Transcript Problem Solving

Warm - up
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?
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Problem Solving
The students will be
able to compare and
contrast the problem
solving approaches of
John Dewey, George
Polya, and the NCTM.
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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.
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NCTM Standards
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.”
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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.
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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.
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Summary
The chapter summary on page 117 is
particularly nice.
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Standards for School Mathematics
Prekindergarten through Grade 12
Problem Solving Standard (2000)
Instructional programs from Pre-K through 12th
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.
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Problem Solving Standard
Grades K - 3
Instructional programs from Pre-K through 12th 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?
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Problem Solving Standard
Grades 3 - 5
Instructional programs from Pre-K through 12th 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?
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Problem Solving Standard
Grades 6 - 8
Instructional programs from Pre-K through 12th 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?
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Problem Solving Standard
Grades 9 - 12
Instructional programs from Pre-K through 12th 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
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did the watermelon then weigh?
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.
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Assignment
Study for the mid-term, and
prepare your algebra lesson
plan for the 12th and
Read Posamentier pages 171188; and Johnson Chapter
3, and Johnson p 47-54.
(This last assignment was
not on your syllabus.) for
the 24th
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