# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.10

## Math Is Everywhere: A Problem Solving Teaching Unit

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## WHY IS THE DEVELOPMENT OF PROBLEM SOLVING SKILLS IMPORTANT?

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80% of the nine year olds responded correctly to addition word problems.

60% of the nine year olds responded correctly to subtraction word problems.

80% of the thirteen year olds responded correctly to the addition and subtraction word problems.

The results of the multiplication and division word problems were low. This was anticipated for the nine year olds, since it is at this level that these concepts are first introduced. However, when compared to previous assessments, this group performed 22% lower on word problems involving finding the product of a 1digit number by a 2digit number. This same group performed well on exercises which solely involved direct computation. What are the implications of this? Is less time being spent on problem solving? Are the students’ incorrect responses due to reading errors? Is more time being spent on isolated computational skill practice?

Only one word problem involving multiplication was presented to the thirteen year olds:

____ ____ “One rabbit eats 2 pounds of food in a week. There are 52 weeks in a year. How much will 5 rabbits eat in one week?”

____ *56% of the 13 year olds responded correctly to this item.

____ *This result was typical of any word problem which contained extraneous information. The results were significantly higher where extraneous information was not included.

Nine year olds had the same difficulty with problems containing extraneous information.

Performance was low overall on problems involving division.

Generally, the results imply that the students did not take the time to think through how to solve the problems. Also, one could reasonably conclude that a large portion of the students did not possess the skills that one needs to systematically figure out
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how
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to solve the problems.

Further, the Iowa Test of Basic Skills, which has recently been administered to New Haven students, and the proficiency test for ninth graders throughout the State of Connecticut have illustrated the need for developing problem solving skills in our students. These tests have produced nearly the same results that the National Assessment did. Students generally do well in computation, but do poorly on items which involve reading a word problem and solving it

The techniques or methods that a teacher uses in problem solving appear to be of secondary importance to producing success in problem solving. A systematic way of solving problems and a great deal of practice for students is of primary importance in the teaching of problem solving skills. The more practice that a student receives, the sharper his/her skills will become. Also, as outlined later in this paper, discussions between students and teacher, coupled with the proper lead questioning by the teacher, should produce positive results.

To develop competency in problem solving requires the teacher to view problem solving from the perspective of presenting mathematical concepts for the purpose of developing “problem sense” The proverb “I hear, I forget; I see, I remember; I do, I understand” has particular merit in the area of problem solving. Problem solving offers the opportunity for students to make the connection between the mathematical concepts that are taught in school and the real world Therefore; it becomes necessary to make the learning process as concrete as possible. It is also important that students learn a systematic manner in which to accomplish the assigned tasks, to facilitate his/her independence in, and mastery of solving mathematical problems. “The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student.”
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In the early stages of the learning process of how to tackle word problems, it is absolutely necessary for the teacher to provide a great deal of guidance to the students through discussion.

There are basically two types of word problems which are frequently assigned to students; those which require the direct translation of the verbal languageto mathematical language, and the subsequent application of the math skills (s)he possesses, and those problems which require the student to apply mathematical skills and concepts in a discovery manner. “Solving a problem means finding a way out of a difficulty, a way around an obstacle, attaining an aim that was not immediately attainable.”
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Both types of problems require the student to draw upon present knowledge and past experiences, but it is the latter which offers the greatest challenge to the student, and which has the greatest potential for helping a student to understand the many ways in which math relates to the other fields of study.