# Term Paper: Achievement of a Teaching Task

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Both the traditional and contemporary style of teaching mathematics has concepts that profoundly allow the learners to use their intellectual abilities to solve problems. The difference however is in the manner of their approach in establishing the interest of the learners. The contemporary approach allows the learners to engage themselves more in activities such as the use of computer technology, while the traditional approach is more on engaging the learner on individual activity of problem solving. M. Klein states one consequence of how the contemporary positively affects the learner.

A as students engage themselves in those learning processes that educators recognize as powerful and productive, they are simultaneously subject to positioning within the familiar storylines and practices of the classroom.

This means that the classroom activities where the learners engaged themselves not only allow them to learn mathematics, but also allows them to be conscious with the social practices within the classroom.

The Need for Reform

In the midst of several reforms that have evolved in the practice of teaching, particularly in mathematics, the concept of the subject remains the same: analysis, computation, and solving. Traditional and contemporary style of teaching mathematics present problems to the learners while the learners do their job of solving the problem. The traditional style though may be seen, if compared today, requires more intellectual abilities for the learner to think over and go through profound analysis due to lack of materials that can enable him to have a better idea of a problem. In the use of a formula for instance, the traditional style of teaching only explains how the formula is computed and what are the relationships of each variable to the others. The learner often has vague idea, or do not have any idea at all, as to where a formula can be used. All the learner knows is how to use and compute the formula. In contrast, the curriculum of mathematics in the contemporary style provides the learner with more schemes of the usage of formulas. Through the help of computer technology, where formulas are shown and applied through different representations, such as how a formula can be used in architecture, mathematics learning is made clearer. Carol Findell, in her Mathematics Education Then and Now: The Need for Reform, indicates that Current curriculum materials present students with relevant problems to solve, and require exploration and data analysis. We need to produce citizens who are able to understand the power of mathematics and work together with others to use mathematics to solve problems encountered in their personal and professional lives.

The need for reform in the manner of teaching mathematics is the concern of Findell in her article as she finds the subject useful in our daily lives, whether personal or professional. This was also her concern to be able to provide the citizens of the United States the same capacity and ability in mathematics as other nations, like Japan, demonstrates.

Large Class Instruction in the Past vs. Small Class Group Active Learning in the Present

The number of learners in a learning classroom is a factor in the result level of a learning process. The more learners there are in a classroom, the more vague the understanding of a lecture becomes to students. However, the lesser learners there are, the more learning opportunity are made available to the students.

Comparing the student occupancy in a mathematics class of the past and the present, research and studies show that there are more exclusively classrooms today. Nowadays, there are different learning institutions that provide a small class group active learning services where students are limited per class. This method is a good approach when the concern is to ensure that each student is able to follow every class lessons. Aside from this, a small class group allows the instructors to directly monitor the progress of every learner.

The large class instruction of the past may not present problems when it comes to the outcome of the learning process. This is due to the limited amount of learning that the past approach of teaching mathematics offer. In the past, mathematics deal with the basics, while today, mathematics deals with deeper amount of learning. This was indicated by Carol Findell and provided the following example.

During this era (1950's and 1960's), students were introduced to the theory of sets, and simple operations were defined in set terms. For example, addition was defined as the union of two disjoint sets, and multiplication was defined as the Cartesian product of sets. Great distinctions were made between a number and a numeral, which was a symbol representing that number. This approach, while mathematically elegant, was not aligned with the ways in which children learn.

In this "new math," not only was our base-10 number system explored, but students were asked to perform computations in other bases. For example, the sum 12 + 23 is 40 if the computation is done in base-5.

This difference though has been an issue in that the contemporary students, parents, and teachers, are not satisfied with the complexity that mathematics has gone today. This, however, should not become an issue since we are all witnesses to how such complexity became an instrument in the achievement of today's technological developments. Without the usefulness of the complex mathematics that emerged from the past, the existence of state-of-the-art technologies might not come into reality. There might be no computers today should mathematics remained a study of basic formulas. The different amazing architectures that we have today, such as the leaning tower of Pisa, or the skyscraping buildings, might not exist if the different complex mathematical formulas are not discovered.

Research and studies show that the large class instruction of the past is a factor that limited the growth of mathematics. Due to large number of learners, instructors find it hard to monitor the achievements and progress of their students. Hence, opportunity for curiosity is hindered. Compared to today's condition in classroom learning, curiosity makes the learning process a discovery of another learning. The capability of instructors to monitor each student provides a door to the discovery of new things. Through the questions that students raise, discovery became a part of learning.

The concept of traditional learning of mathematics is to understand the mathematical procedures from the already-ingested knowledge of the instructors. The knowledge is then passed on to the learners through class lectures. In contrast, the contemporary style of learning mathematics is student-centered, where the learners are given the chance of engaging themselves in activities that serve as learning resources and instructions for them. Findell suggests that The use of manipulative materials allows students to create models for mathematical operations. These concrete representations help some students understand the processes. However, unless the manipulations with these concrete models are connected to a symbolic representation, many students will not be able to use their knowledge effectively. Somehow, we must ensure that students understand the mathematical processes and can use these processes to solve problems.

Nowadays, the size of a learning environment is an essential factor when parents and students determine their choice of educational institutions. In terms of learning mathematics, small group active learning is considered as one of the best methods in making the teaching of mathematics effective. Especially in the secondary level, where the establishment of mathematical concepts and ideas start, it is important the every learner must receive all the necessary support from his instructor. This is made possible by a small group active learning.

Conclusion

Comparing the method of teaching in secondary school of the past and present learning processes presents similarities and dissimilarities. The similarity basically lies on the objective of mathematics while the difference generally lies on the method and approach of presenting information to students. The traditional form of teaching mathematics is a less active form, where the learners are mostly focused on solving problems. The contemporary form, on the other hand, presents learning through different activities where students learn mathematics while engaging themselves in other essential subjects (such as the use of computer technology in learning mathematics).

The diverse achievements in our current technology are proofs of how a growth in the study of mathematics can lead us to progress. We should not, however, account our progress in the present method of teaching mathematics. The contemporary form of mathematical learning is also an essential contributor to this growth.

How mathematics is taught to students is an important factor in learning mathematics. Both the traditional and contemporary forms of teaching mathematics have proven their worth as we see the developments that happened in their respective times. However, as time goes by, it is necessary that better approaches should be considered. As Carol Findell suggests,

Effective teaching of mathematics requires teachers who are trained in the new mathematics and pedagogy. Certification programs must include substantial mathematics components in order for this effort to succeed. Teacher training institutions must provide…
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