The Comparative Research Of Three Middle School Mathematics Textbooks In China

Acute Angle Trigonometric Function(AATF)plays an important role in junior mathematics.It is also the exam-compulsory knowledge point in high school entrance examination.AATF provides an useful tool for calculating the unknown angle and side based on the known angles and sides which has a wide application in practice.It also provides an opportunity for AATF to connect with practical matters.The appearance of AATF further widening our sights is the fulfillment of function conception firstly involved in algebra.Master some relative knowledge of the Pythagorean Theorem and Similar Triangle and then start to learn AATF.Then students learn to use the relative knowledge of trigonometric function to solve some easy and practical problems of right triangle.Thus to combine number and shape and promote the ability to analyze and solve problems.It is not only the application of the previous knowledge we have learned but also the important preliminary knowledge during high school.Its learning contains profound mathematics thought and method,i.e.Mathematics modeling,transforming thought.Due to the particular status and significance of the acute triangle and limited textbook researches in this field,this paper choose the AATF in Middle school's textbook of People Educational Press(PEP),Beijing Normal University Press(BNUP),East China Normal University Press(ECNUP)as the research object to make a comparative study.The main research methods include documentary method,content analysis and comparative study.Statistical diagram is the tool.This paper will make a comparative study of the AATF in three editions' textbooks from macroscopic and microcosmic aspects.In macroscopic,compare the textbooks of three editions from five aspects in terms of the arrangement of textbook,teaching goal,class hour,design solution,and chapter form.In microscopic,compare the textbooks of three editions in terms of lead-in form,example,and exercise to find out their characteristics and differences Then draw some conclusions.Firstly,in the perspective of the characteristics of text book arrangement,the PEP edition attaches more importance on step-by-step arrangement of the textbook,and highlights the guidance to students' learning method.The main characteristics of the BNUP is fully furnishing learning materials for students,which will benefit for students' learning process while the main characteristics of the ECNUP is the stimuli-presenting mode,which highlights practicalness and research.Secondly,in the perspective of teaching goal,the PEP and the BNUP only study three kinds of acute angle function while the ECNUP studies four kinds of AATF.And the learning of cotA exceeds the requests of curriculum standard.Thirdly,in the perspective of class hour arrangement,the PEP edition and the BNU edition attach great importance on the fundamental knowledge of acute triangle function.The ECNUP emphasizes the part of right triangle solution,which fully illustrates the fact that this edition values the learning application ability.Fourthly,in the perspective of the design thread of textbook,the ECNUP creates situations of the measurement of flagpole firstly After which it studies four kinds of AATF and applies related knowledge to solve practical problems of right triangle.The textbook of the ECNUP starts with the level of the tilt and then leads to secant,cotangent and cosine while lots of practical problems interleave among it.The PEP derives the conception of the sine of acute angle from special cases to common cases and derives sine,cosine and tangent by analogy.And it applies respective knowledge to solve practical problems.Fifthly,in the perspective of the form of the textbooks' form,the content and knowledge structure of the PEP and the BNUP are more simpler while the ECNUP emphasizes the relation within knowledge.Both three editions' integral structures are roughly the same in the order of practical needs,inquiry learning,and learn to meet practical needs.Sixthly,in the perspective of lead-in,the BNUP and the PEP establish question situations to lead in the class while the textbooks of the ECNUP whose lead-in approaches are less tends to teach knowledge to students directly.And the PEP has more activity operation ways than the other two editions.Seventhly,in the perspective of example comparison,the number of AATF's examples in the BNUP textbook is twice the Right Triangle Solution".The background of the textbook pays much attention to common sense and the type of reasoning is mainly simple reasoning.The inquiry level of its examples which presents a straight line is the most evenest and its difficulty level is moderate.Its subjects which have respective models and versions are typical and progressive.As for the PEP,the number of the example for AATF is less than the part of Right Triangle solution.The compilation of examples focuses more on direct teaching.For the type of reasoning level,the number of simple reasoning is twice complex reasoning.For the type of inquiry level which is the most difficult among the three editions,it focuses on understanding and it is supplemented by inquiry and memorization.Its type hierarchy is not obvious comparing to the BNUP.The number of example within the ECNUP's AATF part is slightly more than Right Triangle part.The background compilation in this edition is more understandable to the tasks.For the type of reasoning level within examples,simple reasoning assumes absolute superiority while alternative memorization and understanding are the majority.The difficulty level of its examples which contain elementary and difficult questions is relatively simple.Eighthly,in the perspective of exercise comparison,the number of the after-class review exercise of the PEP is the largest and the number of its in-class exercise is the least.The setting of after chapter-exercise for different levels is moderate.The number of after-class exercise of the PEP is the largest and the number of in-class review exercise and after-chapter review exercise are similar,however,it pays less attention on the exercise types focusing on the calculation-operation memorization level and analysis-exploration understanding level.On this basis,this thesis puts forward some immature suggestions on the content of the textbook's AATF:the textbook of ECNUP more emphasizes on the fundamental conception and operation,whose examples' difficult level are moderate.It is suggested that the exercise type should be various and fully demonstrates the practicability of the AATF.And the matched-degree of its exercise and example is not enough.For the PEP,its examples' difficulty level and flexibility is high,which is not suitable for student with lower intermediate grade.There are more exercises in its textbook,which has the largest number of after-class exercise and the least number of in-class exercise.It is suggested to reduce after-class exercises appropriately.For the textbook of ECNUP,it is suggested to increase more situation lead-in and increase the difficulty level of its examples for the original ones are relatively simple,which will be beneficial for top students.And the number of after-class review exercises is the largest,which is suggested to decrease accordingly.Finally,this paper puts forward recommendation for future research in view of existing problems.