Vocational students on three-step instructional design of mathematical optimization

Abstract: higher Mathematics is the basis of theory of vocational colleges, vocational schools in China at present relatively poor quality of students, this paper, the characteristics of vocational college students to explore how the teaching process as a system to optimize the instructional design proposed teaching advanced Mathematics to optimize the design of the three-step method.

Keywords: Higher; advanced Mathematics, teaching design

Institutions of higher Mathematics is the basic theory of vocational courses, the students follow courses of study and thought the quality of training plays an important role in students of vocational colleges now relatively poor quality, relatively high content of higher Mathematics, more difficult, many vocational students of higher mathematics terrified, scared and stop. proved blindly abstract math teaching, the curriculum of students likely to cause fatigue and learning inertia, so that students gradually lose their motivation to learn, while students are new things with sensitivity and curiosity to explore and solve problems with desire, according to this mentality, teachers should change the traditional teaching methods, focus on instructional design, to design innovative teaching and learning process, the conversion of abstract mathematical knowledge to teach students willing to explore activities.

instructional design (ie, systematic approach to lesson planning for teachers to use a variety of curriculum resources for the organic integration of the process of teaching each other to make the various parts of the overall arrangement of a vision, that is, to achieve teaching objectives, what to teach, how to teach, to what results for planning. instructional design is a complex task, because the object of instructional design, their design is the main man and is the most complex, most difficult to grasp, while the factors that affect the instructional design is changing, so the teaching process as teachers need to design a system, available from the following three aspects, known as "three-step method."
Starting point: context to be accurate, clear goals to
American psychologist Bruner said: "Whatever we choose what subjects to teach, be sure to enable students to understand the basic structure of the discipline." Was the logical sequence of knowledge systems context, both easy to remember, and easy to think of and application of advanced mathematics subjects knowledge of context is particularly logical.

The total content of higher mathematics is the context: the limits of thought of the soul to the core calculus, differential is a function from the microscopic to reveal the partial nature of integration from the macro function to reveal the nature of the whole of which, through the knowledge of the derivative the entire contents of the context of higher mathematics, is essential to clarify the context of derivatives, for example, in the context of derivatives to optimize the design of teaching, you can make the following plan.

1. "Derivative of the geometric meaning of" a smooth curve tangent in the point-slope equation y-y0 = f '(x0) (x-x0.

2. "Derivative applications" in the Luo Bida rule expression and derivative first derivative f '(x symbol discrimination and the monotony of the second derivative f "(x symbols to distinguish concave.

3. "Indefinite integral concept" and "definite integral Newton - Leibniz formula" in the integrand function and the relationship between the original function f (x = F '(x.

4. "Analytic geometry of space" in the space curve tangent point to the-equation and the equation of normal plane and curved surface of the cut plane equation and normal equation.

5. "Infinite series" in the function of the Taylor series expansion of the general term and the integral curves of Green's formula.

Etc. At the same time, the use of higher mathematics context structure of the vertical and horizontal linkages, conscious knowledge to help students build their own structural context, for example, in the use of curved trapezoidal area seeking to introduce the concept of definite integral, the basic context of thinking is: division, similar to replace, sum, taking the limit, the conclusion that the concept of definite integral, while seeking to resolve this song the same way the top cylinder volume, the quality of space objects, the quality of curve segments and other issues, except that the take limit tends to zero when the specific element is different. Instructional design of each chapter, this chapter focuses on knowledge to the mathematical structure inherent in the context of this chapter, the key and core approach to enable students to grasp the essence of truly change from passive learning to active learning, actively construct their own context of the mathematical structure of this chapter, and can block diagram showing the intrinsic link between knowledge.

Robert Gagne in the <<Instructional Design>> a book, said: "Teaching is designed to confirm the direction of the expected learning outcomes, that is to set teaching goals."
Optimal design of teaching objectives must be to in-depth study programs and materials based on the knowledge to grasp the point and the class-based characteristics, the target set out, determined the requirements because of higher Vocational Education has its own characteristics, teaching goals but also from the application of the arrangements point of view or needs to solve practical problems, follow-up courses from the professional needs and the actual needs of society, to consider and identify the teaching objectives. Teaching objectives to be set at just the right, reference is too high, too low or ambiguous, are not easy to implement and, therefore, mathematics teachers to change the past and do not communicate with the Professional Teachers, fragmented state, where students often visit Department of the Ministry, refer to the relevant professional materials, especially the new understanding of the relevant professional expertise, knowledge of the new curriculum requirements in mathematics, find the combination of mathematics courses and specialized courses point to develop appropriate teaching goals.

For example: the same is the infinite series of power series of teaching objectives should be based on the characteristics of different professions, highlighting both the foundation, but also strengthen the relevance, reflecting the application of.

Agricultural class professional goals are: (1 would find the convergence radius of power series, (2 knows its power series converges in the range of some basic properties, (3 know Taylor (Taylor formula and function expansion into Taylor series necessary and sufficient conditions (not card, can use ex, sinx, ln (1 + x, (1 + xm Mark McLaughlin (Maclaurin expansion of some simple function expansion into power series.

Architectural professional goals are: (1 the concept of power series, power series convergence range, the basic nature of power series, (2 are expanded into Taylor's formula and Taylor series of sufficient conditions, with the ex, sinx, ln (1 + x, (1 + xm Maclaurin expansions of some simple function expansion into power series, (3) power series of simple applications.

Machinery and electronic professional goals are: (1 would seek the convergence radius of power series, (2 knows its power series converges in the range of some basic properties, (3 known Taylor formula and function expansion into Taylor series and sufficient conditions (no permit to use ex, sinx, ln (1 + x, (1 + xm Maclaurin expansions of some simple function expansion into power series, (4 are expanded into a Fourier series to know the full conditions, and can define the period 2π in [-π, π] and [-L, L] on the function expansion into a Fourier series, can defined in [0, L] on the function expansion into a sine or cosine series, Fourier series know that the plural form, (5 to understand the concept of Laplace transform and the nature of the inverse Laplace transform of the concept and nature of several commonly used signal functions: unit step function, δ - function.

Soul: To live
China's traditional teaching methods include: classroom teaching methods, teaching objectives, teaching methods and other heuristics, but in the classroom teaching of history, ancient to modern times, are permeated with "the theory taught - work - and eliminating - understanding "The process basically is" Man Tangguan "teaching methods and teaching job placement to complete the task in optimizing the design of teaching methods, designed according to different content, flexible use of teaching methods, focusing on students interest in learning to mobilize their learning initiative.

Innovative teaching model to improve the teaching of the hierarchy and modularity individualized teaching the basic principles of Education, the teaching of mathematics is no exception, according to the existing defects and individualized teaching principles, we can take in the actual teaching in a multi-level module of teaching, the idea is as follows: the higher mathematics course is divided into three modules, namely: basic modules, application modules, to improve module module-based content to meet the professional setting is to ensure that the demand for mathematics, it some higher mathematics is the most basic elements, are compulsory for all students, teachers must Jingjiang, go into detail, so that students fully understand. application modules can be set by the content of specialized teachers and mathematics teachers to work together on identified professional settings for different characteristics of different application modules. Its main feature is the profession, and all content should reflect a "use", which enable students to experience "math on my side." improve the content of the module is set prepared to continue studies, or the profession of mathematics students with special requirements established in this module introduces some of the ideas of modern mathematics, methods, or some of the content, so that students of mathematical tools and the latest trends understand, in order to meet their future learning needs.

Links to free download http://www.hi138.com strengthen mathematics teaching and the profession of the contact in higher vocational colleges, many students consider themselves non-math majors, there is no need to learn mathematics, which form teachers "hype" students "indifferent" situation. To change, teachers should be teaching students more about the mathematics in which they specialized applications, so that students know that math can solve their professional problems. for example, leads to the concept of derivative according to the different professional describes the different examples, Economics and Management can introduce the "marginal" concept, mechanical and electrical professionals can introduce rate, line density and other problems, agricultural majors can introduce cell reproduction rate, the marginal production and maximum profit margins fertilizer problems, etc. Another example is the establishment of the differential equation model is more difficult, introducing differential equations, they can give mortgages to buy a car, buy a house problems, population growth and many other examples, further information on the Logistic model, indicating the ingenious idea enhance the mathematical knowledge point of memory "memory of the most basic point is that the memory images of things through", there are many formulas of higher mathematics and the nature of the needs of students down to the abstract, something not easily be turned into images familiar with their favorite link up the appearance of specific example, for everywhere in the derivation, the idea of ​​memory as follows: the derivative of trigonometric and inverse trigonometric formulas required memory modules, their symbols followed by "after first being negative, positive and negative cross." triangle The size of the derivative of the function are "more than the first two each, followed by the remaining two middle two square, the latter two is to not move the copy, and then with the tangent and cotangent, respectively." inverse trigonometric formula for the derivative of two groups of equal size, the form of another mind. It should be noted that the formulas and rules of variables that appear only a symbol, said one thing, while the right side of the equal sign is the expression on the left shows what the result of derivation for the derivative of composite functions question, as long as the middle packaged into a variable thing, the first function of the original derivation of this thing, and then multiply this thing on the final variables (ie variables) of the derivative, even if there are many intermediate variables, repeated use of the method is nothing more than nothing.

Endpoints: Exercise should be fine
As the old saying goes: "Give a man a fish, rather teach people to fish." Teachers to teach students in the classroom in addition to book knowledge, there is a very important purpose, which is the spirit of "competency-based 'thinking by classroom teaching, autonomous learning, good to explore the ability of students to logical thinking, abstract thinking ability, imagination and students the practical application of space capabilities, etc. This is our ultimate goal. The students good study habits and a variety of abilities, not by paper, you can not rely on overnight train, but usually a little bit by the trained. Mathematics is a science to solve problems, often require to solve problems through access to knowledge and training to develop capacity, so math teachers with particular emphasis on recitation of the design.

Rational design kinds of questions in order to achieve knowledge transfer and teaching the students lay the foundation for optimization. Well-designed content, focusing on teacher-student interaction in the teaching. Kinds of questions is the means, the content is the core, "Less" is the contents of the selected subject in the selected exercises, in addition, according to the syllabus, the knowledge to a large coverage, the focus should be prominent, to moderate difficulty, exercises must be representative, enlightening, can set a "trap", beware of knowledge points omitted. knowledge point coverage, heavy and difficult to review, correct the error-prone points, you can design a small problem, such as choice, fill in the blank, determine to review and make up. methods and problem-solving skill can be designed to inspire and guide students to large problems themselves, the teacher induction Summary.

For example, "L 'Hospital rule," the exercise class designed to:
1. Knowledge Review: (1 "" type and "" type, (2 "0 · ∞" type; (3 "I ∞" type ﹑ "00" type ﹑ "∞ 0" type, (4) "∞ - ∞ "type.

Analysis: The common denominator of the way into general use as a "" type and "" type, then use the Luo Bida replacing rules and requirements equivalent infinitesimal limit.

2 error-prone points: (1 is best to use the factor of zero is equivalent to infinitesimal substitution, (2 non-zero due to the limits of style can find out first.

3 teacher-student interaction: find the limit.

4 missing point: rules can not be solved with the Luo Bida "" type and "" type: if.

Bloom said, "People can not expect the results generated by teaching the full range is not unexpected results, do not become the art of teaching." Teachers in the teaching of the need for instructional design before, but in the teaching process and not rigidly stick to in instructional design, instructional design has been hands were tied. all should be student-heavy, to teach and promote learning, students should be moving, but moving, you should change the situation changes, changes in the classroom teaching a variety of comprehensive grasp of time to make the right judge, take effective measures.

References:
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[3] Lin to play. Exercises teaching higher mathematics, I see [J]. Education, art, 2006, (3:57.

[4] Miao Lin. On the teaching of math skills Problem [J]. Fujian Institute of Education, 2006, (12:55-56.

[5] Zhao Hanhua, Julie. On the new curriculum design concept [J]. Ningbo University (Educational Science Edition, 2003, (4:42-44. Links to free download http://www.hi138 . com