Study On Instructional Design Based On Optimization Of Learning Trajectory

Mathematics education is the foundation of education, and primary mathematics education is to play the role of enlightenment. In the new mathematics curriculum reform, in which the main point is to emphasize "understanding of learning mathematics." Moreover, in the primary mathematics learning, so that students experience mathematics learning process is of practical significance, Mathematics learning not only enable students to learn computing, problem solving skills, more important is to develop students’ thinking ability, logical ability, and so on. Especially in the calculation of teaching, not only to let students learn calculation methods, but also to enable students to understand the truth of calculation, As the saying goes, "Give a man a fish, than giving the fish". Only by allowing students to really understand the calculation of truth, even if they forget algorithm, they still can deduced out of their own, this is the meaning of learning mathematics. Therefore, in the face of the new curriculum reform today, teachers should constantly improve their teaching level, to improve the quality of teaching, however, to achieve teaching objectives and improve quality of teaching are based on the premise that instructional design. This will affect the experience and efficiency of mathematics learning. Therefore, the continuous optimization of instructional design became the fundamental of improving the teaching quality.Division of fractions as a carrier, this paper study the instructional design through the study of teachers’teaching, discussion with development director of education and interviews with teachers and students. In the paper, we focus on three issues. They are (1) What are the deficiencies of instructional design based on the optimization of learning trajectory. (2) How to improve the task sequence of instructional design? And what is the optimized instructional design? (3) Is improved instructional design perfect? Do students understand the truth of calculation?Through this study, we get the following conclusions:First, we can understand that the task arrangements of instructional design have some shortcomings. In division of fractions, the task of teaching should make students from visual to abstract understanding gradually. Teaching arrangements should have emphasis. Teaching task should progressive layers. Eventually to equip students with calculation of truth, and reached abstraction level of understanding.Second, through the data, we can see that students understand the calculation of truth more profound by the optimization of instructional design. However, according to our research data obtained can be seen that there are fewer students achieve the level of understanding abstract. It is 30% lower than the students that reached intuitive understanding. Basically the students are able to achieve the level of understanding of the program, more than 80% of students reached intuitively understanding and more than 40% of students reached the abstract understanding. So I suggest that teachers should pay attention to students’ understanding of calculation of truth, but also designed to meet students’ cognitive level of instructional design according to the actual situation of the students.Third, in the course of the study, Students have certain difficulties in the scores divided by the fraction of an intuitive understanding. Most students can’t use an intuitive graphical representation of it, Only 30 percent of students are able to use the correct visual diagram that out, so the teachers in teaching should strengthen students’ understanding of this level. In addition, teachers should contact the score by an integer teaching, so that students can make knowledge together to form a complete division of fractions knowledge.Finally, the basis of our research, the following recommendations for teachers (1) Teachers should change the traditional concept of teaching. (2) Instructional design should be consistent with students’ cognitive law. (3) Instructional design should adapt to changes in teaching methods. (4) Teachers should focus on students’ intuitive understanding.