The Development of Secondary Mathematics Teachers’ Pedagogical Identities in the Social Context of Classroom Interactions

Research demonstrates a disjuncture between the practices encouraged by teacher education programs and what teachers actually do in the classroom. It also informs us that the cognitive and social characteristics of individual teachers such as their attitudes, beliefs and knowledge contribute to their classroom practices. This qualitative study investigates how the teacher identity of mathematics teachers – the person’s sense of who he/she is as a mathematics teacher – is related to the disjuncture between encouraged and actual classroom practices. Specifically, the study looks into how mathematics teachers form their teaching practices in the social context of their classroom interactions, and tries to understand the nature of the discomfort that teachers sometimes experience in the process of shaping their classroom role and teaching practices. The study takes a dialogical approach to identity, seeing the self as something that an individual develops through interactions between his or her core “substantial self” and context-dependent “situational selves.” The qualitative data were collected from four in-service high school teachers in the United States. The study sheds light on the variability of the process of shaping teaching practices; it discusses factors in this variability, and explores how teachers develop and settle into their practices through negotiation between the substantial self and situational selves in the classroom context

Rotation Correction Method Using Depth-Value Symmetry of Human Skeletal Joints for Single RGB-D Camera System

Most red-green-blue and depth (RGB-D) motion-recognition technologies employ both depth and RGB cameras to recognize a user\u27s body. However, motion-recognition solutions using a single RGB-D camera struggle with rotation recognition depending on the device-user distance and field-of-view. This paper proposes a near-real-time rotational-coordinate-correction method that rectifies a depth error unique Microsoft Kinect by using the symmetry of the depth coordinates of the human body. The proposed method is most effective within 2 m, a key range in which the unique depth error of Kinect occurs, and is anticipated to be utilized in applications requiring low cost and fast installation. It could also be useful in areas such as media art that involve unspecified users because it does not require a learning phase. Experimental results indicate that the proposed method has an accuracy of 85.38%, which is approximately 12% higher than that of the reference installation method

The Expected Value of a Random Variable: Semiotic and Lexical Ambiguities

In calculus-based statistics courses, the expected value of a random variable (EVORV) is discussed in relation to underlying mathematical notions. This study examines students’ understanding of the mathematical notions of EVORV in connection with its semiotic and lexical representations. It also assesses students’ computational competency revolving around EVORV. We collected qualitative data via surveys and interviews from eight students enrolled in a calculus-based university statistics course. The results suggest that while the students in general had the computational accuracy to correctly calculate EVORV, they struggled to understand the notion, and in particular to make sense of the term “random” in “random variable” and the symbol E() in the mathematical context. The study provides a basis for understanding potential challenges to students’ learning of EVORV and other related statistics topics and how such challenges may emerge from the semiotic and lexical ambiguities inherent in terms and symbols used in statistics

Generic features of the cosmological evolution of density parameters

The evolution of various energy components with dark energy was examined. Recently many non-standard gravity models were suggested to explain the current observational data showing an accelerating phase since the recent past. All suggested models should mimic ΛCDM somehow, especially from the near past to the current epoch. However, most of them do not try to explain or predict what happens if their model were extended to the far past and/or the past. In this paper we want to address this point by analyzing the critical points of the evolution equations and their stability. Standard ΛCDM gives three critical points, radiation dominated, matter dominated, and cosmological constant dominated. Furthermore, the radiation-dominated point corresponds to the past stable point, the matterdominated point to the saddle point, and the cosmological-constant–dominated point to the future stable point. This means that this model predicts that the universe starts from radiation domination then passes through a matter-dominated era and finally evolves into a cosmological-constant–dominated era, that is, the future de Sitter phase. We applied these creteria to few f(R) gravity models to determine viable parameter ranges

Physically-based simulation of ice formation

The geometric and optical complexity of ice has been a constant source of wonder and inspiration for scientists and artists. It is a defining seasonal characteristic, so modeling it convincingly is a crucial component of any synthetic winter scene. Like wind and fire, it is also considered elemental, so it has found considerable use as a dramatic tool in visual effects. However, its complex appearance makes it difficult for an artist to model by hand, so physically-based simulation methods are necessary. In this dissertation, I present several methods for visually simulating ice formation. A general description of ice formation has been known for over a hundred years and is referred to as the Stefan Problem. There is no known general solution to the Stefan Problem, but several numerical methods have successfully simulated many of its features. I will focus on three such methods in this dissertation: phase field methods, diffusion limited aggregation, and level set methods. Many different variants of the Stefan problem exist, and each presents unique challenges. Phase field methods excel at simulating the Stefan problem with surface tension anisotropy. Surface tension gives snowflakes their characteristic six arms, so phase field methods provide a way of simulating medium scale detail such as frost and snowflakes. However, phase field methods track the ice as an implicit surface, so it tends to smear away small-scale detail. In order to restore this detail, I present a hybrid method that combines phase fields with diffusion limited aggregation (DLA). DLA is a fractal growth algorithm that simulates the quasi-steady state, zero surface tension Stefan problem, and does not suffer from smearing problems. I demonstrate that combining these two algorithms can produce visual features that neither method could capture alone. Finally, I present a method of simulating icicle formation. Icicle formation corresponds to the thin-film, quasi-steady state Stefan problem, and neither phase fields nor DLA are directly applicable. I instead use level set methods, an alternate implicit front tracking strategy. I derive the necessary velocity equations for level set simulation, and also propose an efficient method of simulating ripple formation across the surface of the icicles