Examining Mathematics Classroom Interactions: Elevating Student Roles in Teaching and Learning

Abstract

Abstract:This article introduces a model entitled, "Responsive Teaching through Problem Posing" or RTPP, that addresses a type of reform oriented mathematics teaching based on posing relevant problems, positioning students as experts of mathematics, and facilitating discourse. RTPP incorporates decades of research on students' thinking in mathematics and more recent research on responsive teaching practices. Two classroom case studies are presented. A high school unit on functions is explored utilizing individual research on the part of the teacher to enact RTPP lessons. A middle school teacher enacts a RTPP lesson on proportions and utilizes this model to bridge students' incorrect additive reasoning strategies with correct multiplicative reasoning strategies. The results showed that both teachers were able to elevate students' roles in classroom discussions through implementation of RTPP. Individual research conducted by the high school teacher informed his RTPP approach while participation in professional development sessions with a classroom embedded component influenced the middle school teacher's enactment of RTPP lessons. Both teachers used specific teacher moves within RTPP to relinquish their role as mathematics experts in order to elevate their students' roles in classroom discussions. The RTPP cycle is offered as a potential model for studying mathematics teaching and learning across a variety of secondary mathematics classrooms.

Teacher-student interactions for enhanced learning in upper secondary mathematics classroom

“…We noticed that the teacher did most of the representations and manipulations of concepts such as models, graphs, and drawings instead of allowing students to manipulate and explore concepts (statement 2 [6] to reach the destination. However, we found them making much effort to talk to teach instead of talking for learning.…”

“…This means that a student familiar with being given a table of coordinates is more likely to develop procedural knowledge with a total lack of understanding. Teachers are encouraged to ask productive questions [6], consider openended tasks, and give room to reasoning. Lai [29] emphasized the need for careful design, planning, and implementation of the lesson.…”

“…Table 3 also shows that students played their role in the learning process (statements 3, 12, 14 and 15 scored high, 70% and above) that teacher role (only statement 6 scored 70% and above). Thus, there is a need to elevate students' roles in the learning process [6]. However, the lesson structure, guiding the problem-solving process, and classroom discourse should be at a high level to keep interactive learning between students, with the teacher, and with the content.…”

Students’ Concept Image and Its Impact on Reasoning towards the Concept of the Derivative

“…Examples are therefore paramount in mathematical teaching and learning. Even according to Kent (2017), responsive teaching involves a deeper exploration into the content of mathematics at the core of the lesson based on the students' understandings and interpretations. For example, how the students solve , or for increasing function To solve , it can be used , or , or by using derivative of composition of function (Varberg et al, 2007).…”

The impact of mathematics learning environment supported by error-analysis activities on classroom interaction

“…Many researchers (Apriliyanto et al, 2018;Dallimore et al, 2004;Davadas & Lay, 2018;Kent, 2017;Mccarthy et al, 2016;Tatar, 2005) emphasized that in order for students to develop their abilities and establish an indepth understanding of mathematical knowledge and skills, mathematics learning practices must concentrate on classroom teacher-students, students-teacher, and students-students interactions.…”