Reflect or Check Your Work These steps are better known as Polya’s Problem Solving Approach and were developed by George Polya in 1945. In Polya’s approach, the drawing came after understanding.You listed out the known information, you underlined the key terms and circled the numbers, but you just can’t figure out what to do. During this step students ask themselves: Can I draw something from this information? Students must dive deeper into the problem by drawing models and determining which models are appropriate for the situation.
Checking and Looking Back Summary here University of Utah I've used the diagram below to help students when working on investigational problems (diagram is stuck in the back of each students book).
wiki How is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. Problem solving and posing is an educational theory that demands thinking process, data analysis, evaluation, and reflection.
This article is one of a series which seeks to help teachers understand the nature of mathematical problem solving, why it is important and then how to assist students to develop mathematical problem solving skills.
In part, the thorny issue of addressing problem solving in maths classrooms both in Australia and elsewhere is caused by unclear definitions.
A collection of 83 problems for students This 14-page document has the 12 examples and 12 similar exercises and another 71 exercises for a total of 83 problems.
Solutions to the 83 problems This 17-page document has 'hand' solutions to the 83 problems.
By ‘real’, Polya did not necessarily mean ‘from the real world’ (although they well may be), but rather questions relating to a subject and which are ‘non-routine’ or new to the student .
Later in this series on problem solving, we will look at several different types of mathematical problem solving that students might be asked to work on either in the classroom or in real world, contextual situations.
STRATEGYWhen I was in school, we had a set of steps for problem-solving. Although these steps always sounded like a good idea and did get students thinking through the math problems they were facing, they didn’t always get the job done…What happens when you can’t get past step 1? In this approach, the drawing helps lead to the understanding.
Some teachers would change it up a little, but most were pretty close to:1. You read the problem over and over and still can’t make sense of it. DRAW a picture that represents the information given. Drawing a model helps students see which operation or operations are needed, what patterns might arise, and which models work and don’t work.