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Strategies For ‘Attacking’ Maths Problems, A Guide For Students And Teachers
In a previous article, “How to Answer Questions in a Formal Exam – A Student’s Guide”, I explained how to answer questions to get the best possible results on an exam. This article continues this theme, but this time in relation to answering questions on a formal math exam. The strategies mentioned in the previous article should be applied to the math exam as well as those discussed below.
It is important to define what I mean by a problem in mathematics before I begin to study the strategies for solving them.
These problems are almost entirely “word” problems. More often than not, the student must use a variety of mathematical skills or ideas to arrive at a solution. Often, especially in the later 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 required to achieve a result. Finally, the answer is not obvious.
Below is a list of strategies that, when used together, will help you solve real math problems better, not just the ones you have practiced. However, remember that if you don’t know your math basics, no set of strategies will help you solve problems.
So strategy number 1 is and always will be:
“Know all your work and learning procedures as well as you can.”
The remaining strategies are:
2. Remember that everything you need to solve the problem is in the question itself. (So list the data the problem gives you as a starting point).
3. Verification is a mandatory part of every problem you need to solve. Here is a verification procedure to use:
• It’s best to check as you go through each step of the problem, as it saves time and often avoids unnecessary extra work.
• Make sure you only did what you were asked to do. Make sure you have answered the question completely.
• Check that you have correctly copied all the question data.
• Check that your answer (its size, etc.) fits, from a practical point of view, into the scenario/context of the question.
4. Make sure you have been clean, orderly, organized, logical, clear and concise. This will help you in your verification and allow the examiner/teacher to follow your logic easily.
5. This strategy was mentioned in the first article. It is an integral part of the answer to any exam problem, especially in mathematics. It is: List the steps you need to follow, in order to get a solution.
Here is an example of what I mean by this strategy in math.
The pool problem
“How long does it take to fill a 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 answer: “There are no dimensions”
Your response: “You don’t need them. If I gave them to you, what would you do?”
Step 2: I now ask students to write down the steps they would use.
Step 3: Next, I discuss the steps chosen by the class and list the steps on the board.
for example Find the volume of the swimming pool.
Find the volume of the bucket.
How long does it take to fill the bucket and pour it into the pool?
How many buckets of water do I need to fill the pool?
Find the total time to fill the pool.
Step 4: Now I clarify that the above steps do not mention the dimensions of the pool. No matter what it measures, you always follow the same process.
Step 5: Finally, I emphasize that a correct answer depends on the correct steps, i.e. the method of solving.
As a student, you cannot learn these strategies overnight and expect them to “come” easily to you in a formal exam situation. You have to practice using them. Make a list of strategies and have them with you as you try each new problem. Evaluate how well you use them and work to improve the ones you find most difficult to use or easily forget. Ask your teacher to help you with this process. Remember, when taking an exam, be disciplined, write down the list of strategies you will use before you start, and use them to problem solve.
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