Design and Implementation of a Mathematics Tutoring Application for Secondary School Students (A Case Study of God Saves Schools)
Chapter One
AIM AND OBJECTIVES OF THE STUDY
The aim of the system is to design a tutoring application for secondary schools using God saves schools as a case study.
In this study therefore, the researchers hope to accomplish the following objectives:
- To solve the problem of limiting students to teachings of their teachers in the classroom.
- To create a readily available mathematical dictionary where students can get meaning of mathematical terms
- To create a readily available module that contains a list of some mathematical formulas.
- Provision of readily available tutorials in form of reading materials.
- To design a system that will have a question and answer session at end of each topic to test the knowledge of the student.
CHAPTER TWO
LITERATURE REVIEW
INTRODUCTION
The use of mathematical applications and softwares in education is still relatively rare but the growing body of research and the interest suggests that its extended use is imminent. The underlying concepts and proofs of many mathematical concepts involve difficult and abstract ideas that present a mountainous obstacle to many students. Mathematical systems offer both an opportunity and a challenge to present new approaches that assist students and teachers to develop better understanding of the concepts. They can be used to change the emphasis of learning and teaching of mathematical concepts away from techniques and routine symbolic manipulation towards higher-level cognitive skills that focus on concepts and problem solving. Two of the key indicators of deep learning and conceptual understanding are the ability to transfer knowledge learned in one task to another task and the ability to move between different representations of mathematical objects.
Mathematical systems are multiple representation systems and they have the ability to facilitate graphical, algebraic and numerical approaches to a most of the mathematical concepts. Most of the mathematical applications also provide a high-level programming language, which helps the users to prepare their own set of library files to suit their needs. It thus allow learners to discover rules, to make and test conjectures and to explore the relationship between different representations of functions and other mathematical objects using a blend of visual, symbolic and computational approaches. Students enjoy the power and versatility of computer algebra and are encouraged to become reflective, deep learners.
While its usage in many countries in teaching and learning mathematics have made a significant impact at all levels of education, the progress and awareness of these technology has been really very slow in our midst. Mostly, it has been confined among the researchers and handful of students and college teachers in well-established research institutes.
COMPUTER ALGEBRA SYSTEMS
Computer algebra systems (CAS) are special kind of mathematical applications providing users means for doing symbolic, algebraic and graphical manipulations with computers. This means that instead of only counting with numbers, computer algebra systems can also manipulate symbols and, when possible, carry out complex calculations exactly. These systems can be roughly divided into two main categories: special purpose systems and general-purpose systems. Special purpose systems usually deal with some specialized branch of mathematics, viz. dynamical solver for differential equations, singular for algebra and algebraic geometry, gap for group theory, magma for number theory, CoCoA, Macauly2 for commutative algebra/ algebraic geometry, Octave for numerical computations etc. General-purpose system, on the other hand, usually try to cover as many mathematical areas as possible. This generality makes general-purpose systems ideal for open learning environments in most cases.
Albano G. & Desiderio M., 2002 further explained that most CAS allow the user to write sequential programs for complex tasks, and have all features of high-level programming languages. CAS also have most of the features of numerical systems for visualization of 2D and 3D-plots, numerical computations and animations. It is therefore an ideal tool for directing learning towards multiple-linked representations of mathematical concepts. Through carefully designed activities, students can investigate the links between different representations of objects, recognize their common properties and begin to construct their personal structures of mathematical knowledge. Student activities have to be designed with very detailed cognitive steps in mind. Appropriate teacher intervention will usually be required to ensure that the students follow through the required learning stages, in particular, the reflective thinking.
A typical student approach to problem solving is to find a suitable worked out example to mimic and then carry out the computation. Clearly, this strategy is limited by the extent of the students’ memory bank of similar problems and inhibits flexible thinking. A better approach is to consider alternatives, experiment, conjecture and test, then analyze the results. A computer algebra system can be a major factor in developing an exploratory approach to learning mathematics and, in particular, investigating problems from multiple representational perspectives. Using CAS to produce graphs, carry out calculus operations or perform repetitive calculations, students can be encouraged to make and test conjectures, to consider alternative solutions and to tackle open-ended problems. Removing the burden of manipulation and computation allows students to spend the more time on these other activities. This approach can make the study of mathematics more enjoyable, more relevant and more rewarding to it. At present most of their time is spent practicing routine skills. Perhaps it is not surprising that students view mathematics as a collection of formulae (to be memorized) and to do mathematics is to compute. If more routine computation is done on, a computer more time is available for concentrating on concepts, motivation, applications and investigations.
With the traditional undergraduate curriculum, students do not often regard themselves as active participants in mathematical exploration. Rather they are passive recipients of a body of knowledge, comprising definitions, rules and algorithms. Computers offer a number of didactic advantages that can be exploited to promote a more active approach to learning. Students can become involved in the discovery and understanding process, no longer viewing mathematics as simply receiving and remembering algorithms and formulae.
The power of computer algebra goes beyond routine computation. It has the potential to facilitate an active approach to learning, allowing students to become involved in discovery and constructing their own knowledge, thus developing conceptual understanding and a deeper approach to learning, (Chiasson & Yearwood, J, 2006).
CHAPTER THREE
RESEARCH METHODOLOGY
INTRODUCTION
The design methodology used in the proposed system is parallel because of the fact that parallel methods support the use of the proposed system side by side with the existing system in order to test for the system efficiency.
Waterfall approach is used as well in the design because it allows the analysis of the system to be carried out one after the other.
ANALYSIS OF THE EXISTING SYSTEM
The existing system involves that students go to the library, get some textbooks to read on their own. After which they leaves for their various destination, hoping to come back on a later date. During this process there are lots and lots of events like inappropriate arrangement of books, time spent is searching and accessing desired textbooks and so on happening there by leading to all sorts of malpractices and resulting to partiality in the test.
OVERVIEW OF THE PROPOSED SYSTEM
The mathematical based tutor application is a computer based mathematical solution, which allows students to be able to have quick access to reading materials, formulae, meaning of mathematical terms. It has the following features
CHAPTER FOUR
SYSTEM TESTING AND IMPLEMENTATION
INTRODUCTION
This chapter illustrates the system testing and implementation phases. The testing phase involves some modification to the pervious design phase and system testing has been done to minimize the programming and system error. At the implementation phase, system requirements such as hardware and software will be defined. Besides that, the system prototype interfaces and functionalities (module) will be fully demonstrated to users.
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATION
SUMMARY
Mathematical tutoring applications have potential to facilitate an active approach to learning, to allow students to become involved in discovery and to consolidate their own knowledge, thus developing conceptual and geometrical understanding and a deeper approach to learning. Emergence of such mathematical tools and its ability to deal with most of the mathematics students cannot be ignored by mathematics educators.
CONCLUSION
A mathematical based software is a tool not a self-contained learning package or encyclopedia of mathematical knowledge. It is the way in which it is presented to and used by students that determines its ability to influence learning. Much emphasis these days is placed on student-centered learning and less on the teaching but teaching and learning are equally important. It is necessary to first understand the learning process and then design teaching and learning activities to achieve these. Only then will students become deep learners.
There are many implications of using computers in the teaching and learning of mathematics at schools. As students often point out that it is very exciting, enjoyable and productive to use computers in class and libraries. They are keen to use computers, so the environment becomes more conducive for learning. Students’ natural curiosity can be utilized to its fullest potential because they are keen to explore and discover.
REC0MMENDATION
Irrespective of the software packages used, it is important to remember that the software should support the learning and curriculum and cannot substitute good teaching. Traditional teaching methods must be supported with modern tools for problem solving. It does not imply a reduction in the standard of education or of necessary subjects, but it is vital that the curriculum is carefully considered and that passive teaching is replaced in favor of new methods, which promote active participation of students.
For further research work to be carried out. I hereby suggest the following
- Mathematical Application should be developed that can work on any platform
- Diagrammatic representation as a teaching aid should be included in an a mathematical based tutor
- It should also be extended to other field of study such as chemistry, English Biology Agricultural science and many others.
REFERENCES
- Jo, B. (2016). An Overview of Modern Library Management. Retrieved from https://www.omicsonline.org/open-access/seeing-as-understanding-the-importance-of-visual-mathematics-for-our-brain-and-learning-2168-9679-1000325.php?aid=80807 on March 25, 2018
- Chiasson, K & Yearwood, J. (2006). Education and Human development. Retrieved from https://education.und.edu/teaching-and-learning/_files/docs/yearwood-vita.pdf on March 27, 2018
- Klien, C. (2014). Using Distributed Objects for Mathematical Applications. Retrieved from https://arxiv.org/pdf/1409.7236 on March 23, 2018
- Maple Software (n.d). Maplesoft Maple Mathematics Software. Retrieved from https://acms.ucsd.edu/services/software/license-info/maple-math.html on June 3, 2018
- Mathematica (n.d). What is Mathematica. Retrieved from https://www.calstatela.edu/its/services/software/mathematica.php on June 3, 2018
- Zlatkin, O. (2016); Assessment of Learning Outcomes in Higher Education. Retrieved from https://www.tandfonline.com/doi/full/10.1080/02602938.2016.1169501 on March 24, 2018
