Paper 1: Preservice Teachers’ Mapping Structures Acting on Representational Quantities

In this article, I write about my research on five preservice secondary teachers’ (PST) understanding and sense making of representational quantities associated with magnetic color cubes and tiles. Data came from individual interviews during which I asked PST problems guided by five main tasks: prime and composite numbers, summation of counting numbers, odd numbers, even numbers, and polynomial expressions in x and y. My work drew upon an analysis framework (Behr et. al, 1994) supported by a unit coordination construct (Steffe, 1988) associated with linear and areal quantities inherent in the nature of figures produced by these PST. Linear quantities can be thought of as generated via linear measurement units (e.g., inches, centimeters, units) whereas areal quantities are generated via areal measurement units (e.g., square inches, square centimeters, square units, etc.) I used thematic analysis supported by constant comparison and retrospective analysis to explain my theories and hypotheses concerning PST’s representational quantities. I developed a data analysis framework which I named “Relational Notation” to describe these PST’s understanding of linear and areal units. PST also treated the quantitative multiplication and addition operations as some kind of functions, mappings, when expressing the area of their growing rectangles made of magnetic color cubes and tiles as sums and products. Their behavior necessitated the existence of another component for my data analysis framework which I called “Mapping Structures

A Bayesian time-to-event pharmacokinetic model for sequential phase I dose-escalation trials with multiple schedules

Phase I dose-escalation trials constitute the first step in investigating the safety of potentially promising drugs in humans. Conventional methods for phase I dose-escalation trials are based on a single treatment schedule only. More recently, however, multiple schedules are more frequently investigated in the same trial. Here, we consider sequential phase I trials, where the trial proceeds with a new schedule (e.g. daily or weekly dosing) once the dose escalation with another schedule has been completed. The aim is to utilize the information from both the completed and the ongoing dose-escalation trial to inform decisions on the dose level for the next dose cohort. For this purpose, we adapted the time-to-event pharmacokinetics (TITE-PK) model, which were originally developed for simultaneous investigation of multiple schedules. TITE-PK integrates information from multiple schedules using a pharmacokinetics (PK) model. In a simulation study, the developed appraoch is compared to the bridging continual reassessment method and the Bayesian logistic regression model using a meta-analytic-prior. TITE-PK results in better performance than comparators in terms of recommending acceptable dose and avoiding overly toxic doses for sequential phase I trials in most of the scenarios considered. Furthermore, better performance of TITE-PK is achieved while requiring similar number of patients in the simulated trials. For the scenarios involving one schedule, TITE-PK displays similar performance with alternatives in terms of acceptable dose recommendations. The \texttt{R} and \texttt{Stan} code for the implementation of an illustrative sequential phase I trial example is publicly available at https://github.com/gunhanb/TITEPK_sequential

Takotsubo Syndrome: Still Graveyard of Case Reports?

Takotsubo syndrome, or previously named as Takotsubo cardiomyopathy, is an increa-singly recognized acute reversible form of heart failure, which is typically seen in post-menopausal women following emotional or physical stress. Although several mechanisms regarding pathophysiology had been proposed, the most common ones include catecholamine toxicity, diffuse epicardial coronary artery spasm and microvascular dysfunction. A vast majority of patients with TTS (>90%) have good prognosis as they regain normal left ventricular systolic function in 3–6 months after the acute phase. Increased awareness among physicians led to the recognition of a great number and variety of conditions associated with TTS and played a key role for the development of new diagnostic criteria. However, there are still big gaps in the management and treatment of this syndrome to be supported with further well-designed randomized controlled trials

PRİZMALAR KONUSUNDA DRAMA YÖNTEMİNİN UYGULANMASI

Bu araştırmada, geometri öğretiminde drama yönteminin uygulanmasının öğrencilerin bu yönteme bakış açılarını ve geometriye yönelik özyeterlik inançlarına etkisini belirlemek amaçlanmıştır. Araştırmaya ilişkin denel işlem 2006–2007 öğretim yılı bahar döneminde İzmir‟de bir ilköğretim okulunda gerçekleştirilmiştir. Çalışma grubunu altıncı sınıftan 20 öğrenci oluşturmaktadır. Araştırmada ilköğretim altıncı sınıf "Dik Prizmaların Yüzey Alanları ve Hacimleri" konusunda drama yöntemi kullanılmıştır. Veri toplama araçları olarak öğrencilerin özyeterlik inançlarını belirlemek için "Geometriye Yönelik Özyeterlik Ölçeği" ve "Görüşme Formu" kullanılmıştır. Araştırma verileri normal dağılıma uyduğu için verilerin analizinde ilişkili ortalamalar t testi kullanmıştır. Araştırmanın sonucunda elde edilen verilere dayanarak, öğrencilerin bu yöntemi eğlenceli ve yararlı bulduklarını ifade ettikleri ayrıca öğrencilerin geometriye yönelik özyeterlik inançlarında beklenen düzeyde bir etki yapmadığı yargısına ulaşılmıştır. ABSTRACT: The purpose of this study is to determine the students‟ views as to the fact that drama method be used in teaching geometry and also to establish their viewpoints concerning this method and its effect on their self-efficacy towards geometry. The procedure relating to the research was implemented at a primary school in Izmir during the 2006-2007 academic years‟ spring term. The participants of the study were composed 20 sixth grade students. In the study, drama method was used on the subject of the surface areas and volumes of vertical prisms in mathematics of sixth grade. As for data collection tools, "Self-Efficacy toward Geometry Scale" and "Interview Form" were used to determine the students‟ beliefs of self-efficacy. In the analysis of the data, Paired Samples t-Test was used as the data of the research were compatible with normal distribution. Based on the data obtained from the investigation, it was found that the students said that the creative method was entertaining and useful. Besides, it was seen that there was no meaningful differences in favor of using drama method in Mathematics lessons