An Empirical Study On The Teaching Of Mathematics Conceptions In Middle School Level From The Perspective Of Learning Opportunity

Pursuing for excellence is the eternal theme of education,while real purpose of most educational reform are looking for the way to cultivate better people.With the development of large scale of international assessment,the question related with the cultivation of the core competency of students has been paid much more attentions than ever before.And requirement to solve it through practicing in the mathematics classroom is becoming more and more pressing.As we known,students' acquisition of knowledge and cognitive thinking might be effected by the quality of instruction.That is why the quality of instruction is the key factor to the development of students' core discipline literacy.So,how to ensure that teaching is helpful to prompt students to construct knowledge and improve their literacy development ? Obviously,valid classroom evaluation will be the answer beacause that usually should be considered earlier than instruction.Even though collaboration and interaction during the teaching process are advocated highly based on most of the teaching theories,especially in the Constructivism Theory and the Theory of Social and Cultural Learning,most of methods of classroom assessment in the reality practice are based on the Behavioralism Theory,which highlights stimulation and reinforcement,or Modernism Theory,which highlights quantitative criteria.This is incompatible with the teaching idea or requirement of students' cognitive thinking ability under the background of curriculum reform in China.At present the systems of classroom teaching evaluation that we used emphasize too widely but not in-depth comprehensive methods,which could not deeply reflect the essence of classroom teaching,i.e.relation between teaching and learning.And teachers can hardly find out the solution to develop their instruction from the results which is too abstract for them to understand.Thus,the teaching evaluation can hardly be used to improve the quality of instruction or support the professional development of teachers.He who has a stone may attack jade.The development of mathematics classroom evaluation has been developed much better at abroad.With the understanding of weakness of comprehensive evaluation methods,which could not valid to improve the quality of instruction and the professional development of teachers,many classroom evaluation tools based on specific perspectives(such as mathematical tasks and classroom interaction)were developed from the mathematical educational reform projects arisen began from 1980 s in the USA.And learning opportunities were developed as evaluation tools for assessing the quality of classroom teaching from these projects.At the same time,the item of “learning opportunity” also has been used for describing the possibility of students' engagement in the process of knowledge construction from the prespective of thinking,while that was just as the external factors for explaining the academic achiment difference of students from different regions.Thus,we try to develop new classroom evaluation tool from the perspective of Learning Opportunity based on the research findings abroad.The key questions in this research are as follws:1)how to evaluate the learning opportunities in the process of mathematical conceptual teaching in classroom by using the techque of discourse anlysis?2)how to promote teachers' professional development based on the result of evaluation?Firstly,based on the research findings from the projects of QUASAR and IQA,we develop an evaluation model of “learning opportunity” for analyzing the quality of instruction in mathematics class,which includes two main dimensions as feature of mathematical instructional task and feature of classroom discourse.The first dimension is about the characteristic of Mathematical-Instructional-Task,developed to analyse the different catagories of mathematical tasks,which contain “Task of Recall or Review”,“Tasks of Procedural Opreations”,“Tasks of Explanation or Anlysis” and “Tasks of Inquiry Activity”.We analyse the latter dimention from the charactericstic of Classroom-Discourse,which includes discourse content and structure.Discourse content is used to describe the role of teachers in the classroom IRF interaction mode.(including Iniciation and Feedback)while discourse structure is used to discribe how teachers follow the “interation-princepls” when they talk with students by using“ index of leaning opportunity”.Then we collect the data from mathematics classes of 4 teachers' from middle schools from Shanghai by classroom observation,video analysis and teacher interviews.After using the data to evaluate the learning opportunities in classroom instruction(as pretest),we determine the methods for 3-rounds teaching intervention based on the pretest results.In the first round,the stategagies we use are as follows,designing inquiry tasks and discussing predictly the enactment of the tasks with the notice teachers together.In the following round,we add the discussion of that how to follow the communication-principles in interaction of teacher and students after the design of inquiry task.Lastly,without our specific procedure help,notice teachers design tasks by themselves through summarying and introspecting their work.It takes nearly 4 months from the beginning to the end of the study,which is towards to improve several notice teachers' professional development oriented by the evaluation model of Learning Opportunity.As results indicated,there is some obvious change on students' learning opportunities in 3 notice teachers' class after 3-round teaching interventions.That can be presented as follows: 1)from the perspective of Mathematical-Instructional-Task,we can see that the proportion of the tasks with higher cognitive demand have improved;2)from the perspective of Classroom-Discourse,teachers' raise their attentions on the question posing of “exploring mathematics meaning and relation” and “generate discussion” while remain similar on the performance of feedback.Conclusions can be drawn,from the theoretical level: 1)The Evaluation model of “learning opportunity” could reflect the level of mathematical concepts teaching in classroom;2)The cognitive level of mathematics teaching task is not necessarily related to the quality of learning opportunity;3)Mathematical communication discourse is the key carrier of classroom learning opportunities and space.In the practical level: 1)The intervention based on evaluation model of learning opportunity is helpful to improve the level of concept teaching for novice teachers;2)The design of inquiry task based on evaluation model of learning opportunity could influence the performance of teachers' problems from a certain extent;3)Professional skills of problem posing can be acquired more faster than skills of feedback to novice teachers.