# Mathematical Models And Academic Achievement Of Students In Mathematics

## Abstract

This study was carried out to examine mathematical models and academic achievement of students in mathematics using some selected secondary schools in Giwa Local Government Area of Kaduna state as a case study. The study was specifically set to determine whether the use of models has a significant positive impact on mathematics teaching/learning process, determine the effect of the use of mathematical models on students’ comprehension level in mathematics, determine whether the use of mathematical models has a significant positive effect on the retention level of students in mathematics, determine whether the use of mathematical models has a significant positive effect on students’ academic achievement in mathematics and ascertain whether there is any difference in the academic performance of students taught using mathematical models and charts and those that are taught without mathematical models. The survey design was adopted and the simple random sampling techniques were employed in this study. The population size comprise of mathematics teachers and students of some selected secondary schools in Giwa Local Government Area of Kaduna state. In determining the sample size, the researcher conveniently selected 229 respondents and 210 were validated. Self-constructed and validated questionnaire was used for data collection. The collected and validated questionnaires were analyzed using frequency tables. While the hypotheses were tested using Chi-square statistical tool. The result of the findings reveals that the use of models have a significant positive impact on the teaching/learning process of mathematics. Furthermore the result of the findings reveals that the effect of the use of mathematical models on students’ comprehension level in mathematics is positive. Therefore, it is recommended that mathematics periods should be threaded in school time table since modelling is activities base learning and Mathematics teachers should be encouraged to teach modelling by providing necessary materials for the teaching and learning process. To mention but a few.

## Table of Content

- Title Page
- Certification
- Dedication
- Acknowledgement
- Table of Content
- List of Tables
- Abstract

### Chapter One:

#### Introduction

- 1.1 Background of the Study
- 1.2 Statement of the Problem
- 1.3 Objective of the Study
- 1.4 Research Questions
- 1.5 Research Hypothesis
- 1.6 Significance of the Study
- 1.7 Scope of the Study
- 1.8 Limitation of the Study
- 1.9 Definition of Terms
- 1.10 Organisations of the Study

### Chapter Two:

#### Review of Literature

- 2.1 Conceptual Framework
- 2.2 Theoretical Framework
- 2.3 Empirical Review

### Chapter Three:

#### Research Methodology

- 3.1 Research Design
- 3.2 Population of the Study
- 3.3 Sample Size Determination
- 3.4 Sample Size Selection Technique and Procedure
- 3.5 Research Instrument and Administration
- 3.6 Method of Data Collection
- 3.7 Method of Data Analysis
- 3.8 Validity of the Study
- 3.9 Reliability of the Study
- 3.10 Ethical Consideration

### Chapter Four:

#### Data Presentation and Analysis

- 4.1 Data Presentation
- 4.2 Analysis of Data
- 4.3 Answering Research Questions
- 4.4 Test of Hypotheses
- 4.5 Discussion of Findings

### Chapter Five:

#### Summary, Conclusion and Recommendation

- 5.1 Summary
- 5.2 Conclusion
- 5.3 Recommendation
- References
**APPENDIX****QUESTIONNAIRE**

## Chapter One

### Introduction

#### 1.1 Background of the Study

Mathematics has always been recognized as one of the most important disciplines meant at steering economic and technological advancement of any society. The Nigerian government has perceived the significant role mathematics plays in her establishment of logical and mechanical information that is essential in socio-economic development, hence has made mathematics teaching and learning compulsory in both primary and secondary education. The government has also struggled to provide trained mathematics teachers, teaching aids etc. in every school so as to curb the surging students-teacher ratio gap. However, irrespective of the previous efforts made by the government, there has always been poor performance in the subject at national examinations level over the years.

Given the poor performance of the subject locally and nationally, there was a need to address the problem in Nigerian secondary schools. Poor outcomes in mathematics have been credited to different causes going from poor teaching strategies to psychological factors, for example, the poor attitude of learners towards the subject. Taught in mathematics are frequently educated with no considerable reference to their applications, in actuality, circumstances, in this way making the subject boring subsequently resulting students to develop a negative attitude towards the subject. Other factors which have been raised include students’ experience in mathematics class, teacher’s perception of mathematics, cultural, facility and learning equipment in mathematics (Umeka, 2006 and Chuks, 2008). However, the most prime factor that influences teaching and learning of mathematics is students’ experience in mathematics class which consequently influences student’s achievement in mathematics.

Burton (2000) noticed that positive attitude towards mathematics assume a significant function towards science accomplishment and subsequently, instructors’ encouragingphilosophy should fuse uphold structures for learners learning climate. NCTM (2000) distinguishes the cycle guidelines of critical thinking which incorporates thinking and confirmation, portrayal, correspondence, and associations as ways learners ought to be occupied with learning arithmetic substance in order to create both procedural familiarity and reasonable comprehension of science. Learners occupied with critical thinking, for example, Mathematical Modeling (MM) manufacture numerical information and comprehension by wrestling with and tackling authentic issues, instead of finishing routine activities. These assists with building associations among mathematics and different teaches by applying arithmetic to real‐world circumstances. Accordingly, by taking part in these cycles, understudies become dynamic students of mathematics.

Blum (2000) noticed that Mathematical Modeling (MM) as an instructional methodology in mathematics educating has gotten progressively significant in the school mathematics curriculum of numerous nations. Enthusiasm for this region has filled altogether over the most recent twenty years animated by the various and assortment of studies and exploration work done on the learning and instructing of Mathematics. Additionally, International Congress on Mathematical Education (ICME, 2012) report that numerous nations over the world, for example, US’s as of late dispatched educational program, the Common Core State Standard of Mathematics (CCSSM, 2010), India’s National Curriculum Framework (NCF, 2005) have underscored on the significance of MM in instructing and learning of arithmetic in their educational plan and this has had positive effect on understudies’ numerical presentation in these nations.

As indicated by Guideline for Assessment and Instruction in Mathematical Modeling Education (GAIMME) (2016, p. 8-28) MM is a cycle wherein understudy use science ideas and strategies learned in class to speak to, break down, cause forecasts or in any case to give knowledge into genuine marvels. The open idea of MM gives undertakings that advances thinking and critical thinking. Understudies can participate in numerical talk in small and large groups as they figure out mathematics of real-world situations. MM advances both procedural and unique aptitudes with calculated understanding because of displaying measure and the individual commitment with the issue (Lesh and Zawojewski, 2007, p. 763-804). Simultaneously, students in MM, as a cycle of learning mathematics, are tested to build up their numerical deduction, for example, to depict, relate, change and to sum up data that goes past explicit numerical substance or aptitudes (Swan et al., 2007). Gathering work, class conversations and collaboration are particularly supported during MM exercises. Students are needed to explain their plans to build up their argumentation and relational abilities in a numerical setting while at the same time working with peers when solving MM task (English, 2003).

Kaiser (2007) likewise contends that by changing over issues into the way toward taking quantifiable information and demonstrating definition, MM instructing can meet the individual capacities of numerous understudies when contrasted with customary techniques for educating. MM underpins the learning of valuable abilities and methodology in arithmetic that assists with creating coherent reasoning, problem solving (PS) aptitudes and students’ talk. Rather than commonplace critical thinking rehearsed in science class, the methodology has significant mathematical thoughts and connectionsinstalled inside the difficult setting and understudies inspire this as they work through the issue (English, 2007, p. 139-156). In this manner, rather than word issues in which students are essentially needed to apply mathematical control aptitudes learned in class, in MM approach, the specific arrangement way is hazy and may include making suspicion that lead understudies to utilize mathematical abilities and think about whether they were defended in doing as such.

The foregoing leads to better understanding of mathematics concept learned in class. National Research Council (1999) in USA post that students’ accessibility to new information and linking it to previous knowledge or prevailing neuronal webs as they wrestle with multifaceted hitches and testing of new ideas thus neuronal networks are extended and strengthened while in this approach of learning. As much as the practice is a fundamental advance in creating proficient cycle through the mind, direct guidance alone does not normally bring about more profound learning and comprehension of mathematical ideas, this is because of the fact that teaching and learning utilizing course reading simply help learners to take in new information. In any case, when learners are occupied with critical thinking, for example, MM, they have occasions to make the association across numerical regions notwithstanding finding out about applications outside of mathematics classrooms leading to better performance of the subject (NCTM, 2000). Thus, because of this there was a need to examine the impact of mathematical models on the academic achievement of students in mathematics

#### 1.2 Statement of the Problem

It is a common phenomenon that students’ performance in mathematics is not at the desired level in Nigeria as statistics from examination bodies such as WAEC, NECO, NABTEB, GCE etc. attest to the decline in the performance of students, due to the difficulty students faced in understanding mathematical problems and applying formulas. This is evident in the rate of mass failure of students in both internal and external examinations, as revealed by previous studies. Despite the Kaduna stategovernment’s effort towards the provision and renovation of infrastructures in Primary and Secondary schools across the nation, students’ achievement in both internal and external examinations such as State Common Mock Examinations and other qualifying examinations into tertiary institutions is still poor and below expectation of the people. Several studies have identified other factors such as school environment, instructional materials, discipline and physical facilities, teacher quality, class size and over population of students in classroom as being responsible for poor academic achievement scores. Mathematics is generally viewed as a difficult subject to all students and more so to female students but the constraint of gender factor and interest are often overlooked in educational curriculum development in spite of the fact that they have influence on learning experience and achievement scores. Analyzing the constraints that limit the academic achievement of the female and male students and their attendant interest can identify the root issues which may lead to transformative changes to educational system and improved performance standard. Therefore, this study sought to investigate the effect of mathematical modelling on students’ academic achievement.

#### 1.3 Objectives of the Study

The Main Objective of the study is to appraise the effect of mathematical models on the academic achievement of students in mathematics.

The specific objectives include:

- To determine whether the use of models has a significant positive impact on mathematics teaching/learning process.
- To determine the effect of the use of mathematical modelson students’ comprehension level in mathematics.
- To determine whether the use of mathematical models has a significant positive effect on the retention level of students in mathematics.
- To determine whether the use of mathematical models has a significant positive effect on students’ academic achievement in mathematics.
- To ascertain whether there is any difference in the academic performance of students taught using mathematical models and charts and those that are taught without mathematical models.

#### 1.4 Research Questions

The study will be guided by the following questions;

- Does the use of models have a significant positive impact on the teaching/learning process of mathematics?
- What is the effect of the use of mathematical modelson students’ comprehension level in mathematics?
- Does the use of mathematical models have a significant positive effect on the retention level of students in mathematics?
- Does the use of mathematical models have a significant positive effect on students’ academic achievement in mathematics?
- Is there a significant difference in the academic performance of students taught using mathematical models and chartsand those that are taught without mathematical models?

#### 1.5 Statement of the Hypothesis

**Ho: **Mathematical models has no significant positive effect on students’ performance in mathematics.

**Ha: **Mathematical models has a significant positive effect on students’ performance in mathematics.

#### 1.6 Significance of the Study

It is expected that the findings of the study will help to disclose whether or not there is a need for modification of teaching and learning materials used by teachers and students in order to improve performance of mathematics. It is hoped that the findings of the study will help curriculum formulators to establish whether or not there is a need to emphasis on use of MM approach in teaching and learning of mathematics. The outcomes of the study will also help the Ministry of Education and other policy formulators in deciding on whether or not there is a need in planning for further development of teaching as a profession during training of mathematics teachers.

#### 1.7 Scope of Study

This study is structured to focus on the effect of mathematical models on the academic achievement of students in mathematics. The study will be conducted in 3 selected secondary schools in Giwa Local Government Area of Kaduna state. Hence, mathematics teachers and students will serve as respondents for this study.

#### 1.8 Imitations of the Study

In the course of carrying out this study, the researcher experienced some constraints, which included time constraints, financial constraints, language barriers, and the attitude of the respondents. However, the researcher were able to manage these just to ensure the success of this study. Moreover, the case study method utilized in the study posed some challenges to the investigator including the possibility of biases and poor judgment of issues.

However, the investigator relied on respect for the general principles of procedures, justice, fairness, objectivity in observation and recording, and weighing of evidence to overcome the challenges.

#### 1.9 Definition of Terms

##### Model Defined

Models are simplified representations of more complex systems which enables scientists simplify the knowledge they acquire for easy understanding thereby making models very essential and indispensable in scientific research and communication.

Mathematical modeling: A procedure or process whereby learners apply numerical ideas learned in class to new and new circumstances.

#### 1.10 Organization of the Study

The study is categorized into five chapters. The first chapter presents the background of the study, statement of the problem, objective of the study, research questions and hypothesis, the significance of the study, scope/limitations of the study, and definition of terms. The chapter two covers the review of literature with emphasis on conceptual framework, theoretical framework, and empirical review. Likewise, the chapter three which is the research methodology, specifically covers the research design, population of the study, sample size determination, sample size, abnd selection technique and procedure, research instrument and administration, method of data collection, method of data analysis, validity and reliability of the study, and ethical consideration. The second to last chapter being the chapter four presents the data presentation and analysis, while the last chapter(chapter five) contains the summary, conclusion and recommendation.

## Chapter Five

### Summary, Conclusions and Recommendations:

#### 5.1 Introduction

This chapter summarizes the findings on mathematical models and academic achievement of students in mathematics using some selected secondary schools in Giwa Local Government Area of Kaduna state as a case study.The chapter consists of summary of the study, conclusions, and recommendations.

#### 5.2 Summary of the Study

In this study, our focus was to examine on mathematical models and academic achievement of students in mathematics using some selected secondary schools in Giwa Local Government Area of Kaduna state as a case study. The study is was specifically carried out to determine whether the use of models has a significant positive impact on mathematics teaching/learning process, determine the effect of the use of mathematical models on students’ comprehension level in mathematics, determine whether the use of mathematical models has a significant positive effect on the retention level of students in mathematics, determine whether the use of mathematical models has a significant positive effect on students’ academic achievement in mathematics and ascertain whether there is any difference in the academic performance of students taught using mathematical models and charts and those that are taught without mathematical models.

The study adopted the survey research design and randomly enrolled participants in the study. A total of 210 responses were validated from the enrolled participants where all respondent aremathematics teachers and students of some selected secondary schools in Giwa Local Government Area of Kaduna state.

#### 5.3 Conclusion

Based on the findings of this study, the researcher concluded that;

- The use of models have a significant positive impact on the teaching/learning process of mathematics.
- The effect of the use of mathematical modelson students’ comprehension level in mathematics is positive.
- The use of mathematical models have a significant positive effect on the retention level of students in mathematics.
- The use of mathematical models have a significant positive effect on students’ academic achievement in mathematics.
- There is a significant difference in the academic performance of students taught using mathematical models and charts and those that are taught without mathematical models.

#### 5.4 Recommendations

Based on the findings of the study, the following recommendations are proffered.

- Mathematics periods should be threaded in school time table since modelling is activities base learning and Mathematics teachers should be encouraged to teach modelling by providing necessary materials for the teaching and learning process.
- Male and female students should be encouraged to put more effort in learning mathematics.
- It is the educators’ primary responsibility to design engaging and nurturing learning environment that will help the students attain their maximum potential.
- The students especially, young learners would need their teacher to provide guidance and to facilitate the learning journey. This teacher should know when to relinquish the control and little by little allow the learners to gain more autonomy to express their learning among their peers and to the teacher. This is possible when the teacher will always consider the needs of the students at all times.
- The school principal should monitor the teachers’ learning media, especially mathematics teachers, as an effort to improve students’ academic engagement.
- Training activities on learning models/approach should be carried out more frequently, especially related to biological materials.

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