| Functions are the key objectives of the first year students’ mathematics invocational high schools. As the major branches, exponential functions andlogarithmic functions are very difficult for the students to understand due to theabstract while learning them makes the students have a general knowledge of thefunctions and a good command of study methods. The current studies mostlyfocus on the error analysis, the students’ cognitive level and teaching theory andexperience; but seldom on the deep cause of students’ learning difficulties andthus the teaching countermeasures and strategies.This study analyzes students’ cognitive errors in exponential functions andlogarithmic functions learning and develops the teaching strategies.Using the qualitative analysis method, this study analyze the students’ cognitivelevel from the questionnaires and the functions knowledge tests and thusconfirms the following cognitive errors in exponential functions and logarithmicfunctions learning: a) misunderstanding of mathematical definitions, symbols; b)difficulty understanding the text representation; c) lack flexibility of therepresentation transform; d) weak drawing knowledge e) fail to apply the knownconcept correctly in problem solving.In accordance with the cognition errors, this study develops the followingteaching strategies to correct them:1) value the proper teaching of themathematical concepts;2) transform training of the functions representations;3)training of the drawing and reading;4) expand the problem solving ideas;5)develop the reflection ability.Base on students’ reflection experience, interview records and analysis ofthe academic performance before and after the experiment, this study concludesthat extracting from students’ self cognitive reflection of functions, the teacherscan develop and carry out the effective teaching countermeasures to enhance thestudents’ understanding of functions. |
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