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We discuss below several that will be of value for problems on this web-site and in books on problem solving.In this site we have linked the problem solving lessons to the following groupings of problem solving strategies.The idea is that you use your first incorrect guess to make an improved next guess. In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess. Children themselves take the role of things in the problem.
This is really just a start to help you on your way.
The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems! I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.
21 (2 1=3) No 23 (2 3 = 5) No 25 (2 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. By using the strategy elimination, we have found our answer.
Strategies are things that Pólya would have us choose in his second stage of problem solving and use in his third stage (What is Problem Solving? So they are some sort of general ideas that might work for a number of problems. As speaking in riddles isn’t likely to be of much assistance to you, let’s get down to some examples.
First, the student is taught a 7-step process for attacking a math word problem (cognitive strategy).
Second, the instructor trains the student to use a three-part self-coaching routine for each of the seven problem-solving steps (metacognitive strategy). I will reread the problem if I don’t understand it.” Ask: “Now that I have read the problem, do I fully understand it” Check: “I understand the problem and will move forward.”Say: “I will highlight key words and phrases that relate to the problem question.” “I will restate the problem in my own words.” Ask: “Did I highlight the most important words or phrases in the problem” Check: “I found the key words or phrases that will help to solve the problem.”Say: “I will compute the answer to the problem.” Ask: “Does my answer sound right” “Is my answer close to my estimate” Check: “I carried out all of the operations in the correct order to solve this problem.”Students will benefit from close teacher support when learning to combine the 7-step cognitive strategy to attack math word problems with the iterative 3-step metacognitive Say-Ask-Check sequence.But if there are not enough children you might be able to press gang the odd teddy or two. It is an effective strategy for demonstration purposes in front of the whole class.On the other hand, it can also be cumbersome when used by groups, especially if a largish number of students is involved.At least as important, though, is that the student must also possess the necessary metacognitive skills to analyze the problem, select an appropriate strategy to solve that problem from an array of possible alternatives, and monitor the problem-solving process to ensure that it is carried out correctly.The following strategies combine both cognitive and metacognitive elements (Montague, 1992; Montague & Dietz, 2009).Hopefully that exploration will lead to a more efficient strategy and then to a solution.Guess and improve is slightly more sophisticated than guess and check.It consists of a page per strategy with space provided to insert the name of any problem that you come across that uses that particular strategy (Act it out, Draw, Guess, Make a List).We have found that this kind of poster provides good revision for children. Through these links, children can see that mathematics is not only connected by skills but also by processes.As the site develops we may add some more but we have tried to keep things simple for now.Common Problem Solving Strategies We have provided a copymaster for these strategies so that you can make posters and display them in your classroom.