Investigation And Research On The Understanding And Teaching Of "Combination Of Number And Shape" Among Junior High School Mathematics Teachers

Teachers’ understanding of subject knowledge directly affects students’ mathematics learning."Number-shape combination" is a familiar everyday term in teaching,but the investigation of existing literature found that there is no formal and clear definition for "number-shape combination".There are not many related researches on the understanding of "number-shape combination" by junior high school mathematics teachers.Based on this,the article mainly studies the following questions:（1）What is the junior high school mathematics teachers’ understanding of "number-shape combination" ?（2）What is the current status of the classroom teaching of "combination of numbers and shapes" for junior high school math teachers?（3）What is the relationship between junior high school mathematics teachers’ understanding of "combination of numbers and shapes" and the current situation of classroom teaching?Drawing on the existing research,the understanding block diagram of "number-shape combination" is developed,and the understanding of "number-shape combination" is divided into the understanding of "number-shape combination" to solve problems and the understanding of "number-shape combination" teaching.The problem-solving comprehension of "combination of numbers and shapes" is divided into three types of questions: "analyzing shapes with numbers,solving numbers with shapes,and combining numbers with shapes"."The understanding of teaching is divided into the understanding of basic concepts,the awareness of teaching content and the understanding of teaching content.The current situation of classroom teaching of"combination of numbers and shapes" is investigated from three dimensions: teaching application,pre-class preparation and classroom implementation.And prepare corresponding questionnaires,test papers and interview outlines.Some junior high school mathematics teachers in Urumqi were selected as samples to investigate and analyze their understanding of"combination of numbers and shapes" and the current situation of teaching.The survey found that in terms of comprehension of "combination of numbers and shapes" :（1）For the understanding of "combination of numbers and shapes" to solve problems,84.92% of teachers can reach the level of memory comprehension,79.37% of teachers can reach the level of interpretive comprehension,and only 4.76% of teachers can reach the level of interpretive comprehension.% of teachers are able to achieve the level of inquiry understanding.Teachers’ understanding of "solving numbers with shapes" is higher than that of "analyzing shapes with numbers",and their understanding of "combining numbers and shapes" is not comprehensive enough.（2）For the understanding of the "combination of numbers and shapes" teaching,more than 90% of the teachers have a good grasp of the knowledge within the textbook,but have a poor understanding of the creative and exploratory content outside the textbook.In terms of the teaching status of "combination of numbers and shapes" :（1）85% of teachers believe that the combination of numbers and shapes is helpful for teaching,but they do not pay enough attention to the use of combination of numbers and shapes in teaching.（2）84.13% of teachers think it is necessary to design the combination of numbers and shapes into the teaching content,but due to the lack of systematic understanding,few teachers can do it.（3）In classroom teaching,87.30% of teachers believe that "number-shape combination" is important,but lack of teaching consciousness of number-shape combination.In terms of the relationship between the understanding of "number-shape combination" and the current situation of classroom teaching: there is a weak correlation between junior high school mathematics teachers’ understanding of "number-shape combination" and the current teaching situation.Based on the research findings,suggestions are put forward for the teaching of "combination of numbers and shapes" for junior high school mathematics teachers.