The Effect Of Positive And False Example Combinations On The Migration Ability Of Mathematics Analogies Of High School Students With Different Cognitive Levels

Researches of learning transfer not only contribute to revealing the essence of human learning and its regularity,but also provide certain theoretical basis for instructing the teaching process and promoting learning effect.And the interaction between studying principles and the transference of knowledge in worked-example learning has been one of the focuses of learning transfer researches in the past few decades.Although learning correct examples could improve students' learning effect,some researchers in western countries gradually recognized the usefulness of erroneous example and paid more attention to studying erroneous examples.This research mainly focuses on the combination of correct examples and erroneous examples,which sets about from the combination's presentation and the erroneous examples' proportion,to explore how the analogical transfer ability of high school students with different cognitive levels is affected by the combination of correct-erroneous worked example in mathematics learning.It could not only provide theoretical basis and practical guidance for mathematical teachers to optimizing the process of example teaching and improve the efficiency of classroom teaching,but also provide the guidance for instructors to compile supplementary reference materials and for learners to choose proper learning methods.What's more,it could enrich the research of erroneous example and learning transfer in worked-example learning to some extent.In order to obtain the relevant data comprehensively,this research has used the test method and the questionnaire survey method to carry on the data collection on one high school's part of grade one students in Xi'an,and analyzed the research data with the statistical analysis.Thus these conclusions are drawn:(1)The effect of analogical transfer in composite material is higher than that in complete correct type and the far-transfer's effect reach a significant level,while those students with low cognitive level fail to reach the significant difference.Besides,the combination of correct-erroneous example is more popular with high school students.(2)In the presentation of correct-erroneous example,the effect of analogical transfer in interactive type is higher than that in block type and the significant difference is only seen between the medium cognitive level students.In addition,lots of students are more willing to learn the interactive one.(3)In the proportion of correct example to erroneous example,the effect of analogical transfer in 1:1 and 3:1 are both higher than that in 1:3,and no significant difference is seen between the low cognitive level students.What's more,most of students are more inclined to the material that the ratio of correct example to erroneous example is 1:1 or 3:1.(4)The effect of analogical transfer in the composite material that in interactive or blocked type and the ratio of correct example to erroneous example is 1:1 or 3:1 are higher than the others.And the significant difference is more obvious with the increase of the cognitive level.Thus,this paper puts forward the following suggestions on mathematical worked-example learning and example teaching:emphasizing on the effect of erroneous example on learning transfer;properly controlling the number of erroneous example and its frequency of use;attaching great importance to individualized teaching and strengthening the skill of example design.