Self-Learning Geometric Transformations: A Framework for the “Before and After” Style of Exercises

The purpose of this research is to evaluate the type and accuracy of the visual representations that the pre-service teachers generate in the pedagogical solution of the word problems in terms of the spatial skill levels of the pre-service teachers. It is designed as a descriptive study in the screening model in accordance with the purpose of the study. The research was carried out in 2017 with 55 pre-service teachers attending the Primary School Teacher Education programme at Ordu University. The data on participants' spatial competence levels were obtained through Purdue Spatial Visualization Test and on the type of visual representations were obtained by coding the data obtained from the solution of a word problem given to the participants according to the criteria specified by the researchers. In the analysis of the data, descriptive analysis and content analysis were applied. As a result of the research, the visual representation types (schematic and pictorial) generated by the pre-service teachers have been determined and it was found that the pre-service teachers with high spatial ability generated correctly structured schematic representations; whereas candidates with low spatial skills usually generated pictorial representations.

In this article, we examine how the international computer graphics (CG) community can be empowered by disseminating and recognising peer-reviewed educational work. Over the past years, we have developed a technical platform to support these activities. However, to move forward, we need to gather and rally the online community around it. Indeed, we require providing the social scaffolding for personal involvement and ownership to enhance the growth of the community tool. To this end, we conducted a survey in late 2005, the results of which are presented here and we discuss the actions derived and directions entailed by our latest findings. Apart from removing barriers to participation, we concentrate our efforts on adding peer-recognition through member profiles ('who's who in CG education') and on disseminating the different, community-borne, views on CG curricula.

Logarithmic arithmetic (LA) is a very fast computational method for real numbers. And its computation precision is much better than a floating point arithmetic of equivalent word length and range. This paper shows a method of fixed point number computations by LA—just to do numeric conversion before and after LA computations. It is used to handle discrete coordinate addresses and pixel intensity data of digital images. The geometrical transformation is a typical application of the method. Linear (affine) and non-linear transformations with three interpolations of "nearest neighbor," "bi-linear" and "cubic convolution" in LA are demonstrated. It is the processing of coordinate addresses and pixel intensities of fixed point numbers. Experiments by 16-bit personal computer program showed that quality and speed are surprisingly high. The latter is comparable to that by using the floating point hardware chip. Some other examples of the applications are shown—curve drawing, three dimensional computer graphics and fractal image generation—all excellent.

In this article, the usage of matrices and matrix operations in computer graphics is shown. A brief overview of geometric transformations in computer graphics is given. The "Matrix - Computer Graphics" application software is created for the representation and easier understanding of relations between geometric transformations and matrix calculus.

A virtual environment was developed for PC and Android to be used with a desktop display and the Gear VR, respectively. The goal with it is to measure and enhance the spatial skills of people, because the latter can be achieved by solving simple geometric problems. Originally, this virtual environment consisted only of three such tests, namely the Mental Rotation Test, Mental Cutting Test and Purdue Spatial Visualization Test. Measurements were done in the past with these tests, but now the Heinrich Spatial Visualization Test is also included in the virtual environment. In this paper, its implementation and future measurement plan are presented.

In this study, the popular Purdue Spatial Visualization Test – Visualization by Rotations (PSVT-R) in isometric drawings was recreated with CAD software that allows 3D solid modeling and rendering to provide more realistic pictorial views. Both the original and the modified PSVT-R tests were given to students and their scores on the two tests were compared to investigate whether there was improvement in performance on spatial visualization tests with realistic 3D views. The study involved 157 first year community college students in engineering and technology majors and 34 high school seniors from a technical careers high school, all of whom were taking an engineering graphics course or a CAD course at the college when taking the tests. The test scores were analyzed in four groups: graphics classes, CAD classes, high school students, and a comparison group. In all four groups, the mean scores of the realistic 3D test were higher than the mean scores of the isometric test, which shows enhanced performance on the spatial visualization test with realistic 3D views.

This work describes a study of graphics interpretation in a common test of spatial ability, the Purdue Spatial Visualization Test: Rotations (PSVT:R).Tests of spatial abilities have long been considered to assess a cognitive ability of manipulating shapes in the mind's eye, and are often used for student assessment in engineering educational contexts.However, researchers are increasingly finding that some widely-used assessment instruments are confounded by other factors that do not necessarily fit within the confines of the traditional understanding of spatial ability.The purpose of this study is to investigate the images used as stimuli in the revised PSVT:R to determine whether they are naturally perceived as three-dimensional forms.The PSVT:R utilizes black and white isometric line drawings of shapes of various complexity, which test takers are supposed to "mentally rotate" into different orientations and select the correct view of the shape from an answer bank.Some researchers have suggested that the isometric shapes on the PSVT:R can look confusing and can be mistaken for flat patterns instead of 2D images.Hoffman's rules related to the principles of generic views explain why many of the shapes would be difficult to interpret as 3D forms.For example, lines that would not be coinciding in 3D coincide in the isometric drawings in the PSVT:R.In our study, we showed a subset of the shapes on the revised PSVT:R to a group of 111 engineering students enrolled in an introductory engineering graphics course, and had them perform a sorting task to determine which shapes they viewed as real 3D shapes and which they did not.Our results showed that at least 19% of the answer bank shapes in the PSVT:R were not viewed as real 3D shapes by most participants, and at least 38% were not viewed as real 3D shapes by some participants.We conclude that the use of isometric views in the PSVT:R presents a threat to instrument validity if the test is to be considered to assess mental rotation ability.Performance on the test is likely impacted by the test-taker's acquired knowledge of the conventions of isometric drawing in the Cartesian coordinate plane and the use of deductive reasoning to relate ambiguous generic views to 3D forms.

The purpose of the study was to compare the influence of dynamic geometry software activities and influence of the physical manipulatives and drawing activities on the spatial ability and van Hiele levels of pre-service primary school teachers in a geometry course. A quasi-experimental statistical design was used in the study. The participants were 61 pre-service primary teachers in the second year of their undergraduate program in the Department of Elementary Education at Afyon Kocatepe University. A total of 32 pre-service teachers (computer group) were trained in the dynamic geometry based activities and 29 pre-service teachers (physical-drawing group) were trained in the physical manipulative and drawing based activities. In order to determine the two groups of the pre-service teachers’ geometric thinking levels, the van Hiele Geometry Test and in order to determine the two groups of the pre-service teachers’ spatial ability, The Purdue Spatial Visualization Test was used as the pre-test and post-test. The results of the study showed that there was no difference on the post-test of the two groups related to the van Hiele levels and spatial abilities. Moreover, both groups have significantly higher achievement on the post-test compared to the pre-test.

The Purdue Spatial Visualization Test: Rotations (PSVT:R) is commonly used in engineering education to measure spatial ability in efforts to predict academic or vocational success, or as a placement test. However, the politics of the instrument are rarely discussed. Here I provide a critical review of the historical literature that provides the basis for current work using the PSVT:R. I examine the validation and popularization of the PSVT:R, discuss how the instrument may not actually measure mental rotation, and explain how the construct of ‘gestalt processing’ was created in an effort to raise the status of spatial instruments which favored men. I argue that the isometric imagery style used in the test, which is rooted in the masculinized discipline of engineering graphics, further politicizes the test. I discuss the usage of the PSVT:R in spatial training efforts targeting historically excluded groups, and how understanding the politics of the PSVT:R should inform future efforts.

Active Teaching Techniques Using Virtual Didactics: Novel Experience From a National Neurosurgery Resident Course

In the realm of virtual reality (VR) research, the synergy of methodological advancements, technical innovation, and novel applications is paramount. Our work encapsulates these facets in the context of spatial ability assessments conducted within a VR environment. This paper presents a comprehensive and integrated framework of VR, eye-tracking, and electroencephalography (EEG), which seamlessly combines measuring participants’ behavioral performance and simultaneously collecting time-stamped eye tracking and EEG data to enable understanding how spatial ability is impacted in certain conditions and if such conditions demand increased attention and mental allocation. This framework encompasses the measurement of participants’ gaze pattern (e.g., fixation and saccades), EEG data (e.g., Alpha, Beta, Gamma, and Theta wave patterns), and psychometric and behavioral test performance. On the technical front, we utilized the Unity 3D game engine as the core for running our spatial ability tasks by simulating altered conditions of space exploration. We simulated two types of space exploration conditions: (1) microgravity condition in which participants’ idiotropic (body) axis is in statically and dynamically misaligned with their visual axis; and (2) conditions of Martian terrain that offers a visual frame of reference (FOR) but with limited and unfamiliar landmarks objects. We specifically targeted assessing human spatial ability and spatial perception. To assess spatial ability, we digitalized behavioral tests of Purdue Spatial Visualization Test: Rotations (PSVT: R), the Mental Cutting Test (MCT), and the Perspective Taking Ability (PTA) test and integrated them into the VR settings to evaluate participants’ spatial visualization, spatial relations, and spatial orientation ability, respectively. For spatial perception, we applied digitalized versions of size and distance perception tests to measure participants’ subjective perception of size and distance. A suite of C# scripts orchestrated the VR experience, enabling real-time data collection and synchronization. This technical innovation includes the integration of data streams from diverse sources, such as VIVE controllers, eye-tracking devices, and EEG hardware, to ensure a cohesive and comprehensive dataset. A pivotal challenge in our research was synchronizing data from EEG, eye tracking, and VR tasks to facilitate comprehensive analysis. To address this challenge, we employed the Unity interface of the OpenSync library, a tool designed to unify disparate data sources in the fields of psychology and neuroscience. This approach ensures that all collected measures share a common time reference, enabling meaningful analysis of participant performance, gaze behavior, and EEG activity. The Unity-based system seamlessly incorporates task parameters, participant data, and VIVE controller inputs, providing a versatile platform for conducting assessments in diverse domains. Finally, we were able to collect synchronized measurements of participants’ scores on the behavioral tests of spatial ability and spatial perception, their gaze data and EEG data. In this paper, we present the whole process of combining the eye-tracking and EEG workflows into the VR settings and collecting relevant measurements. We believe that our work not only advances the state-of-the-art in spatial ability assessments but also underscores the potential of virtual reality as a versatile tool in cognitive research, therapy, and rehabilitation.

Line segment clipping is a basic operation of the visualization process in computer graphics. So far there exist four computational models for clipping a line segment against a window, (1) the encoding, (2) the parametric, (3) the geometric transformation, and (4) the parallel cutting. This paper presents an algorithm that is based on the third method. By making use of symmetric properties of a window and transformation operations, both endpoints of a line segment are transformed, so that the basic cases are reduced into two that can be easily handled, thus the problems in NLN and AS where there are too many sub-procedure calls and basic cases that are difficult to deal with are tackled. Both analytical and experimental results from random input data show that the algorithm is better than other developed ones, in view of the speed and the number of operations.

Geometric transformations are most commonly represented as square matrices in computer graphics. Following simple geometric arguments we derive a natural and geometrically meaningful definition of scalar multiples and a commutative addition of transformations based on the matrix representation, given that the matrices have no negative real eigenvalues. Together, these operations allow the linear combination of transformations. This provides the ability to create weighted combination of transformations, interpolate between transformations, and to construct or use arbitrary transformations in a structure similar to a basis of a vector space. These basic techniques are useful for synthesis and analysis of motions or animations. Animations through a set of key transformations are generated using standard techniques such as subdivision curves. For analysis and progressive compression a PCA can be applied to sequences of transformations. We describe an implementation of the techniques that enables an easy-to-use and transparent way of dealing with geometric transformations in graphics software. We compare and relate our approach to other techniques such as matrix decomposition and quaternion interpolation.

Background The COVID-19 pandemic has resulted in innumerable unprecedented challenges in the medical education system. Among other factors, personal protective equipment restrictions, contact limitations, and social distancing measures have all significantly altered the structure of undergraduate medical education and have required rapid adaptation to an ever-changing environment. For the majority of institutions, in-person courses and clerkships were halted abruptly in mid-March as schools were forced to transition to a completely virtual learning environment for the remainder of the 2019-2020 academic year. Heading into the 2020-2021 academic year with the knowledge that the COVID-19 pandemic would affect the fall semester at the very least, many medical schools developed plans to reopen in some capacity. Methods The publicly available reopening plans of U.S. MD programs were evaluated at the start of fall semester and at the end of fall semester. Results All schools adopted a version of hybrid medical education, and mask use, social distancing of more than 6 feet at all times, and enhanced disinfection of common areas were universally implemented. 23 of 25 medical schools continued to require that students attend activities like anatomy lab and clinical skills simulations in-person. Every school prohibited clinical students from taking care of patients with a confirmed or suspected diagnosis of COVID-19. Discussion As the pandemic surpasses one year in duration and the undergraduate medical education system concludes its first full pandemic year, this paper focuses on how medical schools have responded thus far to this crisis, where the current data stands in relation to safety of school reopening, and how the structure of undergraduate medical education has been changed forever.

PurposeThe disruption of undergraduate medical education (UME) by the COVID-19 pandemic has sparked rapid, real-time adjustments by medical educators and students. While much is known about online teaching in general, little guidance is available to medical educators on how to adapt courses not originally designed for the online environment. To guide our faculty in this transition we conducted a needs assessment of students enrolled in virtual courses across all 4 years of UME training.MethodsUsing a mixed-methods approach, we conducted a single-institution virtual learning needs assessment in May and June of 2020. We developed and disseminated a survey to assess student experiences with virtual learning. We conducted quantitative and qualitative analysis of responses (n = 255 or 39%) to identify emergent themes.ResultsWe identified six interdependent themes that need to be met for medical students to fully reach their learning potential: access to stable internet and quiet study spaces, flexible course design with asynchronous, self-paced components, clear expectations for engagement with content and each other, a sense of connectedness with faculty and peers, synchronous classes that maximize interactivity, and assessments that foster a sense of learning over performance. Interpersonal relationships with faculty and peers affected students’ sense of learning more than any other factor.ConclusionsBased on our findings we propose a hierarchy of needs for virtual learning that provides guidance on adapting existing medical school courses to the remote setting and overcoming common challenges. We highlight opportunities for how virtual elements may enrich in-person courses going forward, including in the clinical setting. Although the solutions required to meet the threshold of need at each level may differ based on the context, attending to these same fundamental needs can be extrapolated and applied to learners across a range of environments beyond the virtual.