Constructing formula of pyramid volume by comparing volume of prism with the beach sand and container media in junior secondary school: A lesson study

Abstract

Geometry is the most difficult topic for majority of junior secondary school students. An endeavor to handle these students' difficulties, the teacher works collaboratively with mathematics educator in a lesson study setting. Learning materials for teaching the volume of pyramid was designed collaboratively. Prism and pyramid container were made for preparing the lesson. Prism and pyramid which have equal base area and height were designed. As many as 40 students of the eight grade were grouped into 8 cohorts of 5 students. Each cohort got one set of geometric containers and beach sand. Students learn the lesson in an open lesson setting. All cohorts work in cooperative group lesson to observe and find out the formula of pyramid compare to the formula of prism which was known previously. Students were manipulating the materials to relate the volume of both pyramid and prism and to compare between the volume of pyramid and the volume of prism by measuring out using the beach sand Learning process was set in lesson study context and was attended by the group of mathematics teachers for at least 30 teachers. In the apperception session, the teacher reminded the students for the formula of prism volume. After manipulating the learning materials which consisted of model of prism, model of pyramid, the beach sand, and worksheet, measuring the volume of pyramid and prism by using sand, comparing, and contrasting, then the students in each group discussed all information from their activity to find out and conclude the volume pyramid. The results are surprising; the students found that the volume of pyramid is one third of the base area times height of the pyramid. From the reflection session we can analyzed that such learning model of mathematics was expected by most mathematics teachers in Bandung. The teachers knew that this kind of teaching emphasized on students active learning, but the teachers need examples, or models for teaching which enable students to re-invent or discover mathematical concepts. This lesson study can be considered as a model to activate students learning mathematics.