Using A Matrix Tutorial Program to Improve Students’ Performance in Elementary Mathematics

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Published on International Journal of Biology, Physics & Mathematics
Publication Date: April 11, 2019

Mangut Mafulul Hosea, Thomas Godwin & Amula Apake
Department of Computer Science, University of Jos
Nigeria

Journal Full Text PDF: Using A Matrix Tutorial Program to Improve Students’ Performance in Elementary Mathematics.

Abstract
The purpose of this study was to develop an elementary matrix tutorial program for University of Jos students in order to improve students’ performance in MTH 101: Elementary Mathematics 1 (Algebra & Trigonometry) and related courses. It was necessitated by the large classes associated with these courses which makes it difficult for students to comprehend and take notes during lectures. The study examined the population’s experience regarding the use of Information and Communication Technology (ICT) in learning. Results from the survey emphasized the need for the provision of suitable tutors to aid the learning of mathematics in the university. It also revealed the importance of ICT and the need to promote its usage in improving different aspects of the educational system. This research indicated interest in solving these problems by building a prototype for an elementary matrix tutorial program to enhance the learning of elementary mathematics. Tools used in designing the software were Java, Eclipse IDE and WindowBuilder. The different functionalities of the tutor program were then tested against initial requirements and the results were impressive. In future the tutor can be appended to a larger mathematics tutorial program as a module for elementary matrices.

Keywords: Elementary matrix tutorial program, Information and communication technology, Educational system, & Module.

1. Introduction
The recurrent massive failure of students in mathematics and other computational courses is an issue of growing concern in Nigeria. Examination bodies including schools hardly record any significant improvement in student’s performance, especially in mathematical courses. This research work is an attempt to mitigate the recurrent massive failure associated with mathematical courses in our schools.
In modern day educational system, ICT has affected both the quality and quantity of teaching, learning and research in conventional and distance educational institutions. One of the benefits derivable from the use of ICT in education is the provision of educational tools such as tutorial programs which can be used to facilitate independent learning. It is worthwhile to note that in University of Jos, only few students are aware of the existence of such learning aids. The mathematics tutor commonly used by these students is the Stroud Engineering Mathematics Personal Tutor. It was meant to serve as a companion tutor to buyers of the Engineering Mathematics textbook (on a CD-ROM) and its sole aim is to help improve users understanding of the various topics contained in the text.
This research work recognize the need to provide a localized mathematics tutor which could be made available for both online and offline use to the University of jos community and beyond, through the University of jos Learning Management System (LMS) which will aid the teaching of mathematics and other computational courses. It is in accordance with this, that this research shall attempt to obtain a standalone and cost effective Matrix tutor (to be called “Matrix Companion”) to aid the teaching of elementary mathematics in University of Jos and elsewhere).

2. Literature Review
Information and Communication Technology (ICT) is an important component of the digital world. It has successfully presented us the need to adjust our culture and society to appropriately meet the challenges of this knowledge age (Yusuf 2005).
Some merits of ICT in education includes: assisting students in accessing digital information efficiently and effectively. ICT is used as a tool for students to discover learning topics, solve problems, and provide solutions to the problems in the learning process. ICT makes knowledge acquisition more accessible. Based on learning through ICT, students are more capable of using information and data from various sources, and critically assessing the quality of the learning materials. ICT provides more creative solutions to different types of learning inquiries. Learners can access all types of texts from beginner to advanced levels with ease through digital devices.
ICT promote collaborative learning in a distance-learning environment. It enables students to communicate, share, and work collaboratively anywhere, any time. For instance, a teleconferencing classroom could invite students around the world to gather together simultaneously for a topic discussion. Hence, offering them an opportunity to analyze problems and explore ideas as well as to develop concepts. The students will not only acquire knowledge together, but also share diverse learning experiences from one another in order to express themselves and reflect on their learning.
At present, many fields (education inclusive) have embraced the use of online and offline tutors (also called tutorials). This is due to the enormous benefits derivable from the practice such as independent learning, flexible learning, managed learning etc. Therefore, this research emphasizes the need for provision of a tutorial program to enhance the teaching and learning of mathematics in the university community.

3. Data Analysis/ Findings
3.1 Methodology
The “Matrix Companion” was developed to deliver lessons and exercises/quizzes on elementary matrices. These operations will be modelled using a use case diagram. Use case diagrams are used to represent the different interactions users can make with the system.

The matrix tutorial prototype comprised of two main sections – “Lessons and Exercises” and shall cover the following matrices operations:
1. Matrix arithmetic
a. Addition
b. Subtraction
c. Scalar multiplication
d. Multiplication
2. Transpose of a matrix
3. Determinant of a square matrix
4. Cofactors
5. Adjoint of a square matrix
6. Inverse of a square matrix
7. Simultaneous equations
a. By inverse method
b. By cramer’s rule
However, users should note that the following operations were not included in the exercise/quiz section:
• Product of square matrix and its inverse and
• Gaussian elimination method for solving a set of linear equations
The tutor was designed using Java, WindowBuilder (for GUI) and Eclipse. The scope of the Matrix Companion is strictly elementary mathematics with specifics to matrices. Therefore, the Matrix Companion shall tend to focus on the various sub topics of matrices as contained in the MTH 101 notes of Mathematics Department, Faculty of Natural Sciences, University of Jos.
Programs of this nature do generate some data during their execution and these data may need to be stored in some secondary storage devices for future use. For this particular Matrix Companion, the use of a DBMS to store these generated data may not be considered. Therefore, new program data will be needed any time the program is launched.

Below are the Functional requirements of the Matrix Companion System.
 The System shall allow users to choose only the lesson section or the practice (quiz) section of the system at a time.
 System shall allow user to choose a lesson on matrix operation of choice.
 System shall allow the user to practice (take a quiz) on the matrix operation of choice.
 System shall show the correct answer to the question asked after a number of failed attempts.
 System shall allow user to view the full working of the question asked.

Below are the Non-Functional requirements of the Matrix Companion System.
• System should provide a flexible form of navigation.
• System should provide an interactive usage.
• System should inform users some relevant applications of matrices.
• System should have the conventional about button to provide user with some information concerning it.
• System should run on multiple platforms.

4. Testing
Different modes of testing including unit testing, integration testing, system testing and acceptance testing were carried out regressively to ensure the tutor met its initial specifications. Individual units and components were tested before bringing them together. These tests were carried out thoroughly from start to finish of the program. The developed prototype was tested by different users which include the researchers and students of University of Jos through alpha testing.
The different tests carried and results obtained while evaluating the effectiveness of the program are presented in the table below.