Research On Implicit Learning In High School Trigonometric Functions

In1967, Reber, an American psychologist, published an article—Implicit learning ofartificial grammars, and put forward the conception of implicit learning for the first time. Theresearch of implicit learning began since then. But until the1980s, implicit learning started toattract more and more attention, and slowly became hot and frontier research of studyingpsychology and cognitive psychology. The research on implicit learning of mathematics inprimary and secondary schools came into being. But most of the research results concentrated inthe theoretical research or teaching ideas, the empirical research generally placed in lab andartificial materials, and although the influence factors of implicit learning involved, they were allnot comprehensive and systematic. So based on previous research, I try to use questionnairesurvey method and interview to investigate implicit learning and its influence factors underrealistic situation of senior high school students’ trigonometric function in this paper, formulateteaching strategies based on implicit learning, and service in teaching practice better.The order: first to propose the main research questions and research significance combiningwith the research background of implicit learning. Secondly, the current and relevant researchsummarizes include implicit learning, mathematical implicit learning, and the learning of seniorhigh school students’ trigonometric function. Thirdly, elaborate the concept and characteristicsof senior high school students’ implicit learning of trigonometric function, and construct fourinfluence factors of implicit learning combining with previous research: students’ priorknowledge and experience, learning objects, learning contexts and learning motivation. Fourth,referring to previous research of implicit learning and combining with senior high schoolstudents’ learning of trigonometric function, compile a questionnaire of senior high schoolstudents’ learning on trigonometric function, carry on the questionnaire survey, and use theSPSS17.0to count the survey results. Analyzing the questionnaire, I get the effective one. Then Icontinue to process and explain the data to get corresponding research conclusions. Finally,through interview, analyze deep the influence factors of senior high school students’ implicitlearning of trigonometric function, find out the problems in senior high school students’ implicitlearning, formulate teaching strategies of trigonometric function based on senior high school students’ implicit learning, and obtain some teaching inspirations.The research chooses the students of second grade in senior school as the object, and mainlyachieves the conclusions as follows:First, on implicit learning of senior high school students’ trigonometric function, there aresignificant differences between boys and girls; there are no significant differences betweenliberal arts and science students; students are no significant differences between experimentalclasses and regular classes. Implicit learning of senior high school students’ trigonometricfunction contains implicit learning of knowledge acquisition and knowledge application. Seniorhigh school students’ mathematical achievement of trigonometric function has nothing to dowith implicit learning of trigonometric function. From the point of concepts, rules andproblem-solving learning of trigonometric functions, boys and girls in learning mathematicalconcepts and rules have no significant differences; on the problem-solving, although there aredifferences, the differences are not very significant; there are none of significant differencesbetween liberal arts and science students; students have no significant differences betweenexperimental classes and regular classes, neither.Second, students’ prior knowledge and experience, learning objects, learning contexts andlearning motivation effect implicit learning of senior high school students’ trigonometricfunction. Every factor has a different degree of influence. The differences of implicit learning inacquisition and application of knowledge are not the same. So we can think that the influencefactors of implicit learning effect implicit learning in acquiring and applying knowledge, andthere are different effects on both of them. During analyzing differences of influence factors, wecan find boys and girls differ in the learning objects and learning contexts. There are differencesin learning objects between liberal arts and science students. And students from experimentalclasses or regular classes have differences in knowledge and experience.Third, though interview, I find boys and girls or liberal arts and science students on theperception of learning objects have a little difference. Students from regular classes can realizethe effect of prior knowledge and experience better which has on implicit learning. Students feelthe interesting, abstract and repeated knowledge is more advantageous to their implicit learning.Students think the problems of implicit learning are mainly in students themselves, math teachersand classroom atmosphere. Fourth, according to theoretical analysis and empirical research, I put forward severalteaching strategies of trigonometric function based on senior high school students’ implicitlearning as follows:1. Introducing strategies: consider students’ prior knowledge and experience,rely on fun learning materials and create context which is advantageous to implicit learning.2.Organizing strategies: in teaching process, teachers should make rational use of teachinglanguage, arrange well implicit learning and explicit learning.3. Management strategies: createan contexts which is advantageous to implicit learning.4. Behavior strategies: value student’smathematics activities.Fifth，this research gives math teachers some teaching enlightenments: they should fullyrealize the effect of implicit learning; pay great attention to student’s practice training; enhancethe students’ mathematical learning motivation.