| In recent years,mathematical communication has become one of the important mathematical process abilities,its related research has attracted the attention of extensive scholars all over the world.On the one hand,it can not effectively strengthen mathematical understanding and improve mathematical thinking.On the other hand,it can also improve children's emotion and attitude towards mathematics.Started from the conceptual connotation of 3-6-year-old children's mathematical communication,the elements system of mathematical communication ability has been constructed in this study,and then the researcher systematically investigated and analyzed the performance of the constituent elements of communication ability including mathematical understanding and mathematical expression.Study 1: The construction of elements system of mathematical communication ability for 3-6-year-old children.Firstly,the concept connotation of mathematical communication has been formed step by step coding of the researchers' elaborations on the concept of mathematical communication.Secondly,the content and characteristics of early children's mathematical language was analyzed combining with the characteristics of children's age in this research.Thirdly,the elements of mathematical communication ability has been extracted from the perspectives of information processing,text analysis and communication effectiveness.Fourth,the elements system of mathematical communication ability for children aged 3-6 was analyzed based on the mathematical language.Finally,the reliability and validity of above elements system constructed in theory has been verified through the Delphi survey of 16 experts and two rounds.At the end,Mathematics Communication Ability Elements System for children aged 3-6 years has been formed,which includes two primary indicators,five secondary indicators and 10 judgment criteria.Study 2: The development of the Mathematical Situation Understanding/Mathematical Expression Evaluation Tool for Children aged 3-6 years.First of all,the item content of the mathematical situation understanding/mathematical expression evaluation tool for children aged 3-6 years has been compiled based on the core experience of early childhood mathematics,the content of kindergarten mathematics curriculum and children's mathematical operation materials.Secondly,195 children aged 3-6 were invited for pre-test,and the dimensions and contents of the tool were determined through item analysis,exploratory factor analysis and reliability and validity test.Thirdly,the research invited 490 children aged 3-6 to join in the formal test,and the structural validity and measurement stability of the tool were determined through confirmatory factor analysis and measurement equivalence test.Finally,the Mathematical Situation Understanding/Mathematical Expression Evaluation Tool for3-6-year-old Children has been formed including six dimensions composed of number concept and operation,quantity comparison,quantity conservation,spatial orientation,classification and mode and 27 items.Study 3: The analysis of performance in mathematical understanding of the elements of mathematical communication ability of children aged 3-6 years.In order to figure out the features of the understanding of mathematical concepts and mathematical sentences,433 children aged 3-6 were chosen to measure the five basic concepts and three mathematical sentences of children by using the Breaken Basic Concept Scale.It has been shown that the overall level of understanding of basic concepts of children aged 3-6 is high,there are significant gender differences in some dimensions,and the age class differences is significant in the five basic concepts.Besides,there are multiple potential profiles of different levels in the conceptual understanding for children aged3-6 and in different age groups.It remains low for the overall level of 3-6-year-old children's understanding of mathematical sentences,there are no significant gender differences but age class differences in each dimension.multiple potential profiles of different levels have been found in the understanding of mathematical sentences among3-6-year-old children and in different age classes.For the sake of the early children's understanding of mathematical situations,490 children were selected to investigate their performance in six mathematical situations by using Mathematical Situation Understanding/Mathematical Expression Evaluation Tool for 3-6-year-old Childrenthe Assessment Tool for Mathematical Situational Understanding for Children Aged 3-6 years.The results show that 3-6-year-old children are able to understand the relevant situations of other mathematical contents such as number concept and operation,quantity comparison,spatial orientation,classification and pattern,but except the conservation of quantity.Its overall level is above medium,and there are no significant gender differences but age class differences in mathematical situations,there are multiple potential profiles of different levels in the understanding of mathematical situation among 3-6-year-old children and children in different age classes.Study 4: The analysis of performance and influencing factors of mathematical expression ability in the elements of mathematical communication ability of children aged 3-6 years.For the overall performance of mathematical expression,490 children aged 3-6 were selected and tested with the Mathematical Situation Understanding/Mathematical Expression Evaluation Tool for 3-6-year-old Children.The results showed that the overall mathematical expression was at the medium level,there are no significant gender differences but age class differences in each dimension.There are multiple potential profiles of different levels in the overall performance of mathematical expression among 3-6-year-old children and children in different age classes.For the oral language expression,through the transcription and analysis of the oral language of 383 children,it has been found that there are significant differences in the frequency of different types of mathematical vocabulary,mathematical sentences and error types among 3-6-year-old children.In terms of the written expression,3-6-year-old children showed the characteristics of "unclosed figures and mismatched figures " in geometric figures,and "mirror error,bit value error,symbol use error" in the written expression of number symbols.In terms of the influencing factors,the family factors and language expression ability were tested of 310 children aged 3-6.The results showed that the mathematical reading materials/mathematical activities in the family were significantly correlated with mathematical expression ability.The mathematical expression ability can be predicted merely by mathematical activities,and mathematical expression played an intermediary role in mathematical activities and mathematical ability.Besides,there exists a significant positive correlation between language expression and mathematical expression,and it can be used to effectively predict the ability of mathematical expression.After controlling for age,gender and language expression,mathematical expression can still be used for significantly predicting numerical ability.Based on the research results of the above four aspects,the researcher carried out a comprehensive discussion from three aspects containing constituent elements of mathematical communication ability of children aged 3-6,development and verification of mathematical situational understanding/mathematical expression tools for children aged 3-6,performance of the elements of mathematical communication ability of children aged 3-6.It has been suggested that we should focus more on the process performance of communication skills regarding competence elements as a starting point.And we should encourage and guide children to obtain conceptual understanding with the assessment tools as reference.Most importantly,we should pay attention on children's mathematical understanding and expression by means of open-ended questions. |
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