Problem Solving In Mathematics Education Literature Review Outline Examples
In a lesson about problem solving, students might work on a problem and then share with the class how using one of these strategies helped them solve the problem.
Inevitably, someday, every one of your students will encounter problems that they will not have explicitly studied in school and their ability to find a solution will have important consequences for them.He asks students to compare Idea 1 to the thinking used to compare A and B. ” (“Rabbits per square meter,” the students answer.) The teacher then asks the class to look for similarities across the five ideas, which are all visible on the blackboard.He writes on the board: “If either the area or the number of rabbits is the same, it's easy to compare.” The student with Idea 2 says, “I found a way to make the area the same,” and explains. Some students note that Ideas 2 and 3 use multiplication while Ideas 4 and 5 use division, a superficial similarity.They studied George Polya's , they began exploring what it would mean to make problem solving “the focus of school mathematics.” And they succeeded.Today, most elementary mathematics lessons in Japan are organized around the solving of one or a very few problems, using an approach known as “teaching through problem solving.” “Teaching through problem solving” needs to be clearly distinguished from “teaching problem solving.” The latter, which is not uncommon in the United States, focuses on teaching certain strategies — guess-and-check, working backwards, drawing a diagram, and others.In the Common Core State Standards for Mathematics, the very first Standard for Mathematical Practice is that students should “understand problems and persevere in solving them.”1 Whether you are beholden to the Common Core or not, this is certainly something you would wish for your students.Indeed, the National Council of Teachers of Mathematics (NCTM) has been advocating for a central role for problem solving at least since the release of in 1980, which said, “Problem solving [must] be the focus of school mathematics…He then invites a student to explain Idea 5: “I divided the other way…” A: 6÷9 = 0.66… Students who try using multiplication (Idea 2 or 3) discover that the method is cumbersome.The teacher invites students who used Ideas 4 and 5 to share their calculations, adding them to the lists from before: Idea 4: A: 9÷6 = 1.5 C: 8÷5 = 1.6 D: 15÷9 = 1.66… C: 5÷8 = 0.625 D: 9÷15 = 0.6 (rabbits/m2) “What do you think about these ideas?This prompts the student with Idea 3 to say, “I used kind of the same approach to make the number of rabbits the same.” When a student with Idea 4 comes up, she begins, “I decided to divide the area by the number of rabbits.” The teacher stops her. But some students notice the more significant connection that 2 and 5 are both about making the area the same, while 3 and 4 are both about making the number of rabbits the same.He writes: “(area) ÷ (# of rabbits).” Then he asks the class, “Why is she doing this? ” Another student says, “That gives the amount of area for each rabbit.” He lets the student finish her idea: A: 9÷6 = 1.5 C: 8÷5 = 1.6 The teacher asks the class to clarify what the 1.5 and 1.6 mean (m2 per rabbit) and what that says about the crowdedness of each cage. “We haven't talked about cage D yet,” the teacher points out. Please try using one of these ideas.” Students work in their notebooks for a few minutes.