Lesson study as a fundamental situation for the knowledge of teaching

Purpose The purpose of this paper is to elaborate on the commonality between the Theory of Didactical Situations (TDS) and lesson study to propose a model of lesson study using both the predominant graphical representation of lesson study by Lewis and the model of the didactical situation at the heart of TDS by Brousseau. Design/methodology/approach Starting by describing and adapting the predominant graphical representation of lesson study by Lewis and the model of the didactical situation at the heart of TDS by Brousseau, the paper integrates the two representations to highlight the commonalities between the students’ learning situation and the teachers’. Based on this integrated graphical representation, the key phases of lesson study are then conceptualised by the mean of the dialectic between didactical and adidactical situation. Findings The reflection about the use of the TDS graphical representation embedded in the lesson study diagram helps the reflection on the use of TDS itself to analyse lesson study. This theoretical analysis describes the process of teacher learning in lesson study and the link between their learning and the student’s. It also shows that lesson study is a good candidate for the fundamental situation of the knowledge for teaching. Originality/value The graphical conceptualisation of lesson study as a learning situation for teachers offers new insight about how teachers learn in lesson study.

ANALYSIS OF DIDACTICAL CONTRACTS ON TEACHING MATHEMATICS: A DESIGN EXPERIMENT ON A LESSON OF NEGATIVE INTEGERS OPERATIONS

This paper presents the analysis of teaching of Math that took place in the classroom to identify the characteristics of didactical contracts that occur as part of a didactical situation. The design experiment was conducted on 31 seventh grade students and a mathematics teacher on negative integer operations lessons. The researchers analyzed the ongoing learning, how the didactical situation stages evolve in the teacher-student interaction that allows the formation of new knowledge or concepts in the student and how the teacher organizes the responsibility for achieving the learning objectives. The Analysis showed that students, at an early stage, can perform negative integers operations by utilizing the basic concepts they get in primary school. This concept can bridge into a new knowledge that identifies the properties of integer count operations and builds power of mind on problem-solving.

Desain Didaktis Bahan Ajar Matematika SMP Berbasis Learning Obstacle dan Learning Trajectory

This study is to correct mathematical learning by didactic design based on learning obstacles and learning trajectory. This is a qualitative study through Didactical Design Research (DDR) by three analytical phase, i.e. 1) didactical situation analysis before learning presented as didactical design hypothesis including ADP; 2) metapedadidactical analysis which analyzes teacher’s ability such as unity, flexibility, and coherency in learning; 3) retrospective analysis which is the correlated analysis between the result of didactical situation hypothesis analysis and metapedadidactical analysis. The result of problem analysis related to integer arithmetic operation, a concept of function, and two triangle similarity concept, implementation of early didactical design could predict probable mistakes done by students and even if the mistakes still there, it was decreased compared to early learning obstacle test. These conditions were reinforced after learning with mathematics score school succeed standard 75% was done.