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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.
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.
Other students applaud, the students sit down, and the lesson ends.
The teacher then displays the pictures in Figure 3. ” the teacher asks, as he puts them up one at a time for dramatic effect. The teacher records this idea on the board: “Karen thinks you need to know the area.” He turns to the first student. He anticipates the following five ideas and notes which students are using them: Idea 1: B and C have the same number of rabbits, but C has a smaller area, so C is more crowded. A would then have 45 rabbits while C would have 48 rabbits, so C is more crowded.
“Are these equally crowded, or do you think some cages are more crowded than others? Idea 3: If you make 8 copies of A and 9 copies of C, they would have the same number of rabbits (72).
5) During most Japanese lessons, the textbook is closed, but the textbook shows how the authors think the lesson might play out.
When the lesson begins, the blackboard is completely empty. Some students notice that some of the cages are different sizes.” asks the teacher, and students respond, “They are easy!” So the teacher writes a summary on the board, “Using division, it is easy to compare crowdedness.” He asks the students to write a reflection in their notebooks.What do your students do when faced with a math problem they don't know how to solve? At best, they seek help from another student or the teacher.At worst, they shut down, seeing their failure as more evidence that they just aren't good at math.Through this discussion, the lesson enables students to learn new mathematical ideas or procedures. Let's illustrate this with an example from a hypothetical fifth-grade lesson based on the most popular elementary mathematics textbook in Japan.(This textbook has been translated into English as and is available at Ed 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.These lessons are usually outside the main flow of the curriculum; indeed, they are purposely independent of any curriculum.In “teaching through problem solving,” on the other hand, the goal is for students to learn precisely that mathematical idea that the curriculum calls for them to learn next.