Paper Title
Comparison of Two Teachers' Problem Posing and Feedback to Students’ Solutions

In the mathematics classroom, teachers’ problem posing and feedback to students’ solutions have a crucial influence on students' mathematics learning. Moreover, as fraction multiplication is a difficult concept for students' learning and teachers’ teaching, this study invites two teachers with different qualifications (one is senior and one is expert) to compare their problem posing, selection of students’ problem-solving records, and the subsequent feedback to students’ solutions in the fraction multiplication class. The methods used include classroom observation and in-depth interview. Here are some discoveries of this study. First, there is a hierarchy between the problems of expert teacher, focusing on the establishment of the relationship among the meaning of the problem, the fraction multiplication formula, and the graphic representation, so that the students understand the format and meaning of the fraction multiplication formula. On the contrary, senior teacher not only misunderstands the teaching sequence but also fails to grasp the goal of the activity. For example, in the topic discussion before the announcement of the fraction multiplication algorithm , senior teacher takes it for granted that students could solve problems by fraction multiplication algorithm. Second, the expert teacher chooses a variety of students’ problem-solving records and give different instructional intentions, including the clarification of the multiplicand and multiplier position in the fractional multiplication formula; the graphic representation should be able to present the meaning of the problems rather than the answers after using algorithm. In the senior teacher's class, fewer students’ problem-solving records are selected, and the focus of discussion is often the external appearance of the graphic representation, such as solid or dashed lines, solid or hollow. Third, When the student's problem-solving record is incorrect or directly uses fraction multiplication algorithm before it is announced, expert teacher keeps asking why, and there are many key questions for reference. On the contrary, after senior teacher's questioning of student records, she is often satisfied with the student's answer and there is little further questioning.