The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson

Abstract

In this paper, we analyse a grade 8 (age 13–14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in which he shifted the focus from individual mathematical solutions to generalised properties. By comparing the teacher’s detailed prior planning of the board work (bansho) with that which he produced during the lesson, we distinguish between aspects of the lesson that he considered essential and those he treated as contingent. Our analysis reveals how the careful planning of the board work enabled the teacher to be free to explore with the students the multiple alternative solution methods that they had produced, while at the same time having a clear overall purpose relating to how angle properties can be used to find additional solution methods. We outline how these findings from within the strong tradition of the Japanese problem-solving lesson might inform research and teaching practice outside of Japan, where a deep heritage of bansho and neriage is not present. In particular, we highlight three prominent features of this teacher’s practice: the detailed lesson planning in which particular solutions were prioritised for discussion; the considerable amount of time given over to student generation and comparison of alternative solutions; and the ways in which the teacher’s use of the board was seen to support the richness of the mathematical discussions.

Farewell to Virtual Environments and Welcome to Post-pandemic Mathematical Problem Posing and Solving

“…The conclusions reached by the Program for International Student Assessment (PISA) are: (a) latent classes demonstrate better mathematical problem solving skills, (b) latent ability influences problem solving ability (c) interactions between skills have a rule [19], so the curriculum should be approached from another angle to obtain better results in mathematics and not always occupy the last places in the PISA results.Teachers in the area of mathematics do not agree with the national curriculum because it prioritizes the content and does not develop skills to address the approach and problem solving, so the teacher encounters serious problems to develop and plan actions to solve problems [20], to improve these difficulties the Peruvian government should socialize and train the topics of the curriculum to implement and readjust for the sake of student development. Better acceptability is obtained by the students when they manage to see an image with the mathematical problem and manage to solve a problem from different points of view, so the results show the important characteristics (detailed planning for the solution of a mathematical problem, exclusive and excessive time for a single problem and an infinity of solution alternatives), that is, there is enough support and richness in the use of the blackboard for the mathematical discussions that are generated from each case raised [23].…”

“…The difficulty of problem solving brings with it the development of personalized type learning models where even interactive novels are included [22], with carefully supervised and planned blackboard work to opine in the form of plenary during the session was with the sole purpose of improving the pedagogical system [23].…”

mise en commun à la mise en dialogue

“…Le choix du support dépend des habitudes de l'enseignant•e, de l'équipement pédagogique dans la classe (tableau noir, tableau blanc, tableau blanc interactif, rétroprojecteur, ipads). L'utilisation et la gestion du support sont bien différentes selon les contextes éducatifs (Baldry & al., 2022 ;Tan, 2021;Tan & al., 2022 ;Train, 2013). De plus, l'enseignant•e organise la mise en commun dans un espace commun.…”

“…Pour les enseignant•e•s japonais•e•s de primaire, la phase de neriage représente le moment le plus important de la leçon en temps accordé et en importance, contrairement aux enseignant•e•s suisses (Clivaz & Miyakawa, 2020). Cette phase s'appuie sur un véritable art de préparation et de réalisation du tableau noir, le bansho (Baldry & al., 2022 ;Tan, 2021). Les recherches (Batteau & Miyakawa, 2020 ;Clivaz & Miyakawa, 2020) montrent l'importance accordée par les enseignant•e•s aux mises en commun dans les leçons de mathématiques.…”

Crisis‐ready educational design: The case of mathematics

“…When they do, they will be expected to discuss the task as “fellow mathematicians.” “Whole‐class” mode : There can be a real gain in bringing together a larger group of students (perhaps the whole class) to present their solutions. The teacher may choose an order that showcases approaches of increasing sophistication, such as is common within the neriage phase of the Japanese problem‐solving lesson (see Baldry et al, 2022; Takahashi, 2006). At the end of each presentation, students may be asked to further develop their own solutions or to tackle a related problem in the light of the discussion. Changeover points : At some point, the teacher will judge that the activity sequence for this task has gone on long enough.…”