If you are interested in a NCTM membership join now. Log In. Toggle navigation. Log out. Good problem solving activities provide an entry point that allows all students to be working on the same problem. The open-ended nature of problem solving allows high achieving students to extend the ideas involved to challenge their greater knowledge and understanding. Problem solving develops mathematical power.
It gives students the tools to apply their mathematical knowledge to solve hypothetical and real world problems. Our students, at the UAE University, have difficulties in mathematical problem solving and we need to be aware of it. My purpose here is to present some of these issues in order to stimulate discussions.
Suggestions on how to facilitate certain aspects of mathematical problem solving, as I apply them in my classes, are also presented. Free Mathematics Tutorials.
About the author Download E-mail. If well facilitated, mathematical problem solving may help students develop and improve the generic ability to solve real life problems, [6] develop critical thinking skills and reasoning, [7] gain deep understanding of concepts, [8 ][9] work in groups, interact with and help each other.
Privacy Policy. This is the side of mathematics that enables us to use the skills in a wide variety of situations. Before we get too far into the discussion of Problem Solving, it is worth pointing out that we find it useful to distinguish between the three words "method", "answer" and "solution".
By "method" we mean the means used to get an answer. This will generally involve one or more Problem Solving Strategies. On the other hand, we use "answer" to mean a number, quantity or some other entity that the problem is asking for. Finally, a "solution" is the whole process of solving a problem, including the method of obtaining an answer and the answer itself. But how do we do Problem Solving?
There appear to be four basic steps. And we mean well before then. The Ancient Greek mathematicians like Euclid and Pythagoras certainly knew how it was done.
Understand and explore the problem; 2. Find a strategy; 3. Use the strategy to solve the problem; 4. Look back and reflect on the solution. Although we have listed the Four Stages of Problem Solving in order, for difficult problems it may not be possible to simply move through them consecutively to produce an answer. It is frequently the case that children move backwards and forwards between and across the steps.
In fact the diagram below is much more like what happens in practice. There is no chance of being able to solve a problem unless you are can first understand it. This process requires not only knowing what you have to find but also the key pieces of information that somehow need to be put together to obtain the answer. Children and adults too for that matter will often not be able to absorb all the important information of a problem in one go. It will almost always be necessary to read a problem several times, both at the start and during working on it.
During the solution process, children may find that they have to look back at the original question from time to time to make sure that they are on the right track. With younger children it is worth repeating the problem and then asking them to put the question in their own words. Older children might use a highlighter pen to mark and emphasise the most useful parts of the problem. However, there are certainly problems where children may find it necessary to play around with the information before they are able to think of a strategy that might produce a solution.
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