Wednesday, August 22, 2012

Strategies For 'Attacking' Maths Problems, A Guide For Students And Teachers

Mathematics (Photo credit: Terriko)
by Richard D Boyce

In an earlier article, "How to Answer Questions in a Formal Examination - A Student's Guide", I discussed how to answer questions to gain the best possible results in an examination.

This article continues that theme but this time in relation to answering questions in a formal Mathematics examination.

The strategies mentioned in the previous article should be applied to the Mathematics examination as well as the ones discussed below.

It is important to define what I mean by a problem in Mathematics before you start to study the strategies to solve them.

These problems are almost entirely 'word' problems. More often than not, the student needs to use a variety of Mathematical skills or ideas to gain a solution. Often, particularly in the senior years of high school, there will be an unfamiliar context in which to use your Mathematical knowledge.

Alternatively, there may be a series of sometimes complex steps necessary to achieve a result. Finally, the answer is not one which is obvious.

Below is a list of strategies, if used together, will help you gain greater success in solving real problems in Mathematics not just ones you have practised. However, remember, if you don't know your basics in Mathematics then no set of strategies will help you solve the problems.

So strategy Number 1 is and will always be: "Know all your learning work and procedures as well as you can." The remaining strategies are as follows:

2. Remember, everything that you need to solve the problem is in the question itself (so list what data the problem gives you as your starting point).

3. Checking is a compulsory part of every problem you are to solve. Here is a checking procedure to use:
• It is best to check as you do each step in the problem as this saves time often preventing unnecessary extra work.
• Ensure you have done only what you have been asked to do. Check, in fact, that you have actually answered the question fully.
• Check you have copied down all the data for the question correctly.
• Check that your answer (its size, etc.) fits, in a practical sense, into the scenario/context of the question.

4. Make sure you have been neat, tidy, organised, logical, clear, and concise. This will help you with your checking and allow the examiner/teacher to follow your logic easily.

5. This strategy was mentioned in the first article. It is part and parcel of answering any examination problem, especially in Mathematics. It is: List the steps you need to take, in order, to gain a solution.
Below is an example of what I mean by this strategy in Mathematics.

The Swimming Pool Problem: "How long does it take to fill a swimming pool with a bucket?"

Here is how I teach this strategy:
Step 1: I write the above problem on the board. When I do this, I ask the students for their reaction:
It will be: "We can't do it"
You ask: "Why?"
Their reply: "There are no dimensions"
Your reply: "You don't need them. If I gave you them to you what would you do?"
Step 2: Now I have the students write down the steps they would use.
Step 3: Then I discuss the steps the class select and list the steps on the board.
e. g. Find the volume of the pool.
Find the volume of the bucket.
How long does it take to fill the bucket and pour into the pool?
How many buckets of water do I need to fill the pool?
Find total time to fill the pool.
Step 4: Now, I make the point that the above steps do not mention the dimensions of the pool. It doesn't matter what it measures you still follow the same process.
Step 5: Lastly, I emphasise that a correct answer depends upon the correct steps, i.e. method of solution.

As a student, you can't learn these strategies overnight and expect that they will 'come to you' easily in a formal examination situation. You must practice using them.

Make a list of the strategies and have them with you as you try each new problem. Evaluate how well you use them and work to improve those you find hardest to use or are easily forgotten. Look to your teacher for help with this process. Remember, in an examination, be disciplined, write out the list of strategies you will use before you start and use them to solve the problems.

Rick Boyce has taught for over forty years, specializing in Mathematics for the last thirty-five years. For the fifteen years before retirement, he was the Head of Mathematics in a large Australian school.

During that time, he concentrated on developing an approach to the teaching of problem solving. He gained a reputation as an innovator and he shared his ideas in many professional development workshops. Rick has written a series of eBooks including one on his approach to Problem Solving in Mathematics which is published on the website

Article Source:,-A-Guide-For-Students-And-Teachers&id=7222955

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