This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become "thinkable" the…

The aim of this study was to investigate pre-service primary school teachers' (PPSTs) pedagogical content knowledge (PCK) on quadrilaterals. In this study, the PCK components of knowledge of understanding students (KUS) and knowledge of instructional strategies (KIS) were used. The participants of the study consisted of 83 PPSTs studying at the…

Generating mathematical conjectures is an important mathematical habit of mind for preservice teachers to develop so that they can, in turn, help their students to develop this skill. In this paper we present a classroom episode in which preservice mathematics teachers experience conjecturing in the context of a rich, open-ended task. They also…

This article highlights the importance of re-defining units unconventionally with fractions. We provide three examples of tasks Grade 5 students engaged in; we highlight the creative ways that they flexibly re-defined units and engaged deeply with fractions. We offer suggestions for supporting unconventional units for promoting conceptual…

A recirculating water vacuum pump was constructed from inexpensive materials. The recirculating water vacuum pump has a smaller footprint compared to many commercial models and features a novel, 3D-printed water aspirator pump that also functions with a standard laboratory faucet connection. The performances of both the recirculating water vacuum…

Large drop towers let you experience a couple of seconds of nearly free fall before stopping gracefully in magnetic brakes or bouncing a number of times on compressed air, as in the Turbo Drop tower considered in this work, where many complementary representations are used. An accelerometer taken along on the ride captured the forces experienced…

The shape bias, a preference for mapping new word labels onto the shape rather than the color or texture of referents, has been postulated as a word-learning mechanism. Previous research has shown deficits in the shape bias in children with autism even though they acquire sizeable lexicons. While previous explanations have suggested the atypical…

Recent research has shown that reducing the perceptual fluency of shape processing can be an effective means for overcoming the interference of the More A-More B intuitive rule among grade 3 students in a perimeter comparison task. From the perspective of cognitive load, the current study focused on the mechanism of perceptual fluency on…

We present a computer-based experiment that simulates the accretion process and generates fluffy aggregates with fractal nature. The Box Counting is performed without the aid of an image processing tool by using the coordinate information of the constituents of the aggregate. A simple algorithm to create aggregate and calculate box-dimension will…

Aksak meters such as 5/8, 7/8, 9/8 are not formed equally and teaching these meters to the students usually takes a long time and learning these measures requires a dedicated effort. The aim of this research is to determine whether the teaching 5/8,7/8,9/8 aksak meters to the students in sixth grade through geometric shapes is more effective than…

The literature reports preservice teachers' overuse of proportionality when solving geometric similarity problems with nonproportional relationships. Changing this type of error is reported as difficult even after applying certain interventions. As a solution to this type of error, this study used augmented reality activities to facilitate the…

In the 21st century we live in, technology is developing rapidly. Inevitably, the technologies used in almost every area of daily life will also reflect in the field of education. Educational technologies, which enable students to grasp abstract concepts more easily and facilitate the teaching process for teachers, have increased their impact in…

This study presents a characterization of prospective early childhood teachers' (ECEPTs) and prospective elementary school mathematics teachers' (EMEPTs) concept images and concept definitions of triangles through a defining task and an example generation task. Data consisted of 62 EMEPTs' and 72 ECEPTs' written statements for the definition of a…

It has been suggested that not only domain-specific factors but also working memory (WM) may play a crucial role in mathematical learning included Geometry, but the issue has not been deeply explored. In the present study, we examined the role of domain-specific factors and of verbal versus visuospatial WM on geometric learning of a new…

The aim of the present study is to determine the elementary pre-service mathematics teachers' understanding on solids. For this purpose, pre-service teachers' definitions and drawings of these objects were examined. Qualitative research method was used. A written questionnaire consisting of sixteen open-ended and multiple-choice questions was…