

Next you need to look at how you can apply this to problems with a precise, preconceived answer, where both the detail and the intentions of the problem setter are important.

When sitting and reading through a problem-solving question, it can sometimes seem as though the question is just sitting there and staring back at you, silently and unhelpfully. When faced with such a question, it is important to interact with it, asking it questions and listening out for its answers. Unfortunately you will have to supply these answers on behalf of the problem - but the answering is the easy bit. Asking the right questions is the bit you need to practice.

The skills and mindset that help you succeed in the game of "Animal, Vegetable, or Mineral?" are the same ones you need for tackling challenging problem-solving puzzles.

Always consider the various approaches you might take to address the problem at hand. When preparing to solve a specific problem, seek out someone who has already navigated it successfully. Asking questions is a highly effective way to understand a problem, as it exposes you to multiple potential solutions.

Simply requesting an explanation might only reveal one method, which may not be the best one. By questioning, you gain a broader perspective and can identify the most effective approach.

Typing Math with Google Docs.mp4

How to show your work

and type math with Google Docs and MS Word

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