# Strategies For ‘Attacking’ Maths Problems, A Guide For Students And Teachers

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 are 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”

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.

# How to Solve Problems in the Mathematics Education Using Calculators

Mathematics is a very important element in the development of the value and standard of the life of the individual and society. Mathematics enters in everything from science, technology and engineering to arts and social sciences to economics and decision making.

It is very important that society constantly produces new generations of well trained mathematicians. This means that the school should increase the student's interest and develop his skills in the subject. To achieve this goal the school should see the reasons why students fear mathematics and why many students do very poorly in the subject.

The fist reason for the difficulty of the subject for students is that mathematics is abstract. It is not tangible they can not hold it. To make them understand a pure concept at this early stage is very difficult. They need to relate it to real life problems that they face in their daily lives. This way they will be stimulated by its importance for them and will see that it is useful and fun. Moreover, the use laboratory experiments using calculators would make concepts more understandable. There are many new innovative software calculators built just for this purpose.

The conventional system of teaching mathematics contributes significantly to the poor performance of students. This is because many teachers teach students how to implement algorithms without teaching them the idea behind the algorithms and there is no stress on the understanding of the concepts. This causes the interest level in the subject to decline and soon students develop a disassociation with the subject. To solve this problem the schools can create a mathematics society and a forum where students can communicate with each other discussing material and asking each other questions. This kind of social behavior may increase the student's interest in the subject.

Students pass early mathematics classes and they are not really fit in the subject. This is because the exams and grading did not reflect the student's true ability. This causes the students to have very big problems in senior mathematics classes which are dependent on the early classes. For example if we look at the early pupil stage we can imagine a pupil who does not understand the concept of divide and multiply. That is to say when should he divide and when should he multiply. Now can this pupil at a later stage know to solve a word problem? The answer is surely no. He will not know what we are talking about. We can also imagine a student who does not understand the concept of the algebraic equations. This student could not be asked to plot a graph because simply he will not have an idea about what we are speaking about. The teachers can use calculators to teach pupils the concepts of multiply and divide. They can let them experiment on their own with many numbers using the calculators. From the observations the pupils will understand the concepts of multiply and divide. Moreover, teachers could use calculators to teach students the concepts of functions and graphing. It is easy and fun using calculators.

Finally, those who are teaching mathematics may have sufficient knowledge in the subject. They usually have a mathematics degree but this is not enough. To be a teacher you certainly got to be strong in the subject but this is only one major factor in being a successful teacher. The teacher should know about education and student psychology. he should also have a strong personality and be a good leader.