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ROLE OF EMERGING ICT TOOLS FOR E-LEARNING OF HIGHER MATHEMATICS
Ashutosh Kumar Pathak1 and Prof. Anil Rajput2
1Research Scholar, Computer Science, Barkatullah Vishwavidyalaya, Bhopal (M. P.), India
2Department of Mathematics and Computer Science, CSA Govt. P.G. Nodal College, Sehore (M.P.), India Author1: [email protected]
Author2: [email protected]
Abstract
There are a number of ways in which ICT is used to support and enhance the teaching and learning of higher mathematics. While a primary concern of teachers is how ICT might be used to enhance students understanding of higher mathematics, there are other aspects of ICT currently used by teachers and students which contribute to and support learning. This paper covers the role of ICT tools and how it can become an important factor in making higher mathematics interesting, interactive, and easily acceptable among the learners. Invented model for E-learning in higher mathematics and its working principles.
Keyword: emerging ICT tools, use of Latex in web, E-learning in higher mathematics.
1. Introduction:
In present scenario still the use of ICT in education arena is less accepted among teachers and learners. In the area of study, of mathematics the use of ICT is still limited up to school level only. My study covers, the role of ICT tools in the area of study of higher mathematics for both the teachers and learners, because still learning of higher mathematics in traditional way is very difficult among the students. The student feels very tedious and boring in learning higher mathematics in conventional way. The concept of any theorem is very lengthy and lethargic so students do not grasp it easily. In my research study, I found that the learners of higher mathematics desire the concept and presentation of their course study material interesting and easily described. The ICT tools are very helpful in describing the mathematical
1123 | P a g e concept of their course of study and making mathematics enjoyable, interesting with full of fun. ICT tools can be presented in any concept of higher mathematics through pictorials representation, live demonstration and many more ways so that the learning of higher mathematics becomes more understanding and easier among the learners.
The focus of present research study is on the benefits that ICT integration in higher mathematics can provide, right from breaking time and distance barriers to facilitating collaboration and knowledge sharing among geographically distributed students.
2. Significance of ICT in Higher Mathematics
The growing use of ICT as tools of everyday life have seen the pool of generic skills expanded in recent years to include information literacy and it is highly probable that future developments and technology applications will see this set of skills growing even more. In the area of higher mathematics, the integration of Information and Communication technologies (ICT) tools is for imparting easily accessible, understandable and quality based higher mathematics learning.
The findings reveal that ICT tools increases the flexibility of delivery of higher mathematics so that learners can access knowledge anytime and from anywhere. It can influence the way students are taught and how they learn as now the processes are learner driven and not by teachers. This in turn would better prepare the learners for lifelong learning as well as to contribute to the industry. It can improve the quality of learning and thus contribute in enhancing the skill to learn higher mathematics. Wider availability of best practices and best course material in higher mathematics, which can be shared by means of ICT, can foster better teaching. ICT tools also allow the academic institutions to reach disadvantaged groups and new international educational markets. Thus, ICT tools enabled higher education will ultimately lead to the democratization of education. Especially in developing countries like India, effective use of ICT tools for the purpose of learning higher mathematics has the potential to bridge the digital divide. These steps would ensure that accountability, quality assurance, accreditation and consumer protection in ICT based education is taken care of.
3. ICT Toolsto Enhance Learning of Higher Mathematics:
1124 | P a g e The use of PowerPoint presentations to demonstrate concepts higher mathematics topic is one example of the way in which ICT can be introduced to provide a learning support for student’s which teachers can share with each other. Although not necessarily contributing to mathematical understanding, such a use of ICT can enhance learning and help improve levels of interest and motivation in the classroom.
Mathematical concepts can be made easier to understand by the use of appropriate specialist software – for example, the limiting process in calculus or the use of 3D geometry. In some cases, taking much of the routine slog out of an investigation (for example, by using a spreadsheet, plotting a graph on Autograph, or factorizing an awkward expression in Derive) can allow students to focus on the key ideas being presented rather than being distracted by spending time on skills they may either already have or may not need at a particular stage. The use of interactive whiteboards can allow such software to be integrated into lessons.
Teachers in a number of colleges and schools have developed interactive spreadsheets to enhance lessons. For example, in one college, spreadsheets are used to demonstrate the relationship between a function, its inverse and the derivative of both. The spreadsheet leads students to the general result for differentiating an inverse function and is made available to students via the college intranet.
PowerPoint presentations have also been used to refer back to work already covered – for example, comparing different types of graphs and showing the effects of changing various attributes, thus taking the focus away from the ability to plot graphs and focusing on the skill of interpreting them.
4. Theoretical Framework: Background Information
4.1. A General Overview on Learning Mathematics:In the field of mathematics education, some models have been developed to determine how students learn mathematics. Conceptual and procedural learning have been addressed by mathematics educators and others. For example, following the well-known Piaget’s theory, Gray and Tall (1994) introduced the idea of a precept and Dubinsky and McDonald (2001) introduced the famous APOS (Action-Process-Object-Schema) theory which has been interpreted by some researchers as an extension of Piagetian theories for the higher level of abstract mathematics. Based on the APOS theory, there
1125 | P a g e has been a set of new developments in teaching approaches and strategies in the field since the given theory provides a variety of ways about how to assimilate and learn abstract mathematics.
Given these developments, Laborde (2007) claimed that various systems of representation in mathematics that have been built over time affect how we do mathematics. Mathematical objects are only indirectly accessible by some representation forms such as diagrams, schemas, figures, formulas, tables, graphics, and algorithms, among others. Moreover, mathematical activities require some manipulations and operations on these different forms of representations (D’Amore, 2003; Duval, 2000).
4.2 Technology in Teaching and Learning of Higher Mathematics:Traditional methods of teaching and learning are no longer adequate to meet the demands of higher education. Many different types of technology can be used to support and improve both learning and teaching experiences in higher education. For example, the communication skills can be promoted via e-mail exchanges and e-groups; the organizational skills can be improved via database and spreadsheet programs;
numerical and symbolic computations and graphing of functions can be made effortlessly by using hand-held technologies such as advanced calculators, and finally the understanding of mathematical concepts can be better promoted with the use of some modeling software programs. Thus, it is important to consider how these technologies differ and sort out which of the characteristics make them important as vehicles for the teaching and learning of mathematics (Burrill et al., 2002; Ersoy, 2003a, 2003b; National Council of Teachers of Mathematics [NCTM], 2000).
Today, there are two main technological tools that are used in teaching and learning of Algebra: the handheld tools (such as advanced calculators) and the mathematical software programs. They help students perform complex matrix computations instantaneously and effortlessly. Thus, instead of spending lots of effort and time on heavy computations, students are able to concentrate on the main questions about the nature of the operations. This is the ultimate goal of many instructors involving technology in their teaching. While some instructors feel that doing some of the matrix multiplications by hand provides insight about why results appear as they do, many others believe that the ability to rapidly investigate a large number of examples
1126 | P a g e makes a valuable contribution to students understanding (Day & Kalman, 1999).
5. Methodology
5.1. Rationale:In contrast to the other areas of mathematics education, current research about the use of the ICT tools in teaching and learning of higher mathematics is still in its infancy. Our ultimate aim in this study was to shed light on the impact of introducing and integrating emerging ICT tools into the teaching environment and setting up a web and mobile mathematics repository on the teaching/learning experiences in higher mathematics. However, as the review of research at the international level (Lagrange, Artigue, Laborde, &Trouche, 2003) pointed out that there are many difficulties one expects to face while integrating computational tools into educational institutions. These difficulties stem from various problems, such as the large number of students in classes, hesitation and unwillingness of the instructors to utilize ICT tools in teaching, and the problem of curriculum changes.
5.2 Goals:This study had two major goals: (1) to investigate how to incorporate ICT into highermathematics; and (2) to develop a series of new instructional materials in different mode viz, CD’s, Web and Mobile on several topics of higher mathematics.
5.3 Research Problems:The research problems/questions in the study were: (a) How an appropriate use of ICT can be organized taking into account of the problems cited above and (b) How can we take full advantage of such powerful tools in order to develop a deep conceptual understanding of higher mathematics topics? One of the original points of this study comes from the introduction of a new dimension of teaching which is a combination of theoretical experimentation (this notion is due to Borwein, Borwein, Girgensohn, and Parnes, 1996) and an algorithmic approach.
The second important aspect of this research study is integration of emerging ICT tools Latex to develop a web repository for higher mathematics.
5.4 Method:A qualitative case study method was used in order to conduct this study. First of all, as clearly indicated in Yin (1994), this approach is appropriate to our above-mentioned research problems. Second, consistent with the case study approach, a set of procedures such as designing teaching materials, observing while teaching and collecting data, analyzing the information and reporting the results were followed in the study. A questionnaire was applied to gather the students
1127 | P a g e views on the designed instructional materials and the benefits of ICT tools in Higher Mathematics. The content analyses were conducted on students written answers as well as on group interviews. Students success was assessed by several homework tasks and specific questions in midterm and final exams. Finally, this study, as its name suggests, was a case study and thus it was not aimed to draw general conclusions within the outlined context.
6. Experimental Approach:
The Details About Sample Size Which is Taken in This Research Work:Based on the experience of interaction with the students, a set of questions was prepared focussing on the present support system, nature of general difficulties of students, improvement measures and the acceptability of mixing the technologies with the conventional teaching methods of Mathematics. The set of questions was sent to some subject experts in order to invite their suggestions.Suggestions will be duly incorporated and a final form of questionnaire was prepared in Hindi as well as English. At the outset, an online & offline survey in selected institution was conducted, in which the sample included students of undergraduate, postgraduate and M.Phil courses. The survey was carried out in various institutions of India. So that, the sample includes students from various universities of the state.
The total 1256 learners of higher mathematics participated and submitted their feedback based on designed questionnaire and detailed analysis was carried out using statistical software packages SPSS.
Frequency Table: Place
Frequency Percent Valid Percent
Cumulative Percent
Valid BHOPAL 475 37.8 37.8 37.8
BETUL(M.P.) 85 6.8 6.8 44.6
PANNA(M.P.) 14 1.1 1.1 45.7
TIKAMGARH(M.P.) 43 3.4 3.4 49.1
JABALPUR(M.P.) 49 3.9 3.9 53.0
DHAR(M.P.) 43 3.4 3.4 56.4
DAMOH(M.P.) 41 3.3 3.3 59.7
REWA(M.P.) 55 4.4 4.4 64.1
RAIPUR 93 7.4 7.4 71.5
CHANDIGARH 112 8.9 8.9 80.4
ABOHAR(PUNJAB) 100 8.0 8.0 88.4
BALODA BAZAR(C.G.) 44 3.5 3.5 91.9
MAIHAR(M.P.) 33 2.6 2.6 94.5
CHHATARPUR(M.P.) 37 2.9 2.9 97.5
CHHINDWARA(M.P.) 32 2.5 2.5 100.0
Total 1256 100.0 100.0
1128 | P a g e Course
Frequency Percent Valid Percent
Cumulative Percent
Valid NOT OPTED 25 2.0 2.0 2.0
BSC FIRST YEAR 529 42.1 42.1 44.1
BSC SECOND YEAR 325 25.9 25.9 70.0
BSC THIRD YEAR 192 15.3 15.3 85.3
M.SC 129 10.3 10.3 95.5
TECHNICAL 56 4.5 4.5 100.0
Total 1256 100.0 100.0
6.1 Learners Feedbacks: Feel About Higher Mathematics:
It is one of the important aspects to take the initiative of this research, without knowing the real experience about their present feeling of learning of higher mathematics all the other effort may seems meaningless. We have collected the learner’s feedback about their feeling of learning of higher mathematics in traditional way on two separate points:
I. Very difficult to understand and express: the causes given to opt are: books in English, poor teachers experience or both and poor background in maths. Out of total 1256 learners of higher mathematics 53% learners not opt the question and 47% opt to response this question. In which from total learners, 15%
selected poor teacher’s response, 8.4% selected books in English and 8.5%
selected both where as 14.5% selected poor background in maths.
II. Easier to understand but difficult to express: The causes given to opt are:
incompetence in language, difficult symbols, lack of practice and lack of teacher’s guidance etc. Out of total 1256 learners of higher mathematics 87.1% learners opt to answer and 12.9% not opted. Where 47.1% selected lack of practices, 18% selected difficult symbols, 11.4% selected incompetence in language, 8.9% selected lack of teacher’s guidance and remaining learners selected more than two options.
Thus, on the basis of received outcomes it seems that the feel about higher mathematics of learners of higher mathematics is not optimal and somehow feeling
1129 | P a g e difficult to understand and express it.
Keeping in view of above feedback we have developed a model to integration of Latex to develop some web and mobile resources for higher mathematics and making it easily understanding, interesting and enjoyable.
6. Invented Model:
However, some ICT tools already utilizing for teaching and learning of higher mathematics. During the study based on the identified hard spot we are trying to using ICT tools applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and Fourier series and approximation, wavelets, and convexity and optimization.
In today’s global era it is very important to sharing and learning the knowledge through different society, place of different geographical area. The effective uses of ICT tools how make very interesting role:
As we all knows in the area of higher mathematics many mathematical symbol and graphical representation is also a part of teaching learning process, a person having simple knowledge of ICT tools facing difficulty to share his/her knowledge or problem in this global arena only because the lack of knowledge of available ICT tools recourses, and also how its utilization befitted to learning of higher mathematics.
As my research topic we have tried to use effective uses of available and developed resources through available ICT tools.
The first general opinion of learners of Higher mathematics is the knowledge of available 86 key of computer key board is not enough sufficient to represent the mathematical symbol and different mathematical expression and they are feeling very helpless.
During the research work we have used mathematical software like, LATEX, MATLAB etc to make ease the representation of symbol, expression, drawing and plotting 2D & 3D picture, graph etc. A new model is also prepared to use in E- learning of higher mathematics to making teaching- learning of higher mathematics interesting and interactive.
1130 | P a g e Keyboard
Figure-1
Latex: The utilization of Latex inside the learning and teaching process of higher mathematics makes ease of representation of mathematical symbol, different mathematical expression and drawing picture. After knowing the syntax of latex software and its applications in proper place of different topics of higher mathematics the learners of higher mathematics feel the power and real use of available key of their computer.
For Example:
(1) Mathematical Expression:
At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:
\[f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N- 1}{2}\] where $h$ is some step.
Then we interpolate points $\{(x_k,f_k)\}$ by polynomial
\begin{equation} \label{eq:poly}
P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}\end{equation}
Its coefficients $\{a_j\}$ are found as a solution of system of linearequations:
\begin{equation} \label{eq:sys}
\left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N- 1}{2},\dots,\frac{N-1}{2}\end{equation}
Input Latex Compiler
[latexpage]
Alphanumeric
Output on Web
Mathematical Notation
1131 | P a g e Here are references to existing equations: (\ref{eq:poly}), (\ref{eq:sys}).
Here is reference to non-existing equation (\ref{eq:unknown}).
It’s processed by Latex and published as:
(2) Mathematical graph:
\begin{tikzpicture}
[+preamble]
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
[/preamble]
\begin{axis}
\addplot3[surf,domain=0:360,samples=40] {cos(x)*cos(y)};
\end{axis}
\end{tikzpicture}
\end{tikzpicture}
1132 | P a g e Latex compiles the graph for cos(x)*cos(y) as:
7. Finding and Result:
Based on collected feedback and invented model the following outcomes we have received:
Technological support prefers for teaching learning of higher mathematics: To know the interest about type of technological support which may give ease of teaching learning of higher mathematics; out of 1256 learners, 92.4 % learners are given their recommendation and 7.6 % not opted.
The total recommendation in percentage for the type of technological support find out as below:
Type of technological
support immCD(%) Web
(%)
Static HTML (%)
ALL (%)
Total (%) 15.0 13.0 3.0 61.1
(% given in decimal one point round off)
8.
Conclusion:
Successful effective implementation of ICT tools to lead change is more about influencing and empowering teachers and supporting them in their engagement with
1133 | P a g e students in learning rather than acquiring computer skills and obtaining software and equipment.
In addition, it will increase flexibility so that learners can access the best suitable resource for learning of higher mathematics regardless of time and geographical barriers. It can influence the way students are taught and how they learn. It would enable development of collaborative skills as well as knowledge creation skills. This in turn would better prepare the learners for lifelong learning as well as to join the industry.
Finally, I found and concluded that incorporation of ICT tools with higher mathematics builds the means for E-learning to evolve and mature as part of the educational change process, so that it achieves its promise of an improved system of learning of higher mathematics.
The step by step integration of ICT tools to the entire curriculum of higher mathematics may very helpful to understand and making its very interesting and setting up a web portal on open source tools can be very useful.
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The
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