*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.*In some problems though, where there are more variables, it may not be clear at first which way to change the guessing.2 Act It Out We put two strategies together here because they are closely related. In the Farmyard problem, the children might take the role of the animals though it is unlikely that you would have 87 children in your class!We discuss below several that will be of value for problems on this web-site and in books on problem solving.

*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.*

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.

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).

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.As problems get more difficult, other strategies become more important and more effective.However, sometimes when children are completely stuck, guessing and checking will provide a useful way to start and explore a problem.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. To Pólya they were things to try that he couldn’t guarantee would solve the problem but, of course, he sincerely hoped they would.There are a number of common strategies that children of primary age can use to help them solve problems.Because it is such a simple strategy to use, you may have difficulty weaning some children away from guess and check.If you are not careful, they may try to use it all the time.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.

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