Research On The Concept Teaching Of High School Function Based On LGEs Learning Strategy

The New Curriculum Reform advocates active and exploring ways of learning to promote students' learning initiative and make students' learning process a "re-creation" one with the guidance of teachers. Foreign scholars Watson and Mason proposed Learner-Generating Examples (LGEs) learning strategy based on the perspective of students' example space. This strategy, as an independent and exploratory learning method, contributes to students' learning by guiding students to construct their own examples. Learners can construct the examples that match certain conditions by themselves under the guidance of thinking. By experiencing the process of construction, they can actively construct mathematical objects, mathematical relations and mathematical problems. Subsequently, students are able to form a schema of learning contents so as to master the relationships between the knowledge and to solve problems successfully. The theoretical foundation of the LGEs learning strategy is constructivism, that is, by experiencing the process of constructing the examples, students construct the understanding of knowledge zealously; the task designs of LGEs learning strategy are based on Variation Theory which aims to lead students to explore the structure of knowledge by the variant construction tasks and consequently complete the integrated construction of knowledge.The function is the core content of middle school mathematics that runs through the whole mathematical curriculum whereas the function concept is the basis of function learning. The characteristics of the function concept are duality, multi-representations and diachrony which determines that the teaching of function concept has long been a hot topic among education researchers. Through the literature review, researchers and education workers has put forward some reasonable suggestions from different perspectives based on different theories, and provided theoretical and practical references for improving the teaching of the function concept. However, there is little research focuses on the function concept learning form the perspective of students constructing their own examples. As a result, this thesis based on LGEs learning strategy and with the function concept as a cut-in point, and mainly explored three questions as follow:(1) How to improve the methods of the function concept teaching based on LGEs learning strategy?(2)Whether LGEs learning strategy is effective for the study of the function concept?(3)Whether there is cognitive load for the study of the function concept by adopting LGEs learning strategy?In order to address the issues above, this research mainly launched from two aspects of theory and practice.In the aspect of theory, first of all, we combed and summarized the relevant researches of function concept learning and LGEs learning strategy; then, we combined the LGEs learning strategy with the characteristics of function concept and explored three levels of the teaching of function concept:(1) Create multiple situations to help students construct function concept initially;(2) Set up exploratory tasks to help students construct function concept once again;(3) Design variant tasks to help students complete the construction of function concept.On the other hand, in the aspect of practice, in order to test the efficiency of LGEs learning strategy, the questionnaires and personal interviews were employed in the study. We analyzed the learning effect and the cognitive load of the function concept based on the LGEs learning strategy by Excel and SPSS. The findings indicated that:(1) LGEs learning strategy was conductive to promoting students' understanding of the function concept;(2) Compared with the traditional teaching, LGEs learning strategy can significantly reduce students' cognitive load of the function concept.What's more, the results of a further analysis showed that LGEs learning strategy can also cultivate students' ability of creative thinking and deepen the internal structure of knowledge.In addition, we reflected and summarized the process of the study, thus concluded three points about LGEs learning strategy that should be noted in teaching:(1) Pay attention to the primary and secondary;(2) Pay attention to the appropriateness;(3)Pay attention to the cognitive levels of students;...