THE EFFECT OF RUSBULT’S PROBLEM SOLVING STRATEGY ON SENIOR HIGH SCHOOL STUDENTS’ ACHIEVEMENT IN GEOMETRY CLASSROOM

Abstract

The study investigated the effect of Rusbult’s Problem Solving Strategy (RUPSS) on secondary school students’ achievement in geometry in Lagos state in Nigeria. A sample of 366 form four students consisting of 186 males and 180 females were drawn from three secondary schools in Lagos state by a multi-stage sampling technique. The Geometry Achievement Test (GAT) was used for data collection. Five experts, three in mathematics education and two in measurement and evaluation validated the instrument. The findings showed that Students exposed to the RUPSS achieved higher than those exposed to CPSS; Males in the RUPSS obtained a higher POSTGAT mean score compared to their female counterparts. The study recommends the teaching/learning of geometry through problem-solving strategies; Problem-solving should be incorporated into the curriculum in all institutions including teacher-training secondary schools Nigeria

Chapter one

Introduction

1.1Background of the study

Mathematics is an essential tool needed for the successful development of any nation. According to Timayi, Ibrahim & Sirajo (2016) Mathematics is a logical language for expressing ideas, shapes, quantities, size, order, change and dynamism of single and complex system. Nkwocha (2016) define mathematics as a science of numbers and systematic reasoning for solving problem. The researcher further explains that, mathematics is a science of numbers and shapes which include Arithmetic, Algebra, Geometry, Statistics and Calculus. Mathematics was viewed as the science of quantity, where science was classified into discrete i.e. the study of Arithmetic and continuous i.e. the study of geometry (Aristotle in Yadav, 2017). It is the relationships that revolve around the practice of counting, measurement and describing shapes and spaces (Soyem, 2001 in Anaduaka, 2008). The importance of mathematics in the development of human being cannot be estimated, this might be the reason why mathematics is made compulsory subject in Nigeria Education Curriculum at both primary and secondary school level of education (National Policy on Education, 2014; Fasasi, 2015).

When two people talk about mathematics problem solving, they may not be saying exactly the same thing. The rhetoric of problem solving has been so pervasive in mathematics education that creative speakers and writers can put a twist on whatever topic or activity they have in mind to call it problem solving. The National Council of Supervisors of Mathematics (NCSM, 1978 p.3) stated, “Learning to solve problems is the principal reason for studying mathematics”. Stanic and Kilpatrick (1988) opined that mathematics is synonymous with problem solving (doing word problems, creating patterns, interpreting figures, developing geometric constructions, proving theorems and so on). Otherwise, persons not enthralled with mathematics may describe any mathematics activity as problem solving. James, Maria and Nelda (2005) said that what is a problem and what is mathematics problem solving is relative to the individual. They urged that teachers and teacher educators should become familiar with constructivist views and evaluate these views for restructuring their approaches to teaching, learning and researches concerning problem solving

In the same line of thought, (Shoenfeld, 2008) said that to be solving a problem, there must be a goal, a blocking of that goal for the individual, and acceptance of that goal by the individual. Shoenfeld stated that what is a problem for one student may not be a problem for another either because there is no blocking or no acceptance of the goal. Shoenfeld situated a problem as having been given the description but do not yet have anything that satisfies that description. Shoenfeld described a problem solver as a person perceiving and accepting a goal without an immediate means of reaching the goal. According to Chris (2005) problem solving, in any academic area, involves being presented with a situation that requires a resolution. Chris said that being a problem solver requires an ability to come up with a means to resolve the situation fully. Chris added that in mathematics, problem solving generally involves being presented with a written out problem in which the learner has to interpret the problem, devise a method to solve it, follow mathematical procedures to achieve the result and then analyze the result to see if it is an acceptable solution to the problem presented.

A problem has an initial state (the current situation, a goal) the desired outcome, and a path for reaching the goal. Problem solvers often have to set and reach subgoals as they move toward the final solution (Schunk, 1991). Problem solving is what happens when routine or automatic responses do not fit the current situation. Some psychologists suggest that most human learning involve problem solving (Anderson, 1993). In the same line of thought, Obodo (1997) said that problem solving technique comprises the identification and choosing of mathematical problems which grow out of the experiences of individual students, placing these problems before the students and guiding them in their solutions. Obodo (1997) believes that this definition follows the steps of scientific method as well as those of reflective thinking. The teacher guides the class in solving the mathematical problem as a group. This technique encourages students to arrange and classify facts or data as well as allow students to learn from their successes and failures, since it permits the students to participate in their learning.

McGraw-Hill (1997) said that problems represent gaps between where one is and where one wishes to be, or between what one knows and what one wishes to know. Problem-solving is thus the process of closing these gaps by finding missing information, re-evaluating what is already known or, in some cases, redefining the problem. McGraw-Hill further stated that a well-structured problem is a typical situation with a known beginning, a known end, and a well-defined set of intermediate states. Solving a well-structured problem consist of finding an infrequently used path connecting the initial state of the problem with its end state. People solve well-structured problems not by exhaustively searching through the set of possibilities, but rather by heuristically identifying good starting places and productive lines of search

The activity of problem solving often consists of general strategies for linking up one stage with another in the search of a solution. A less powerful, though more general, strategy of a simple sort is referred to by computer scientists as generate-and-test and by psychologists as trial- and-error behaviour. It consist of picking a possible answer, trying it out, and if it does not work, trying another. Means-ends analysis and trial-and-error behaviour can require large amounts of time to complete, if the problem is complex, or may not lead to a solution at all in a practical amount of time. They have been successful in mathematical games and relatively simple problem-solving tasks. The activity of problem solving involves the use of problem-specific and knowledge-intensive methods and techniques, which are often referred to as heuristics. These heuristics are acquired through experience and represent the basis for expertise in a specific domain of problem-solving tasks such as physics, mathematics or medicine (McGraw-Hill, 1997).

Literature shows that problem solving is very difficult for secondary school students and that it is one of the principal causes of failure in school science and mathematics especially in trigonometry because it is a complex intellectual task. Research reports generally indicate that students’ difficulties are associated with the lack of procedural knowledge/strategies, skills of solving problem and the reasoning skills that go along with them. This is because most mathematics teachers still teach using the conventional method. The conventional approach to teaching mathematics problem-solving (or Conventional Problem Solving Strategies, CPSS) involves the representation of worked examples in textbooks. Most of the worked examples do not teach the effective processes of problem solving in mathematics and the mathematical sciences. The conventional approach does not therefore teach the basic procedural knowledge/strategies and skills of solving quantitative problems

Most people enjoy the stimulating challenge of a good problem and the satisfaction of solving it. You feel this satisfaction more when you master the tools of problem solving (Rusbult, 2005). Rusbult believes that you get “oriented” by using all available information (words, pictures, and free information) to form a clear, complete mental picture of the problem situation. By reading the problem statement carefully, you get accurate comprehension, the meaning of words and sentence structure, so as to gather all the important facts. Most problems are written clearly, so use standard reading techniques to accurately interpret what is written. You may re-read a problem carefully for details, using the “successive refinements” methods. Occasionally, a problem contains useless information (a decoy), so you need to learn to recognize what information to be used and what should be ignored. Study the diagram in the problem or make your own diagram because when the problem information (lengths, angles, forces, velocity and so on) is visually organized on paper, it is easier to understand it. This also helps to decrease your memory load, thus leaving your mind free to do creative thinking. The problem-writer may expect you to assume certain reasonable things about the problem situation (free information), or to use data that is not given in the problem but is available in textbooks, tables or in a special part of the exam

There is a body of research that shows gains in student achievement involving problem solving. Mettes, Pilot, Roosnick and krammer-Pals (1980) observed that undergraduate students’ skills in solving thermodynamics problems improved significantly if the four-stage model (Programme of Action and Method, PAM) they developed was coupled with mastery learning strategy. The National Assessment of Education Progress (NAEP) has shown gains in student achievement in the United States of America (Bay, 2000). Bello cited in Adigwe (2005) found that the Selvarantnam and Frazer model of 1982 significantly improved secondary school students’ skills in solving stoichiometric problems in chemistry if it is coupled with practice, verbal feedback and remedial instructions or with practice and verbal feedback. The Third International Mathematics and Science Study (TIMSS) shows that students in the United States of America (U.S.A) still score well below the international average mark in eight grade mathematics (U.S. National Research Center (NRC), 1996). If the situation in the U.S.A is that bad with the high educational and technological advancements, what then is the situation of Nigeria?

Statement of the problem

The methods and strategies employed to teach difficult topics like geometry in Nigeria need to be given serious attention. Literature has recommended the use of strategies to teach problem-solving involving word problems at all levels of education both nationally and internationally. There is therefore the need for unlimited research efforts geared towards improving the quality of mathematics teaching in Nigeria secondary schools. The problem of this study, posed as a question then is: what is the effect of Rusbult’s problem solving strategy on secondary school students’ achievement in geometry in Lagos state, Nigeria?

Objective of the study

The objective of the study is to investigate the effect of Rusbult’s problem solving strategy on senior high school students’ achievement in geometry classroom. The specific objectives are;

1. To find out Mean achievement scores and standard deviations of senior  high school students in geometry when taught through Rusbult’s problem solving strategy.
2. To find out Mean achievement scores and standard deviations of male and female students in geometry when taught through Rusbult’s problem solving strategy.
3. Interaction effects between strategy and gender of the mean achievement scores as measured by Geometry Achievement Test (GAT).

Research question

The following research questions will are formulated;

1. What are the mean achievement scores and standard deviations of form four students taught geometry through Rusbult’s  problem solving strategy?
2. What are the mean achievement scores and standard deviations of senior high school male and female students taught geometry through Rusbult’s problem solving strategy?
3. What are the interaction effects between strategy and gender of the mean achievement scores as measured by Geometry Achievement Test (GAT).

Significance of the study

The study will be very significant to students, teachers and the ministry of education. The will give a clear insight on the effect of Rusbult’s problem solving strategy on senior high school students’ achievement in geometry classroom. The study will educate on the important of Rusbult’s problem solving strategy on geometry. The study will also serve as a reference to other researchers that will embark on the related topic

Scope of the study

The scope of the study covers the effect of Rusbult’s problem solving strategy on senior high school students’ achievement in geometry classroom. The study will be limited to secondary schools in Lagos state

Limitation of the study

Limitations/constraints are inevitable in carrying out a research work of this nature. However, in the course of this research, the following constraints were encountered thus:

Non-availability of enough resources (finance): A work of this nature is very tasking financially, money had to be spent at various stages of the research such resources which may aid proper carrying out of the study were not adequately available.

Time factor: The time used in carrying out the research work is relatively not enough to bring the best information out of it. However, I hope that the little that is contained in this study will go a long way in solving many greater problems

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