A Study On The Comprehension Level Of Seventh-grade Students' "using Letters To Express Numbers" And The Consistency Of Teachers' Estimates

Grasping learning situations accurately is an important guarantee for effective teaching.This study is based on the content of "Express Numbers with Letters" which is important both in the content itself and in the development of the students' thinking,and the researcher conducted the combination of empirical,quantitative and qualitative research on the level of alignment of seventh-grade students'understanding level of "Express Numbers with Letters" and teachers' prediction.(1)In terms of theory,?the author carried out the collation and analysis of the relevant content of "Express Numbers with Letters" in the "Curriculum Standards",the primary school mathematics textbooks of Jiangsu Education Edition and the the junior high school mathematics textbook of Jiangsu Phoenix Science and Technology Press,and according to which the "Express Numbers with Letters" will be divided into three dimensions of perception,expression,and operation;?the researcher focuses on the SOLO classification theory,SEC alignment analysis model,and Gavin's research on the standard of conformity assessment,and constructed a scoring standard of understanding level and analysis tools for calculating the level of alignment.The average value(?)of the alignment index P,the threshold values(P0.95?0.99)corresponding to quantile 0.05 and quantile 0.01 are used as the criteria for classification;the levels of alignment are defined as highly significant,significant,not significant,and no alignment.At the same time,according to the calculated D value,it is reflected whether the teacher tends to underestimate or overestimate the understanding level of students in the estimation.(2)On the empirical side,this study conducted preschool surveys on 10 seventh-grade mathematics teachers and 10 classes in three middle schools in Nanjing and Wuxi.A total of 445 valid student test papers were collected and there are 10 teacher's effective predictor volume meanwhile the author interviewed with teachers.Through the analysis of test results and interview,the researcher analyzed the student's understanding level of the "Express Numbers with Letters",teacher's prediction level of alignment and their influencing factors,and reached the following conclusions:?In terms of the current situation of students' understanding level,there is a certain degree of imbalance in the understanding level of each dimension,in which the students' ability to exemplify and express actual meanings according to the algebraic formula is obviously weaker,and the ability to explore the laws of change and express them with letters need still to be improved.The awareness of proactive use of letters for reasoning is low.?In terms of the current situation of the level of alignment,the teacher's level of alignment is generally low.In contrast,teachers show the lowest level of alignment in the perceived dimensions,the next is the expression dimension,and the operational dimensions are more optimistic.From the perspective of D value,most teachers tend to overestimate the level of understanding of students in terms of perceived and expressed dimensions,while more than half of teachers tend to underestimate in the operational dimension.There is a significant difference in the perceived dimensions of the difference in teaching age at the level of alignment,and the teacher' level of alignment in the 10 years of teaching age is significantly higher than that of teachers within 10-20 years.?In the current situation of the level of alignment,in addition to the influence of the teaching age,the influencing factors mainly include the students' understanding level of "Express Numbers with Letters" in each dimension,the degree of the teacher's grasp of this section of mathematics textbooks and the elementary school mathematics textbooks,and whether teachers have the deep understanding of the students' learning foundation etc.According to the conclusions of the study,the following suggestions are put forward:At the same time pay attention to the three dimensions of content perception,expression and operation of teaching;to strengthen the theoretical study,in-depth study of the curriculum and textbook and the teaching materials of each segment;face up to differences in students,increase the channels and ways of understanding the students;and reflect on the knowledge and teaching in time.