**EFFECT OF POLYA’S PROBLEM SOLVING TACTICS ON ATTITUDE, PERFORMANCE AND RETENTION IN ALGEBRA AMONG JUNIOR SECONDARY SCHOOL STUDENTS IN ZAMFARA STATE, NIGERIA **

**ABSTRACT **

This study investigated the Impact of Polya‟s Problem Solving Strategy on Attitude,

Performance and Retention in Algebra among Junior Secondary School Students in Zamfara State, Nigeria. Quasi-experimental and Control group design involving pretest, posttest and postpost-test was used for the study. The population for this study consisted of all the public junior secondary school three students in one hundred and eighty (180) schools under ZSTSB that are in four Education Zones of Zamfara State. The total enrollement figure in the schools consisted of 27,357 students. Eight out of one-hundred and eighty schools in the four Education Zones were selected by balloting method. Four schools were assigned to experimental groups and the other four as control groups. One intact class was drawn from each of the eight selected schools by balloting method, giving a total of 463 JSSIII students used for the study. The experimental group had 235 students while the control group had 228 students. The experimental groups were taught by Polya‟s problem solving strategy and the control groups were taught by conventional method. The experimental period lasted for six weeks. The instruments used for data collection were SLEWPPT, SLEPT and ASAIQ. These instruments were validated by five specialists in mathematics education and one specialist in language education. The reliability coefficients of SLEPT and ASAIQ were computed and found to be 0.792 and 0.826 respectively. Six research questions and six corresponding null hypotheses were formulated and used to test the significance at 0.05. The independent sample t-test and Mann-Whitney U test were used for data analysis. Findings from the study showed that students in the experimental group performed significantly better than those in the control group. It also revealed that experimental group significantly achieved positive attitude than the control group; also the retention level of students in the experimental group significantly exceed those of the control groups. The results also indicated that males in the experimental group had better attitude and performed significantly better than females. From the findings of this study, it was concluded that Polya‟s problem solving strategy was effective in promoting students‟ attitude and performance in algebra than the conventional method. In addition, students taught algebra with Polya‟s problem solving strategy in small groups have better attitude and performance than students taught algebra with conventional method. Based on the findings of the study, it was recommended among other things that State Government should train mathematics teachers in the effective use of Polya‟s problem solving strategy in teaching various mathematical topics through series of workshops

and seminars in order to improve the attitude performance and retention of students in mathematics at the secondary level.

# CHAPTER ONE

**INTRODUCTION **

## 1.1 Background to the Study

Education is essentially concerned with the growth and development of individual throughout life (Sharma, 2008). It is the bedrock upon which development revolves, and it is an invaluable tool for human growth and development (Abolade, 2009). This development can be achieved only when individuals are equipped with essential knowledge, skills and attitudes for survival and societal progress. Thus, to achieve this goal, the knowledge of mathematics is essentially needed because mathematics trains the mind and fosters creative thinking in people in order to solve problems that often occurred in everyday situations. Yusuf (2009) provides support for this view in which he stated that mathematics is not only considered important in its own right as a field of study and research, but also essential to almost every field of endearvour.

Similarly, Adetunde (2009) noted that mathematics forms the foundation of a solid education, adding that the overall national development of any nation and the building of healthy, happy and prosperous nation cannot be successfully achieved without mathematics. Therefore the position of mathematics in our national curriculum, and its role towards technological and industrial development put it in compulsory position in primary, secondary and tertiary levels of education (Madu & Hogan-Bassey, 2010). Despite the importance accorded mathematics in the educational system of Nigeria many secondary school students achieve very poorly in the subject. Many stakeholders such as the mathematics educators, researchers, governments, parents and the like have expressed their concern about students‟ persistent poor performance in mathematics especially at the external examinations. Nevertheless, in the past few years several research studies were conducted to determine the causes of students‟ poor performance in mathematics with a view to improve their performance (Saritas & Akdemir, 2009; Eniayeju & Azuka, 2010;

Farayola, 2011; Obomanu & Adaramola, 2011; Mbugua, *et al., *2012; Salman, *et al., *2012; Useni, *et al.,* 2012). Findings of these studies identified several factors responsible for this poor performance such as poor teaching method, lack of qualified teachers, lack of instructional materials, attitude, interest and motivation, mental ability, large classes and curriculum among others. Although the last decade, or so, have witnessed attempts on how best to improving the teaching of mathematics education in Nigeria, there still seems to be very little evidence of students‟ improvement in the subject. This is evident by the results obtained by secondary students at the senior school certificate examinations every year. This poor performance was reflected in their ten years of senior secondary certificate examinations reported by the West Africa Examination Council (2009 – 2018):

**Table 1.1: Summary of WSSCE May/June General Mathematics Results from 2009 – 2018**

# Year No. Pass at Credit Ordinary Pass Fail (F9) Candidates (A1-C6) (D7-E8)

**Sat for Exam. **

- 1,348,528 634,382 (47.04%) 344,635 (25.56%) 315,738 (23.41%)
- 1,306,535 548,065 (41.95%) 363,920 (27.85%) 355,382 (27.20%)
- 1,508,965 608,866 (40.34%) 474,664 (31.45%) 421,412 (27.92%)
- 1,658,357 838,879 (50.58%) 478,519 (28.85%) 298,742 (18.01%)
- 1,656,527 897,655 (54.18%) 462,176 (27.90%) 245,263 (14.80%)
- 1,632,377 766,945 (46.95%) 463,271 (28.38%) 402,161 (24.64%)
- 1,629,126 801,127 (49.17%) 452,460 (27.77%) 375,539 (23.05%)
- 1,552,758 822,496 (52.97%) 86,728 (5.59%) 643,534 (42.26%)
- 1,559,083 923,486 (59.22%) 203,445 (13.05%) 432,152 (27.72%)
__2018 1,572,396 786,016 (49.98%) 94,607 (6.02%) 691,773 (43.99%)__**Source:**Test Development Division, WAEC, Lagos.

Several research studies have identified poor methods of teaching as the major factor contributing to students‟ poor performance in mathematics (WAEC, 2009; NMC, 2009; Olunye, 2010; Abakpa & Iji, 2011; Obioma, 2011; Nizoloman, 2013). Moreover, Ali, *et al., *(2010) observed that mathematics is one of the most poorly taught, widely hated and poorly understood subject in our schools. Indeed, one aspect of mathematics that seems to contribute immensely to this poor performance is algebra because it requires higher level of abstraction that involves the use of symbols or letters to represent unknown quantities. These letters are used as mathematical objects in problem solving which makes it difficult for students to understand what these objects represent and how they can be related to realistic situations. Algebra is a branch of mathematics upon which all other branches of mathematics are based. This subject encompasses a wide range of topics, all of which engage the learner in critical thinking during problem solving. Simultaneous linear equation is one of the several topics in algebra that help students engage in critical thinking and model real-life situations. It is used to describe relationships between variables, for example, the relationship between distance, rate and time; length and width; principal, rate and time; plane, trains and automobiles; cost and demand; number of people engage in a job and number of days taken to complete the job.

In spite of the numerous applications, research has shown that many students encounter difficulties in word problems involving simultaneous linear equations in two variables by substitution and elimination methods (Widyastuti, Mardiyana & Saputro, 2016). Therefore to teach mathematics effectively, the teacher needs to employ teaching strategies that will engage students in significant activities in the class to make the subject more meaningful and understandable for the students. This will enable them to learn more, retain more and apply what is learned. In response to the deplorable situation, Ogunyemi

(2010) and Agwagwah (2013) suggested that problem solving strategy should be used in teaching mathematics to improve students‟ achievement and retention in knowledge and skills. Therefore, more research is needed on instructional methods for helping students learn mathematics with understanding. It is believed that problem solving is one of those strategies. Through an emphasis on effective instructional methods such as the problem solving strategy, students can develop positive attitude, improve their performance, and retain more of what they have learned by engaging in significant activities. In the context of this study, attitude is defined as positive or negative feelings students may have towards learning of mathematics especially in algebra. Olarewaju and Popoola (2009) noted that through problem solving strategy, students developed positive attitude and construct knowledge for themselves rather than simply receive knowledge from the instructor. Thus to help students create positive attitude, it is desirable to structure lessons such that students become actively involved with content through manipulation of materials and social interactions.

Performance is also a very important factor in learning mathematics in general and algebra in particular. Nneji (2013) described performance as the gain in knowledge of students as a result of taking part in learning activity or programme. Performance in this study refers to the students‟ cognitive achievement level and academic skills which are measured in terms of marks scored in a test of algebra aspect of mathematics. It can also be described as the student‟s level of performance in algebra. Various studies have indicated the effectiveness of problem solving strategy on students‟ performance in mathematics (Perveen, 2010; Suleiman, 2010a; Suleiman, 2010b; Fajemidagba & Suleiman, 2012; Nneji, 2013; Nfon, 2013; Salman and Ameen, 2014). The results showed that students who were taught by problem solving strategy performed better than students who were taught by conventional method of teaching. Retention is fundamental to students‟ learning. Hornby (2010) defined retention as the ability to remember things. In this study, retention is described as a process by which students hold in their memories the mathematical facts and concepts they learnt and readily retrieve them in examinations. According to Mangal (2012) the power of retention and retrieval are amongst other cognitive factors that affect both the processes and products of a person‟s problem-solving behavior. The use of effective teaching strategy which is stimulating and interesting, can enable students to retain and use the concepts they learnt to a wide variety of situations. Research studies carried out by Nneji (2013) found that students exposed to problem solving strategy retained better than those taught using conventional method. This is because problem solving strategy facilitates better understanding of mathematics concepts which in turns leads to higher performance and retention. Various innovative methods aimed at making the learning of mathematics more meaningful and interesting to students are being used by educators and teachers. One of them is problem solving strategy.

Problem solving is the process of finding an appropriate way to attain a goal when the goal is not readily available (King, 2008). There are several types of problem solving models developed by researchers to explain problem solving processes, including Polya (1957), Greeno (1973), Rubeinstein (1975), Lester (1978), Schoenfeld (1979), Bransford &

Stein (1984), Gick (1986), Woods (1987), Krulik and Rudnik (1987), Kapa (2001) and Rusbult (2005) problem solving models. However, this study focused on Polya‟s (1957) problem solving model. The researcher has chosen Polya‟s model among other models of problem solving because it has received a wide acceptance and provided a foundation for other strategies (Aljaberi, 2015). Moreover, the model was used in this study because according to Aljaberi (2015), “all recommendations and strategies in studies that deal with problem solving in mathematics are editable and can be accommodated one way or another to fit the Polya‟s model”. So, there is the need to evaluate its effect on students‟ attitude, performance and retention in algebra at the junior secondary school level. According to Mangal (2012) there are four basic steps needed in the solution of a problem outlined by Polya: understanding the problem which involves asking relevant questions that often helps students to draw a diagram representing the problem and the given information. In devising a plan, students are guided by the teacher to choose appropriate plan for solving the problem at hand. Then, they carry out their plan independently, checking each step to ensure that it is being properly implemented. Looking back means examining the solution to see whether it is correct or there is any other means of solving the problem. Against t his background, this study therefore, examined the impact of Polya‟s problem solving strategy on attitude, performance and retention in algebra among junior secondary school students in Zamfara State, Nigeria.

## 1.2 Statement of the Problem

Mathematics is a subject that is used in many fields, including natural science, engineering, medicine as well as the social science (Gbolagade, Waheed & Sangoniyi, 2012). Therefore, the importance of mathematics in the development of science, technology and other fields of knowledge cannot be overemphasized. Notwithstanding, poor performance of secondary school students in the subject has become a thorny problem world over, particularly in Nigeria. For example, the data from the West African

Examinations Council on students‟ performance in mathematics (WAEC, 2015) revealed that for the years 2010 and 2011, the percentage of Nigerian students who obtained credit pass in West African Senior School Certificate Examinations in mathematics was below average. Similar results were also recorded in the years 2014 and 2015 (WAEC, 2015). Also, the performance of students in internal and public examinations in mathematics has been attributed to many factors which include teachers‟ method of teaching, students‟ attitudes, and unavailability of learning materials amongst others. Nevertheless over the past two decades, a number of stakeholders have continued to take serious measures that would improve the learning of mathematics in Nigeria. These measures include organizing workshops, seminars, conferences, mathematics competitions and provision of adequate textbooks. Investigation also revealed that students were taught mathematics using approaches such as target task, Jigsaw and delayed formalization among others for the purpose of improving their performance in the subject.

Despite these, students still performed poorly in mathematics. In fact, simultaneous linear equation is one of the several topics in algebra that poses problems to students in the learning of mathematics. Research has shown that many students encounter difficulties in word problems involving simultaneous linear equations in two variables by substitution and elimination methods (Widyastuti, Mardiyana & Saputro, 2016). Similarly, literature consistently shows that most mathematics teachers in secondary schools in Nigeria still teach using the conventional method which typically involves overemphasis on rote memorization, drill and practice, exercise, and the representation of worked examples in textbooks that do not teach the effective processes of problem solving in mathematics. There is the need for effective teaching strategies that are leaner-centred where responsibility is placed on the learner to take initiative to achieve results for the various mathematical tasks during the learning process. Thus, the problem solving strategy has been reported to be one of the active learning methods that have been found to be effective elsewhere in the world but little attention has been paid to its use in Nigeria. Therefore this study was to determined the impact of Polya‟s problem solving strategy on attitude, performance and retention in algebra among junior secondary school students in Zamfara

State, Nigeria.

## 1.3 Objectives of the Study

The main objective of this study was to investigate the impact of Polya‟s problem solving strategy on attitude, performance and retention in algebra among junior secondary school students in Zamfara State, Nigeria. Specifically, the objectives of this study were to:

- compare the attitude of students taught algebra using Polya‟s problem solving

strategy and conventional method.

- determine the performance of students taught algebra using Polya‟s problem solving strategy and those taught using conventional method.
- compare the retention level of students taught algebra using Polya‟s problem solving strategy and those taught using conventional method.
- determine gender difference on attitude of students taught algebra using Polya‟s problem solving strategy.
- determine gender difference in performance of students taught algebra using

Polya‟s problem solving strategy.

- determine gender difference on retention level of students taught algebra using

Polya‟s problem solving strategy.

** **

** **

## 1.4 Research Questions

The main objective of this study was to investigate the impact of Polya‟s problem solving on attitude, performance and retention in algebra among junior secondary school students in Zamfara State, Nigeria. Specifically, the research questions that guided the study were:

- What is the difference in attitude if any between students taught algebra using Polya‟s problem solving strategy and those taught using conventional method?
- What is the difference in performance if any between students taught algebra using Polya‟s problem solving strategy and those taught using conventional method?
- What is the difference in retention level between students taught algebra using Polya‟s problem solving strategy and those taught using conventional method?
- To what extent does gender has any influence on attitude of students taught algebra using Polya‟s problem solving strategy?
- To what extent does gender influence the performance of students taught algebra using Polya‟s problem solving strategy?
- What influence does gender has on retention level of students taught algebra using

Polya‟s problem solving strategy?

## 1.5 Null Hypotheses

Based on the objectives and research questions of the study, the following null hypotheses were formulated and tested at p≤0.05 level of significance.

Ho_{1: }There is no significant difference in attitude between students taught algebra using

Polya‟s problem solving strategy and those taught using lecture method.

Ho_{2: }There is no significant difference in the performance between students taught algebra using Polya‟s problem solving strategy and those taught using conventional method.

Ho_{3}**: **There is no significant difference between the retention level of students taught algebra using Polya‟s problem solving strategy and those taught using conventional method.

Ho_{4}**:** There is no significant difference in the attitude of male and female students taught algebra using Polya‟s problem solving strategy.

Ho_{5: }There is no significant difference in performance of male and female students taught algebra using Polya‟s problem solving strategy.

H_{O6}**: **There is no gender difference in the retention level of students taught algebra using

Polya‟s problem solving strategy.

## 1.6 Significance of the Study

Mathematics plays a fundamental role in our everyday life (Akanmu, Otunla & Fajemidabga, 2015; Santos, Belecina & Diaz, 2015; Acharya, 2017; Rohmah & Sutiarso, 2018). Nonetheless, the existence of poor performance in mathematics among secondary students makes it imperative to search for better teaching strategies for effective learning of the subject. Such teaching strategies require active engagement to promote students‟ cognitive growth. Problem solving has been identified as one of the effective and efficient teaching strategies that enhances mental activities of students in the learning of mathematics (Rodrigues, 2015). Therefore, the findings from this study could hopely lead to other studies in mathematics in general and algebra in particular. These are explained as follows:

**Students in secondary schools: **The study would help secondary students to become good problem solvers. This is because good problem solvers have a repertoire of cognitive learning strategies that help them learn how to take control of their own mathematics learning; whereas poor problem solvers lack knowledge of strategies to perform learning tasks. Thus the knowledge of problem solving strategy would immensely assists students learn how to control and direct their thinking processes to facilitate learning. They would learn how to ask themselves questions, organize their thoughts, justify their ideas, makes sense of complex situations, and learn new ideas both collaboratively and independently. They would also learn how to connect and integrate the new concepts they are trying to learn with knowledge they already possessed. Similarly, if students are taught mathematics with problem solving strategy in small groups, group members will be inclined to generate new and innovative solution to the problem being solved. Such group participation may actually enable students to produce more ideas than those generated by individuals working alone, simply because every member is actively involved in their learning. Moreover, through the use of problem solving strategy students will have greater opportunity to acquire variety of thinking skills and apply them to various new situations. These skills may include comparing, interpreting, observing, decision making, creating and criticizing. The results of this study would also assist students to know what methods are necessary for effective learning of mathematics in general and algebra in particular. **Teachers at the secondary level: **The findings from this study would immensely assist teachers of mathematics in the secondary schools to understand the applications of mathematics in practical ways through problem solving approach and believe that mathematics is useful in our everyday lives. As a result, teachers will be equipped with numerious heuristic activities such as brainstorming, open-ended questions, and discussions in which ideas for consideration are examined. This can easily be achieved by carefully choosing appropriate tasks relative to the students‟ current abilities. As students work to solve problems, the teacher provides guidance and encouragement to help them attain the desired outcomes. Also, through the use of problem solving method, secondary teachers would hoply enhance their teaching effectiveness on algebraic word problems which inturn improve students‟ attitude and performance in mathematics.

**Guidance counselors:** The guidance councilors who work with secondary school students would be enlightened on the different theories of learning (e.g., constructivist theories of learing) that lead to various innovative approaches to teaching such as the problem solving method for motivating students to learn mathematics. In addition, guidance councilors may wish to know about the way a student feels toward the learning of particular school subjects such as mathematics and sciences. The results of this study, then, can assist councilors in identifying and understanding the different learning strategies that help students develop positive attitude toward these subjects. This can be achieved as councilors organize enlightment programme on the importance of various psychological activities in which students are encouraged to talk to themselves and ask themselves about the mathematics problems being solved. Such examples of mathematics thinking and selfquestioning are “What is missing”? “What am I to find”? As students are encouraged to talk to themselves, they will develop their own independence and success in learning mathematics and in monitoring their thinking about mathematics. Through these strategies, students can examine the methods that are used in handling problems. This will help them to eliminate fear of learning mathematics in general and algebra in particular.

**School Administrators: **The findings of this study would serve as a useful guide to the school administrators to know the efficient methods that increase the quality of instruction and encourage teachers to adopt those methods in their schools for improved performance. **Researchers: **It is hope that findings of this study would help other researchers in mathematics education with useful information about various innovative approaches such as the problem solving strategy that are efficient and productive in various teaching situations. This information would probably equip researchers with more knowledge and skills to carry out more investigation into other areas of problem solving in mathematics that would contribute to the development of research for improving the quality of

instruction in schools.

**Textbooks writers: **Textbook writers that are charged with responsibility of books production in the area of mathematics education may need to know the new approaches to the teaching and learning of mathematics such as the problem solving technique to be incorporated in to their work.

**National Education Bodies:** The Nigeria Educational Research and Development Council along with other educational bodies such as Science Teachers Association of Nigeria, Mathematics Association of Nigeria, and National Teachers Institute charged with the responsibility of developing and improving curriculum at both the primary and secondary levels would hopefully benefit from the findings of this study. The result of this study would provide the bodies with useful information on how to handle problems. This would help to enrich the curriculum to ease the understanding of the subject.

## 1.7 Justification of the Study

This study investigated the impact of Polya‟s problem solving strategy on attitude, performance and retention in algebra among junior secondary school students in Zamfara State, Nigeria. To provide a realistic understanding of students‟ learning in mathematics for improve performance, there is the need for clear instructional methods that would focuse on learner-centered and activity-based approaches. Problem solving strategy has been reported as an effective process for enhancing students performance (Rodrigues, 2015 & Lasak, 2017). A review of literature, however, has shown that there are a considerable number of studies that explored students‟ problem solving performance in simultaneous linear equations (Fajemidagba, Salman & Ayinla 2012; Tampuor 2012; Lagasse 2012; Hood 2013; Ogdol & Lapinid 2013; Esan 2015; Adisa & Abiola 2017). However, none of these researches was exclusively sets out to explore students‟ attitude, performance and retention in algebra using Polya‟s problem solving strategy especially at the junior secondary school level.

Additionally, most of the methodology adopted by the previous researchers in the field have not sufficiently and adequately address students‟ attitude, performance and retention in word problems involving simultaneous linear equations using Polya‟s problem solving strategy. Most researches relied on using approaches that did not involve students in collaborative investigations during problem solving. It is believed that students‟ performance is more likely to improve when they are given the opportunity to share their ideas and to become more actively engaged intellectually. Problem solving as an important component of mathematics curriculum is a process that involves the active construction of students‟ knowledge which happens in a social environment. Furthermore, students have constructs which are essential to their mathematical understanding. These include what they know and how is this knowledge organised and represented; they have knowledge and beliefs about group work, and other inter-personal relationships in class; they have personal feelings about various aspects of mathematics. Through Polya‟s problem solving strategy and with a teacher faciliting, guiding and scaffolding during the learning process, students can develop a deeper understanding of simultaneous linear equations. The junior secondary school is the stage upon which firm foundation of basic mathematical knowledge is built in order to support the understanding of more complex concepts and skills that are necessary for future learning. Simultaneous linear equation is an aspect of algebra that deals with numerous concepts and skills needed in learning of other aspects of mathematics. Such valuable concepts like variables, expressions and equations are the basic building blocks in algebra, and word problems introduce a context where the above three components can link to a solution model.

Moreover, the Federal Government of Nigeria has outlined five important objectives of the JSS curriculum. Among them are the two objectives which mainly focus on giving students the opportunity to develop the understanding and application of mathematics skills and concepts necessary to thrive in the ever changing technological world; and to develop the essential elements of problem solving, communication, reasoning and connection within the study of mathematics, Federal Ministry of Education (FME) (2012). These expressions have indicated the need for developing mathematics skills and knowledge which are essential in raising individuals who would become productive citizens in the world work. Further, in a bid to achieve its goals in national development, the Federal Government of Nigeria in the National Policy on Education (2004), clearly stated that the innovative educational techniques such as the problem solving approach should increasingly be used and improved upon at all levels of the education systems. There is therefore the need for unlimited research efforts geared towards improving the quality of mathematics teaching in Nigerian schools especially at the junior secondary level.

## 1.8 Scope/Delimitation of the Study

This study investigated the impact of Polya‟s problem solving on attitude, performance and retention in algebra among junior secondary school students in Zamfara State, Nigeria. Although various models of problem solving have been developed by educators to solve problems in mathematics such as Polya‟s (1957), Greeno (1973),

Rubeinstein (1975), Lester (1978), Schoenfeld (1979), Bransford & Stein (1984), Gick (1986), Woods (1987), Krulik & Rudnik (1987) and Rusbult (2005) problem solving models, this study was delimited to only Polya‟s (1957) model of problem solving. The study was also delimited to Junior Secondary Schools (JSS III) students in eight local governments within the four Education Zones of Zamfara State.These comprised of Anka,

Bukkuyum, Talata Mafara, Maradun, Gusau and Kaura-Namoda. The Junior Secondary School III students were considered appropriate for this study because the researcher wants to get terminal performance of students to prepare them for the senior secondary school level. The samples used for this study were eight public single-sex junior secondary schools in the four Education Zones of Zamfara State. The study was delimited to only three major themes on the JSSIII Mathematics Curriculum, namely; Number and Numeration, Geometry and Measurement. Number and Numeration contains number problems which include word problems involving sums and differences of whole numbers, word problems involving sums and products of whole numbers, two-digit number problems, age word problems, word problems involving fractions, ratio problems, simple interest problems, rate of work problems and mixuture problems; Geometry contains rectangle problems and angle measures problems which include solving problems involving dimensions of rectangles, and problems involving complementary and supplementary angles; Measurement consists of uniform motion problems which includes motion affected by wind and by water current. These topics were treated under algebraic word problems involving simultaneous linear equations in two variables by substitution and elimination methods from JSS III scheme of work. The instruments used for this study are: (1) Simple Linear Equation and Word Problem Pre-Test (SLEWPPT) which was used as a measure of background knowledge and homogeneity of students before the intervention, (2) Simultaneous Linear Eqution Performance Test (SLEPT) which consists of 10 essay items to measure students‟ performance in algebraic word problems on simultaneous linear equations and (3) Algebraic Students‟ Attitude Inventory Questionnaire (ASAIQ) which was used to assess the attitude of students toward algebra at the beginning and the end of the intervention.

## 1.9 Basic Assumptions of the Study

The following basic assumptions guided the planning and conduct of the study.

- Students had sufficient knowledge and skills for solving algebraic tasks at the

Junior Secondary School.

- Students in the sample for this study have been exposed to the same national curriculum.
- Teachers have similar background knowledge and skills in mathematics.

**EFFECT OF POLYA’S PROBLEM SOLVING TACTICS ON ATTITUDE, PERFORMANCE AND RETENTION IN ALGEBRA AMONG JUNIOR SECONDARY SCHOOL STUDENTS IN ZAMFARA STATE, NIGERIA **