1 A giant watermelon weighed 100 pounds and was 99 percent water. While sitting in the sun, some of the water evaporated, so that it was only 98 percent water. How much did the watermelon then weigh? Warm - up

2 The students will be able to compare and contrast the problem solving approaches of John Dewey, George Polya, and the NCTM. Problem Solving

3 Introduction to Problem Solving The introduction to Chapter 4 has the NCTM position (1989) on problem solving, p. 99. We will cover the 2000 standard in more detail later in this lesson.

4 From the NCTM Standards. “ Problem solving is much more than applying specific techniques to the solutions of classes of problems. It is a process by which the fabric of mathematics is both constructed and reinforced.” NCTM Standards

5 John Dewey John Dewey’s five step approach for solving problems from page 99 in the text. Recognize a problem exist. Identify the problem. Form a plan for attacking the problem. Apply your plan to the problem. Evaluate the solution.

6 George Polya George Polya’s approach from page 99 in the text. Understand the problem. Develop a plan. Carry out the plan. Check your results.

7 Summary The chapter summary on page 117 is particularly nice.

8 Problem Solving Standard (2000) Standards for School Mathematics Prekindergarten through Grade 12 Instructional programs from Pre-K through 12 th should enable all students to - build new mathematical knowledge through problem solving; solve problems that arise in mathematics and other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving.

9 Problem Solving Standard Grades K - 3 Instructional programs from Pre-K through 12 th should enable all students to - build new mathematical knowledge through problem solving; solve problems that arise in mathematics and other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving. Problem - I have a box of all red and all white cubes. In how many ways can I build a string of three cubes by using only these two colors?

10 Problem Solving Standard Grades Instructional programs from Pre-K through 12 th should enable all students to - build new mathematical knowledge through problem solving; solve problems that arise in mathematics and other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving. Problem - I have six coins worth 42 cents; what coins do you think I have?

11 Problem Solving Standard Grades Instructional programs from Pre-K through 12 th should enable all students to - build new mathematical knowledge through problem solving; solve problems that arise in mathematics and other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving. Problem - How many handshakes will occur at a party if everyone of the 13 guest shakes hands with each of the others?

12 Problem Solving Standard Grades Instructional programs from Pre-K through 12 th should enable all students to - build new mathematical knowledge through problem solving; solve problems that arise in mathematics and other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving. Problem - A giant watermelon weighed 100 pounds and was 99 percent water. While sitting in the sun some of the water evaporated so that it was only 98 percent water. How much did the watermelon then weigh?

13 Summary Problem solving is a process by which the fabric of mathematics is both constructed and reinforced. Students build new mathematical knowledge through problem solving; Students should solve problems that arise in mathematics and other contexts; Students should apply and adapt a variety of appropriate strategies to solve problems; Students should monitor and reflect on the process of mathematical problem solving.

14 Assignment Study for the mid-term, and prepare your algebra lesson plan for the 12 th and Read Posamentier pages ; and Johnson Chapter 3, and Johnson p (This last assignment was not on your syllabus.) for the 24th