Researchers have reported that preservice mathematics teachers' (PMTs') conceptions for radian angle measure are dominated by conceptions of degrees, memorization, and calculational strategies, and are always expressed in terms on [pi]. In this report, I unpack the mathematical meanings of a PMT, Henry (pseudonym), as he engaged in three…

Action-Process-Object-Schema (APOS) theory and the triad of schema development are used as the framework in this study to investigate students' understanding of the concept of "circle." In this report, results are presented from the data analysis of responses to questions in semi-structured interviews of 15 students enrolled in a college…

This is a preliminary study of design research that investigates preservice mathematics teachers' proof level and the possible task of scaffolding-based interventions in proving the triangle theorem. The research subjects consisted of 58 second-semester mathematics education students at Universitas Negeri Surabaya, Indonesia. This research is…

This paper reports our efforts to develop a measure of pre-service elementary teachers' geometry knowledge for teaching 2-dimensional (2D) shapes and to evaluate the psychometric properties of this measure. Specifically, the GKT-2D scale was designed to assess pre-service elementary teachers' geometry content knowledge, knowledge of geometry and…

Being able to move between different representations levels (macroscopic, submicroscopic, and symbolic) is important to understand a chemical phenomenon meaningfully. The current study investigated how pre-service science teachers moved from symbolic representation to sub-microscopic representation. A total of 205 pre-service science teachers,…

Despite the significance of incorporating technology into geometry instruction, many teachers still find it difficult to teach geometry using technology. This study employed a techno- pedagogical content knowledge (TPACK) survey of 70 pre-service mathematics teachers (29 males, 41 females) from a public university. The goal was to determine which…

The concept of a mathematical definition causes severe difficulties among students during problem solving and proving activities. Students' difficulties with the use of mathematical definitions often arise from the fact that students are often given those definitions instead of constructing them. With the aim of developing an understanding of the…

This study aims to address the teaching of integrals in multivariable calculus concerning the role taken by geometry, specifically, geometrical content dealing with boundaries in integrals that appear as curves and surfaces in R[superscript 2] and R[superscript 3]. Adopting the framework of the Anthropological Theory of the Didactic, we approached…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

Not-knowing is an underexplored concept defined as an individual's ability to be aware of what they do not know to plan and effectively face complex situations. This paper focuses on analyzing students' articulation of not-knowing while completing geometric reasoning tasks. Results of this study revealed that not-knowing is a more cognitively…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

Effects of spaced, repeated retrieval practice and test-potentiated learning on mathematical knowledge and reasoning in an authentic educational setting are investigated in the study. Research participants were a cohort of second-year pre-service mathematics teachers. A revised taxonomy table was utilized to measure the knowledge and reasoning…

Some goals of mathematics teacher education include ensuring that pre-service teachers (PSTs) have strong content knowledge, the skill to anticipate and interpret student thinking, the ability to plan how to respond, and the ability to critically select resources for instruction. These goals are especially challenging for the topic of geometric…

The purpose of this research is to determine the knowledge, perceptions and misconceptions of pre-service primary school teachers about geometric objects through mind maps. For this purpose, the research was designed with a case study, one of the qualitative research methods. The study group of the research consists of 52 pre-service primary…

Objectives: This study aims to investigate the feasibility and efficacy of competency-based course (Conceptual Geometry). In addition, this paper presents the procedures of developing competency-based course which include mapping out competencies of the course, developing a set of assessment instruments (e.g., diagonal, pre-and post-unit…