COMPUTERIZED MATHEMATICS WORD PROBLEM SOLUTION

Diploma

INTRODUCTION

Descriptive evaluation is recognized as an effective method that requires students to write down the problem solving process so that teachers could analyze what the students do not understand and help improve their understanding. During the past 30 years, there has been an increasing emphasis on assessing problem solving by examining the cognitive processes that students use while engaged in problem solving. The multidimensionality of the problem-solving process is certainly made evident as attempts are made to look at all thinking done to solve a problem. Descriptive assessment does not ask simple questions that could be answered with a fact. Instead, they ask students to describe their problem solving process and evaluate the students' advanced thinking skills such as reasoning skills in mathematics. Whang (Whang, 2004) suggested that descriptive assessment is one of the most effective evaluation methods because it allows teachers to know explicitly the thought process of the students. Furthermore, computer-assisted mathematical problem solving systems are rapidly growing in educational usage. These systems help students to better cope with difficulties encountered in solving problems and give them immediate feedback. Some of these systems are based on the four problem-solving stages mentioned by Polya (Polya, 1945): (1) understanding the problem, (2) making a plan, (3) executing the plan and (4) reviewing the solution. However, these computer-assisted problem-solving systems have incorporated all the problem-solving steps within a single stage, making it difficult to diagnose stages at which errors occurred when a student encounters difficulties and imposing a too-high cognitive load on students in their problem solving (Chang et al., 2006).

Moreover, these systems focus more on cognitive thinking process, as well as abstract mathematical concepts and little interest is devoted to procedural skills. However, procedural and conceptual knowledge are highly correlated (Hallet et al., 2010) (Rittle-Johnson et al., 2001). Competence in domains such as mathematics rests on children developing and linking their knowledge of concepts and procedures (Silver, 1986), therefore we propose to develop a computer-assisted problem solving system that rules on both students’ conceptual and procedural skills. The purpose of this paper is to propose a new system that is based on the four problem-solving stages mentioned by Polya. The system assists in achieving addition and subtraction problems for second grade students by assessing cognitive reasoning at each stage and related procedural skills. Moreover, a multi agent system is used to grade students’ answers and displays feedback after the problem solving completion. The paper is organized as follows: In section 2, we discuss the goals of problem based learning strategy and its merits to enhance learning, such as creative thinking, problem solving, logical thinking and decision making. Section 3 focuses mainly on the influence of computer-assisted environments on mathematics instruction and their positive impact on students’ problem-solving. In section 4, we present the proposed problem solving process and we describe student-machine interfaces that are used in each stage besides embedded techniques to assist in achieving a successful outcome at each stage. Section 5 presents the student assessment approach and depicts the role of each agent in the assessment process. In section 6, we conclude on adopted strategy, and future work.


WORD PROBLEMS require practice in translating verbal language into algebraic language. Yet, word problems fall into distinct types. Below are some examples.

Example 1.   ax ± b = c.  All problems like the following lead eventually to an equation in that simple form.

Jane spent N42 for shoes.  This was N14 less than twice what she spent for a blouse.  How much was the blouse?

Solution.   Every word problem has an unknown number. In this problem, it is the price of the blouse.  Always let x represent the unknown number.  That is, let x answer the question.

Let x, then, be how much she spent for the blouse.  The problem states that "This" -- that is, N 42 -- was 14 less than two times x.

Here is the equation:

2x − 14

 = 

42.

 

2x

 = 

42 + 14  

 

 

 = 

56.

 

X

 = 

56
 2

 

 

 = 

28.

The blouse cost N28.

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Example 2.   There are b boys in the class.  This is three more than four times the number of girls.  How many girls are in the class?

 Solution.   Again, let x represent the unknown number that you are asked to find:  Let x be the number of girls.

(Although b is not known, it is not what you are asked to find.)

The problem states that "This" -- b -- is three more than four times x:

 

4x + 3

=

b.

 

 

Therefore,

 

4x

=

b − 3

 

 

X

=

b − 3
   4

.

The solution here is not a number, because it will depend on the value of b.  This is a type of "literal" equation, which is very common in algebra.


AIM AND OBJECTIVE OF THE STUDY

The aim of this study is to help improve the informal and formal math education of Prek-8 students. The emphasis is on providing students with learning environments that help to increase their levels of math maturity. The learning environments stressed in this study include an emphasis on communication in the language of mathematics, the use of math-oriented games, and the use of math word problems.

Objectives of this study are;

·        To make abstract concept in math’s more flexible for easy understanding for pres-8 students.

·        To enable application of computer in mathematics.