Advanced Algebra Curriculum Reform: Theory-based Teaching into Practice-based Teaching

Education Research Frontier March 2016, Volume 6, Issue 1, PP.14-18

Advanced Algebra Curriculum Reform: Theorybased Teaching into Practice-based Teaching Xiaoqiang Guo #, Lichao Feng, Yan Yan College of Science, North China University of Science and Technology,Tangshan, Hebei, 063009, China #Email: guoxq2004@163.com

Abstract A case study in North China University of Science and Technology, we analyze prevalently several issues in the teaching process of Advanced Algebra for mathematics. From the course content, teaching methods, assessment methods and teaching books the four areas, we propose several reform views for realizing from theory teaching into practical teaching in order to improve teaching quality. Thus we can achieve the goal of college training applied talents.

Keywords: Advanced Algebra; Curriculum Reform; Practical Teaching

1 INTRODUCTION In the 21st century, computer technology, information technology and biotechnology have become the most popular disciplines. These disciplines are needed on behalf of the development of algebra. Advanced Algebra is a basic course in math majors. Its theoretical knowledge and research methods not only affect the study of subsequent course but also help to strengthen students' thinking ability and innovation. The teaching of Advanced Algebra is good or bad, which directly impacts on the quality of training of professional students. Therefore, how to improve the teaching quality of Advanced Algebra curriculum has become widespread concern of university teachers. In recent years, the rapid development of algebra, new ideas, and new knowledge is emerging. However the content is basically the results and conclusions century ago. The current algebra curriculum materials content overemphasize the purely theoretical mathematics. That is, these are only the abstract theory, without the formation process of theoretical ideas and the use of scientific methods. They have not introduction on the development and application.

The existing curriculum materials contents are center of knowledge. Focus only imparts knowledge to students, lacks of the spirit of humanism and fun, lacks of theoretical and practical links, not be conducive to the training of sense of innovation and creativity, not to mentions the development of students' personality. Traditional Chinese Universities teaching use the model of "teacher talk, students listen". Students are passive acceptance of knowledge. Because of dull teaching methods, lifeless classroom, content pursuit system, students are rarely free-thinking. And they can not go against teachers and books to innovation, which is incompatible with the current development of science and technology of social. In order to meet the challenges of international higher education curriculum reform, keep abreast of the rapid development of science and technology, follow the laws of development of higher education, and improve teaching quality and efficiency and cultivate innovative talents modernization, we need to reform on Advanced Algebra from course content, teaching methods, guidelines and education ideas.

2 THE PROBLEMS IN THE PROCESS OF “TEACHING” AND “LEARING” OF ADVANCED ALGEBRA Advanced Algebra is a main course for math majors in independent college, which semester is academic year, teaching time 30 weeks, 6/8 hours per week, 12 credits. In the teaching process, there are several problems.

2.1 Students’ Poor Mathematical Basis With the continuous enrollment universities, independent colleges recruit students for admission scores between regular undergraduate and specialist, its low math scores. Math majors enrolled students who are not good at maths.

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And many of them lack the capacity for self-learning. Most of them are generally more confused thinking, and no clear goals, no professional identity. Some of them think that university is a paradise for fun. A lot of students can not meet the university's learning characteristics. Their learning methods and concepts still remain in the high school cognitive level. And they are lack of initiative. For abstract difficult lessons, they are too dependent on the teacher taught. And also they do not engage in active thinking and mastery. For a long time, they are prone to emotional weariness due to difficulties and low self-esteem. According to the survey, most of the students exist the phenomenon in the teaching process, which is the basic lectures can understand, but do no exercises.

2.2 The Textbooks are not Suitable The textbooks are chosen "Advanced Algebra" composed by algebraic groups of Department of Mathematics of Peking University[1]. The textbook is a very good classic, which is also used as a textbook in many colleges and universities. At present, there are many other "Advanced Algebra" textbooks, e.g. Zhang Herui and Hao Bingxin edited[2], but most textbooks are biased towards the theoretical knowledge lacking of application part. Faced with the training objectives of mass education, these textbooks do not apply to students of independent college.

2.3 Teaching Focuses on Theory Independent College offers Advanced Algebra course syllabus formulated remained consistent with the main campus. As abstraction of knowledge, in the teaching process they focus on the culture of computing power, but for the part of proving the requirements for students are able to understand. Teaching only focuses theoretical knowledge, but there is no corresponding practical application. Many students in class always ask me the question that "what is the use of Advanced Algebra to learn?" As a teacher, I always say "learn advanced algebra, we can develop logical thinking ability and computing power, etc." Teaching contents are lack of application practice, which bring students the feeling useless to learn Advanced Algebra and can not reflect the value of advanced algebra.

Therefore, they will not reach the target "Training the ability to solve practical problems".

2.4 Students Have No Interest Because of the poor mathematical basis, the abstract knowledge learned, the more theoretical prove and the complex calculations, these make the new enrolled students completely unable to meet. In [3], Feng Guangting investigated that the performances of difficult in studying Advanced Algebra are lectures, homework and reading materials, etc.

Therefore, the students of math majors in Independent College are not interested in learning Advanced Algebra.

3 SOME OPINIONS ON ADVANCED ALGEBRA CURRICULUM REFORM We have analyzed the poor effect of teaching Advanced Algebra for several reasons, the situation of learing is worrying. In order to effectively improve the quality of teaching Advanced Algebra, in conjunction with myself teaching practice situation, we propose the following aspects of the reform views.

3.1 Course Content Reform, Adding Application Part The new enrolled students are still not out of high school mathematics thinking, good at calculation and analysis of the specific issues. We might appropriately adjust Advanced Algebra contents, delete some theoretical proof and derivation, strengthen calculations, add some practical issues closely linked with life. With the progress of society, algebra is widely used in engineering, economics and management, information security and cryptography and other fields. Looking for the application of classroom teaching is the key. In fact, in both domestic and international Mathematical Contest in Modeling, most of the titles are the practical problems of living close relative, and the methods of solving the problems are more or less used the knowledge of Advanced Algebra. Since 1994 our Independent College has participated in mathematical modeling contest, we have achieved very good results and accumulated a lot of rich resources. The basic idea of mathematical modeling is that observe some phenomena of the objective world, grasp its essential character, abstract concept, construct the model to explore, by intuition, induction, analogy and other methods to make a guess, then further analysis or logical reasoning, reveal the inherent law of things, so complicated phenomenon will become orderly, give the solution of the problem[4]. Therefore, we - 15 www.erfrontier.org

can infiltrate the idea of mathematical modeling to teaching in Advanced Algebra, through the analysis of the application examples to make students truly feel the usefulness of Advanced Algebra.

3.2 Teaching Methods Reform, Leading into Mathematical Software With the development of computer, multimedia technology has been widely used in the teaching process, which effect is of the pros and cons. For teaching advanced algebra, the traditional blackboard teaching plays a main role. And as an important adjunct multimedia, teaching is indispensable. Volkswagen undergraduate education has focused on strong adaptable practical and skilled personnel, emphasized the ability of students to apply the theoretical and practical skills[5]. To achieve the goal, we can introduce mathematical software into the classroom. Common mathematical software has Mathematica, Matlab, Maple etc., which constantly updated version and its functions continuously improved. For advanced algebra some tedious calculations, e.g. the inverse, determinant, eigenvalues, eigenvectors of a higher-order matrix, real matrix triangular decomposition, the use of mathematical software is easy to operate, faster and more accurate calculation. For some discussion of application problems, using mathematical software to analyze is more convenient. This can be not only improving student learning interest but also improving the students' ability to use the computer. In addition, it should strengthen the concept of teaching. Learning mathematical concepts divided into two forms: concept formation and concept assimilation[6]. In the teaching process, introducing some emotional materials can help students understanding the concept, reducing the difficulty of learning concepts to stimulate learning initiative. While consciously guide the students to learn the concept of timely sorting, looking back care to understand the relationship between concepts, in order to achieve that the mathematical concepts learned can form an organic whole, further flexibility to use mathematical concepts to analyze and solve problems. Because we increase the application content, the introduction of mathematical software, we properly carry out seminar, laboratory classes, self-study courses and other courses type in addition to traditional classroom teaching. Teaching in Advanced Algebra, setting up experimental class can achieve knowledge transfer and capacity building in the organic integration[7]. In the course of the teaching experiment, the experimental contents are for a teaching content, which usually have some practical background and a clear purpose of the experiment. Under the guidance of teachers, students are brains and hands, using mathematical software to solve problems raised by the practice. After the experiment by writing lab report they can summarize the harvest experiment course for the innovative in the existing basis. Before the experiment class teachers and students should make full preparation. There would be a clear purpose of the experiment. The experiment content would be reasonable. The experimental process would fully mobilize the enthusiasm of students and play the main role of students. Teachers guide students the problems during the experiment. Through the experiment, teachers shoud teach students to be master of basic concepts and basic theory to be corrected and emphasize students rather vague and fallible place. Thus it can strengthen and promote the quality of classroom teaching. Using a variety of teaching methods, the traditional "Teachers taught in the classroom, students listen to in the hall." Static teaching process changes into a "Two-way interaction of teachers and students together to solve problems." dynamic teaching process.

3.3 Assessment Methods of Reform Now, the assessment methods hospital advanced algebra courses are mainly composed by the usual attendance and peacetime operations (30%) and final exam (70%). In order to better stimulate students’ usual learning initiative, enthusiasm and persistence, as well as to reduce the pressure on students' final exam, we might go from more form to assess students. Assessment follows: usual attendance(10%), peacetime operations(20%), math software experiment(30%) and final exam (40%). For math software experiment part, require students to master skillfully basic commands and commonly using functions of mathematical software based on learing fundamental theorem and basic algorithms of Advanced Algebra. To learn to write some simple math software program, so that both consolidate the basic theory of Advanced Algebra and improve students' programming skills. And require teachers to collect, design some practical problems, group discussions for students, using the knowledge learned to solve, and finally to present their defense in the form of solutions and results. The assessment of this part makes sure students can learn to gather information, analyze practical problems, apply mathematics software to solve problems. And it also exercises the spirit of unity and cooperation among students.

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3.4 Textbook Reform In the target of public education in training application talents, Advanced Algebra textbook focused on theories is no longer applicable to contemporary college students, especially local institutions. To cultivate applied talents, it must be based on its own characteristics to write their own textbooks. The new textbook should include application materials contents while using mathematical software to analyze and solve. In this regard linear algebra textbooks of the non-mathematics has been many successful experiences and achieved good teaching results. Under the new situation, in mathematics majors there is no longer abstract theory-based teaching and also shift application-oriented teaching. Therefore, write application of material is to adapt to a new era and also essential in the institutions.

4 CONCLUSIONS In this paper, we analyze several problems in the teaching process of Advanced Algebra curriculum in math majors of current independent college. The main are students’ poor mathematical basis, unsuitable textbook, teaching focus on theory, students no interest. And we have proposed some opinions about Advanced Algebra curriculum reform.

From course content, teaching methods, assessment methods and textbook the four aspects to reform. We should add application part and experiment part. We should reform assessment methods and textbook. We should focus on cultivating students' interest and improving the teaching quality of Advanced Algebra. With the development of information technology, the means of imparting knowledge are a fundamentally changed. Network teaching and multimedia teaching have become a trend. Teaching of algebra should achieve as soon as possible to teach modern, especially abstract algebra to try to use video and multimedia technology modern teaching methods. That is not only teaching vivid, but also within a short period of time, the amount of information to impart greater knowledge. This can add a lot of new features, such as the realization of two-way interactive teaching. Thus it can be contributed to students' independent, motivated to learn, much to stimulate student interest and improve the efficiency of learning.

At last, we achieve the goal of cultivating talent Independent Institute that is both theory and practice, both adults and taught, training a strong ability to adapt to the culture and development potential, a strong sense of the overall quality and innovative talents of advanced applications.

ACKNOWLEDGMENT This work was supported by the Natural Science Foundation of Hebei Province (No. A2014209083) and the Education Reform Project of North China University of Science and Technology (No. Qz1436-14).

REFERENCES [1]

Algebraic Groups of Department of Mathematics of Peking University. “Advanced Algebra”(Third Edition). Beijing: Higher Education Press, 2003.

[2]

Zhang Herui, Hao Bingxin. “Advanced Algebra”(Fifth Edition). Beijing: Higher Education Press, 2007.

[3]

Feng Guangting. “Advanced Algebra Learning Difficulties and Teaching Strategies”. Journal of Hubei Institute of Education, 2006,Vol.23, No.8, 97-99.

[4]

Gao Fengxia. “Explore on Advanced Algebra Curriculum in Independent Institute”. Fujian computer, 2011(4):214-215.

[5]

Li Yong. “Reflections on Teaching Reform of Advanced Algebra”. Education and Career, 2010(18):140-141.

[6]

Bao Jian. “Explore on the Concept of Teaching in Advanced Algebra”. Higher Mathematics Research, 2007, 10(4):17-19.

[7]

Liu Guirong, Yan Weiping. “Discuss Strategies of Improving the Quality of Teaching in Advanced Algebra ”. Educational Theory and Practice, 2012,32(30):44-46.

AUTHORS Xiaoqiang Guo, Hongtong, Shanxi, China, 1978.11, Postgraduate, Master of Science, Shanxi Normal University, Linfen, Shanxi, China, 2007, Algebra.

In 2007, He worked as a teacher in the North China University of Science and Technology. My published books and articles are following:

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[1] Xiujuan Xu, Xiaoqiang Guo, Nan Ji. “Linear Algebra”. Beijing: Science Press, 2013.

[2] Xiaoqiang Guo, Shuai Zhang, Ying Li. “Key Technologies and Applications of Secure Multiparty Computation”. Telkomnika Indonesian Journal of Electrical Engineering , Vol. 11, No. 7, July 2013, pp. 3774 ~ 3779.

[3] Guo Xiaoqiang, Yang Aimin, Zhang Shumei, Wang Lu, Ku Wei, Wang Zewei. “Study on the Keep-Right-Except-To-Pass Rule”.

Journal of Chemical and Pharmaceutical Research, 2014, 6(7), pp:1042-1049.

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