Preservice Secondary Mathematics Teachers’ Actional Beliefs about Teaching Geometric Transformations with Geometer’s Sketchpad

Abstract

<p style="text-align: justify;">Preservice mathematics teachers' beliefs about actions related to the use of the technological tools in teaching mathematics may affect how they are going to use them in their classroom activities. However, there is a limited evidence of what beliefs they hold on their intended actions of using technological tools in teaching mathematics. This study presents two preservice high school mathematics teachers' actional beliefs related to their intended actions in teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised of a series of five task-based qualitative interviews with each of two senior undergraduate preservice teachers at a medium-sized public university in the Rocky Mountain Region of the United States. This study used a radical constructivist grounded theory (RCGT) with five assumptions—symbiosis, voice, cognition, adaptation, and praxis as a theoretical framework to guide the study process. The thematic findings of the study included four in vivo categories of their beliefs associated with actions of teaching GTs with GSP – assessment of student learning, engaging students in a group activity in exploring GTs with GSP, engaging students in individual activity in exploring GTs with GSP, and exploring GTs with GSP as 'suck it up and do it.' Pedagogical implications of these categories have been discussed.</p>

Epistemic errors in students’ four fundamental operations of whole numbers: a radical constructivist grounded theory (RCGT) approach

“…We applied a theoretical framework of radical constructivist grounded theory (RCGT) based on five assumptions of symbiosis, voice, cognition, adaptation, and praxis (Belbase 2015(Belbase , 2016(Belbase , 2017(Belbase , 2018(Belbase , 2020Belbase et al 2020). These assumptions are based on the principles of radical constructivism, which state that the learner constructs knowledge through active participation in the learning process, but not through the transmission of knowledge from teachers to students, and that the function of knowing serves the reorganization of the experiential world of the learners (von Glasersfeld 1995a).…”

“…These assumptions are based on the principles of radical constructivism, which state that the learner constructs knowledge through active participation in the learning process, but not through the transmission of knowledge from teachers to students, and that the function of knowing serves the reorganization of the experiential world of the learners (von Glasersfeld 1995a). The process of constructing knowledge by learners as research participants and teachers/researchers is grounded in symbiotic collaboration and experiences with mutual voices (Belbase et al 2020). In this sense, the five assumptions of RCGT formed a basis for constructing meaning from the students' expressions and tasks of four operations on whole numbers (Fig.…”

“…Mutualism supports students in learning the operations of whole numbers, and the researcher learns about the errors they commit on a variety of tasks and exercises. Thus, this mutualism is beneficial to both in terms of learning and knowing the significant issues in students' performances and errors they commit (Belbase 2015;Belbase et al 2020).…”

“…Their voices in the task-based interviews have been presented in their words in the form of their narrative intercepts. The researcher has his voice through the interpretive accounts of the research outcomes (Belbase 2015;Belbase et al 2020).…”

“…The third assumption of RCGT, cognition, is related to mental thought processes going on in the students and the researcher during peer or group work and task-based interviews. The construction of the meaning of fundamental operations of whole numbers (addition, subtraction, multiplication, and division) is an iterative process from simple to complex constructions and the generation of meanings from the participants' experiences in the task situations (Belbase 2015;Belbase et al 2020). The process of generation of meaning and the interpretation of different errors committed by the students led the researcher through the iterative grounded process of generating thematic categories of the error patterns (Bryman 2008).…”