¶ … achievement of a teaching task. Despite of the different approach that teachers and instructors used, there is a part in teaching that allows the learners to gain knowledge, or better, to gain skills. The different methods of teaching, since the past years up to the present times, have shown and demonstrated their respective means of imparting knowledge. Each method provides ways of capturing the abilities of the learners, as well as communicating ideas and information. Wherever there is teaching, it is always essential that there must be learning since the essence of a teaching task is to be able to bestow knowledge.

One example where we can see the process of growth in a teaching task is in a mathematics class. Before, mathematics is taught in a more visual manner, "literally" speaking, where the process involves materials such as chalk and board, and paper and pencils. Now, in the days where technology seems to be an important means of learning, teaching mathematics has gone a long way. Students now learn different things from state-of-the-art gadgets and electronics such as the computer. The classic method of teaching with chalk and board seems to be going out with time.

From the traditional form of teaching mathematics that involve the use of traditional materials, up to the emergence of modern teaching channels and instruments, this paper aims to discuss the difference between these methods. The effectiveness of these two methods shall be compared and contrasted to enable the reader grasp information and ideas on how teaching mathematics has evolved through time.

Further, aside from the use of technology in contemporary mathematics class, and as part of this research, large class instruction in the past vis a vis small class group activity learning shall be discussed.

Teaching and Learning of Mathematics

Active participation of learners is considered as an essential aspect in learning mathematics. Interactions within classroom activities make the process of learning more productive. The role of a teacher or an instructor is not the only essential aspect of learning mathematics. Hence, it is a method of many teachers to ensure that there is a wide array of activities from which students and learners can participate during the learning process. According to M. Klein, in Teaching Mathematics In/For New Times: A Poststructuralist Analysis of the Productive Quality of the Pedagogic Process,

The teacher's role is to act as facilitator or guide, rather than a transmitter of information where "students demonstrate mathematical understanding by explaining and justifying their actions on mathematical objects rather than by following procedural instructions to obtain correct answers."

This idea, nowadays, is especially true in the light and emergence of new technologies. Compared from the previous method of traditional teaching of mathematics, today's process of teaching relies more on making sure that learners are able to participate, and not just follow rules and instructions to obtain learning. Further, as M. Klein indicates, the National Council of Teachers of Mathematics (NCTM), the application of knowledge that has been gained is important in the process of learning.

Basically, the philosophy of learning involves presentation of information while allowing learners to apply what they have learning. It is from the application of learning where knowledge can be best introduced in one's mind. This aspect is where the use of technology in today's mathematical teaching and learning comes into play.

The wide array of presentations that computers are able to provide the learners makes it easier to build information into one's mind. In contrast to the traditional form of teaching mathematics, wherein teachers and learners generally rely on paper and pens, or chalk and boards, how students learn from the different techniques computers are able to provide is surprising. For instance, students in the secondary level are found to be more interested in learning during activities where technology involves. The diverse capabilities of computers, such as presentation of graphics, and interactive features, interest learners more than when they are just presented with information using chalk and board. A similar theory to this idea, in terms of learners' unresponsive behavior on traditional process of teaching mathematics, was suggested by Willoughby, as indicated by Klein, states that much of mathematics taught in schools has been taught in such a way as to make students dislike both the mathematics and the learning of it; even if school leavers could use mathematics effectively they would be unlikely to do so.

Technology challenges the traditional task of mathematics teaching. With technology, a new approach to learning was brought to students.

In the large context of the advantages that technology brings, it is not suggested that the traditional teaching of mathematics, with pens and papers, or chalks and...

One important thing that should not be taken for granted is the fact that how instructors face the task of teaching mathematics makes an essential factor in teaching and learning of mathematics. There are teachers who still teach in the traditional form of teaching, without the help of technology, but yet, they were found to be successful and effective providers of mathematical knowledge and skills. This only proves that the measure of the effective of teaching mathematics is not the technology nor the traditional methods, but the approach that instructors incorporate in their task.
If the central theme of mathematics is problem solving, the same theme is the center of instructors' goals in making the task of teaching mathematics, especially in the secondary level, to become interesting and accurate. In cases as such, the magic of technology is never lost. Since computers became of a part of learning curriculums, mathematics instructors have never stopped thinking of possible ways that can make teaching mathematics effective while being informative as well. Through different systems, communicating mathematics with graphics and interactive functionalities, students are helped to grasp the idea of numbers and formulas in a more effective manner. This is achieved through sounds, colors, and images that were found to be instruments for better memory.

Being a learner of mathematics would need access to diverse practices of learning interactions where understanding and application can be applied. The notion on the teaching and learning process of mathematics may always involve a discussion and presentation of formulas.

However, as time goes by, this notion is being changed by technology where computer applications become better channels of learning and understanding. Through computer application features such as 3-dimensional graphics or animations, where mathematical formulas are generally part of, learners learn the real meaning behind "x y z " formulas.

Force of Mathematics Education

The importance of technology in today's learning of mathematics has been suggested by M. Klein through a discussion in the form of discursive spaces in mathematics. Klein suggests

In mathematics education it is important that discursive spaces are made for learners to act in powerful ways, to author personal sense-making processes in the construction of mathematical ideas and come to recognize themselves as competent participants in the discourse.

Such discursive spaces are presentable by computer technologies through 3-dimensional images that facilitate the process of forming knowledge in mathematical relationships and ideas. Unlike in the traditional form of teaching mathematics, which only involves the ability of instructors to show, write, and explain formulas, without other means and approaches of explaining how the formula can be applied, and how that formula can produce a beautiful and amazing output, the use of computer technology in teaching generally makes the study of mathematics an interesting subject.

The driving force in the discovery learning of mathematics, in summary, are the effective methods of transferring the knowledge to the learners.

Insights of Mathematics

Insight was also a key feature of learning and this could be sponsored by activities that allowed students to analyze situations for patterns or structure.

This insight, as stated by John Woodward in his Mathematics Education in the United States: Past to Present is not only possible with the help of technology. Traditional teaching of mathematics can also apply the key feature of learning activities to make the study of mathematics interesting and effective to learners.

The actual nature of mathematics involves numbers and logic of how to manipulate them to be able to solve problems. Apparently, the growth of mathematical methods of teaching has shown much improvement as compared to the past. Before, during the absence of technology, teaching mathematics is more on quantitative side where problems usually deal with numerical problems to solve. Central ideas such as the application of number were found to be missing.

Equally influential as an important factor of teaching mathematics is the instructor's careful explanation and discussion of knowledge. Before, the process of teaching mathematics is not aided by any instruments but by chalks and boards alone. Today, there are several processes that instructors designed to facilitate and explain of knowledge of mathematics. Beyond the mere fact that teaching mathematics, especially in secondary schools, constitutes patience in teaching, the development in the arts and schemes of mathematics will continuously evolve. The more channels become available to learners, the more chance they can obtain knowledge in mathematics.

Both the traditional and contemporary style of teaching mathematics has concepts that profoundly…