Much remains under-researched in how learners make use of domain-specific feedback. In this paper, we report on how learners' can be supported to overcome logical circularity during their proof construction processes, and how feedback supports the processes. We present an analysis of three selected episodes from five learners who were using a…

The purpose of this research is to examine preservice elementary school teachers' geometry learning as investigated by both qualitative and quantitative methods. For the qualitative investigation, narrative analysis and thematic analysis methods were used. The findings of narrative analysis indicated two main kinds of stories: as a learner and as…

We report our research of seven pairs of students enrolled in the second semester of sophomore-level organic chemistry as they attempted to describe (in their own words) and draw, respectively, three electron-pushing diagrams of three-step reaction mechanisms. The tasks' objective was to accurately reproduce the diagrams based solely on the…

The use of dynamic geometry software (DGS) is becoming increasingly familiar among teachers, but letting students conduct inquiries using computers is still not a welcome idea. In addition to logistics and discipline concerns, many teachers believe that mathematics at the lower secondary level can be learned efficiently through practice alone.…

The aim of this study is to find out how designed Geometry Teaching Lesson affects candidate teachers' Van Hiele Geometric Thinking Levels. For that purpose, 14 weeks long study was performed with 44 candidate teachers who were university students in Turkey. Van Hiele Geometric Thinking Test was applied to candidate teachers before and after…

This study is a quasi-experimental research with pretest-posttest control group design, which aims to determine (1) the tendency of students in using various media scaffolding based on gender, and (2) effect of media scaffolding on increasing understanding of students' geometry concepts. Media scaffolding used this study is chart, props, and…

The purpose of the study was to explore how a group of at-risk youth in a South Florida alternative high school experienced a freehand visual arts drawing lesson as a learning portal to the teaching of the basic principles of geometry. These young people were completely devoid of interest in and failed to understand basic geometrical concepts.…

As indicated in numerous research studies, schoolchildren encounter many difficulties and obstacles in learning the multifaceted concept of the angle. In order to explore the possibility of enhancing schoolchildren's understanding of such a concept, the authors present a study that aims at investigating some structural characteristics of…

Science and engineering instructors often observe that students have difficulty using or applying prerequisite mathematics knowledge in their courses. This qualitative project uses a case-study method to investigate the instruction in a trigonometry course and a physics course based on a different methodology and set of assumptions about student…

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students' ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were…

Geometric constructions have already been of interest to mathematicians. However, studies on geometric construction are not adequate in the relevant literature. Moreover, these studies generally focus on how secondary school gifted students solve non-routine mathematical problems. The present study aims to examine the geometric construction…

Unlike a child's observable, physical interactions with mathematical tools (e.g., physically touching blocks in order to count them), the subtle manifestations of imagery construction can be considerably more challenging to identify and act upon. Although there have been substantive examinations of mental imagery in a variety of mathematical…

Within recent years, history of mathematics (HoM) has become an increasingly popular topic. Studies have shown that student reactions to it depend on the ways they use history of mathematics. The present action research study aimed to make students deduce volume rules of frustum pyramids using the dissection method. Participants were 24 grade…

The study we report here examines parts of what Chevallard calls the "institutional" dimension of the students' learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To…

The purpose of this qualitative study was to explore the use of 3-D printed models as an instructional tool in a middle school science classroom for students with visual impairments and compare their use to traditional tactile graphics for aiding conceptual understanding of geoscience concepts. Specifically, this study examined if the students'…