| In the new era of the implementation of new curriculum,the content representation of textbook,the mathematical representation of students and the representation of classroom teaching have been put forward new requirements by curriculum standard.For example,we need to pay attention to the content presentation and language and text,etc.when compiling the textbooks.Students should learn natural language,graphic language and symbolic language to express the object of mathematical research,and should be able to transform different representations.classroom teaching needs to cultivate students' ability to represent the world with mathematical language.Teachers need to cultivate students' ability to represent the world with mathematical language in classroom teaching.Mathematical representation is not only an important concept in mathematical educational psychology,but also an important concept in curriculum and evaluation.Therefore,what are the characteristics of the new textbook in terms of mathematical representation,whether the mathematical representation presented by teacher during teaching process and when the mathematical representation presented by students in attained curriculum is consistent with the curriculum requirements,etc.,are issues that need to be studied urgently in the implementation of new curriculum.To this end,under the same analysis framework,this research analyzed the mathematical representation characteristics of the function content of the intended curriculum,the implementation curriculum,and the attained curriculum.And this framework includes two dimensions: mathematical representation and its function,the translation of mathematical representation and its function.Finally,the characteristics of three types of curriculums are systematically integrated,and suggestions are put forward for textbook compilation,classroom teaching and student learning.The main research results and conclusions include the following aspects:(1)It reveals the characteristics of mathematical representations of the two textbooks in the intended curriculum.Based on the document analysis method,the characteristics of mathematical representation of the function content from two new high school textbooks of the Shanghai Educational Publishing House and the People's Education Press A Edition have been analyzed.It is found that in terms of representation,both textbooks emphasize the use of multiple representations to present function,especially the combination of text and symbol representations.In comparison,the textbook from People's Education Press A Edition pays more attention to the use of diagrams.In the representational function,both textbooks focus on expression and communication,while the textbook form Shanghai Educational Publishing House also emphasizes logical reasoning.In terms of representation translation,the worked examples and exercise problems of the two textbooks are relatively similar,and both emphasize the representation conversion from text to symbol(i.e.,abstraction),followed by the conversion from symbol to diagram to representation(i.e.,intuitive).(2)Analyzed the characteristics of the two teachers' use of mathematical representations in mathematics classroom teaching of implementation curriculum.The teacher's mathematics teaching process in the actual function classroom has been recorded through real-time video recording,and the characteristics of mathematics representation in the teacher's teaching process were analyzed based on the video tape.The comparison found that in terms of representation,both teacher A and teacher B are good at using multiple representations in the classroom,especially the combination of words and symbols.While teacher B also uses diagram representation more frequently.In the representational function,both teachers attach importance to the expression and communication function of representation.In addition,teacher A also pays more attention to the representational function of logical reasoning.In terms of representation conversion,both teachers attach great importance to the conversion from text to symbol to representation(i.e.,abstract),but from the perspective of explanatory function,teacher A uses more symbol to text representation conversion in the classroom,while teacher B does Pay attention to the conversion from diagrams to text to representations.(3)Explored the performance characteristics of mathematical representation of the students in the two schools in the attained curriculum.The test method is used to analyze the performance characteristics of the mathematical representations of students in the learning of the function content,and it is found that the students of the two schools show a certain similarity.The performance of the students in the two schools is better than the performance of the chart and symbol representation.Students can fully obtain the chart representation information when converting the chart to text,and can also completely and accurately transform symbol to the chart representation,but are not good at the conversion of text to chart representation.The representation conversion performance of the conversion of words to symbols and diagrams to symbols is related to mathematical knowledge.Students have a thorough understanding and thorough understanding of the domain of function concepts.They are good at monotonic logical reasoning in the nature of functions,but not good at parity logical reasoning and Symbolic representation of the most value.But the difference is that the students of school A are good at converting symbols into text representations,and most students can get the image meaning behind them when the symbols are converted into text representations;while the students of school B are not good at converting symbols to text,and most of them students cannot get the image meaning behind the symbols when they are converted into words(4)Discussed the relationship of mathematical representation characteristics among the intended curriculum,implemented curriculum and attained curriculum.A comprehensive analysis of the characteristics of the intended curriculum;implemented curriculum;attained curriculum,and the preliminary conclusion is that the representation characteristics of the teacher in the implemented curriculum are close to the intended curriculum,and the characteristics of the intended curriculum can be basically transformed into the classroom teaching,that is,the teacher can compare the characteristics of the expected curriculum.The intended curriculum are well implemented curriculum;and attained curriculum are not very consistent with the intended curriculum,which means that there are still some gaps between the performance of the students and the intended curriculum;the obtained courses are more consistent with the implemented curriculum.Compared with the intended curriculum,students are more likely to receive the impact of the implementd of the curriculum.Therefore,the textbooks have had a certain guiding effect on the teacher's classroom implementation,which reflects the importance of the textbooks,and also shows that the teacher's classroom teaching has a stronger effect on the students than textbooks.The research results of the thesis also have certain enlightening significance for textbooks,teachers and students.Textbooks and teachers really need to pay attention to the conversion from words to symbols,and appropriately strengthen the conversion from words to diagrams to representations.At the same time,it is recommended that the textbook appropriately increase the example exercises for the conversion of diagrams/symbols to characters.Teachers are suggested to focus on concept analysis in classroom teaching,while increasing practical application questions,emphasizing the practical significance of the domain,and strengthening the cultivation of students' abstract ability;if within the limited course time,the conversion of symbols to words can be appropriately increased.Relatively reduce the conversion of graphs to text representations.It is recommended that students read more mathematics textbooks,increase the practice of representation conversion from text to diagrams and text to symbols,and deepen their understanding of mathematical concepts. |
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