Tackling students' learning difference: A learning study mathematics case

This paper describes a Mathematics Learning Study in a Hong Kong primary school. In the past, rote learning was the common practice expected of students in learning mathematics in this school. The teachers mainly used drilling approach by giving a lot of mathematics exercises to the students as they believed that "practice makes perfect". The emphasis was on trying to get the students to do the exercises fast, to memorize the rules of practice in applying mathematical concepts and to get higher marks. However, most students had not attained deep understanding of the concepts. In this Learning Study, a group of teachers, together with the researchers from the Hong Kong Institute of Education worked to enhance the primary 3 students' understanding of the concepts involved in the topic division with remainder'. According to the analysis of the pretest and students' interview before the lesson, the teachers found that the students only memorized the rule of practice without understanding why the remainder must be smaller than the divisor. Based on the learning theory of Variation advanced by Marton and Booth, patterns of variation were incorporated in a series of classroom activities of the research lesson. These patterns of variation were aimed to help the students discern the one main critical aspect: the meaning of the remainder. The students were expected to develop the concept that when the number can no longer be equally shared, it will become the remainder in the division process. Finally, the comparison between the results of the pre- and post-test and students' post lesson interview showed that there was a significant gain in students' learning outcomes with respect to the intended object of learning.