Investigation of the ways prospective mathematics teachers respond to students’ errors: An example of the equal sign

This study aims to determine how prospective middle school mathematics teachers respond to students’ errors in the questions about the equal sign. This study utilizes case study method. In this case study, hypothetical scenarios, involving three common error types related to the equal sign, have been prepared by using the possible examples of student work. Through these scenarios, one-to-one interviews were conducted with seven prospective middle school mathematics teachers. In line with the data obtained in these interviews, it was seen that the prospective teachers used seven different ways to respond to students’ errors related to the equal sign: showing the error, showing the right solution, guiding to find the right answer, guiding to find the error, re-explaining the concept, in-depth research, and false intervention. In addition, it was determined that two prospective teachers intervened incorrectly by taking an approach that could support the thought that led to the error. In the light of the findings, it was seen that the prospective teachers had a limited understanding of the equal sign. This study suggests that mathematics educators should create appropriate learning opportunities to improve prospective teachers’ understanding of the equal sign and their ability to respond to students’ error

Turkish Pre-service Secondary Mathematics Teachers: An Examination of TPACK, Affect, and Their Relationship

Pre-service teachers\u27 knowledge, beliefs or attitudes gained during their undergraduate education is one of the most influential factors shaping their future teaching in their field. Technological Pedagogical Content Knowledge framework (TPACK; Mishra & Koehler, 2006) identifies the knowledge domains needed by teachers to effectively integrate technology into teaching their field. Due to the fact that pre-service teachers\u27 TPACK domains cannot be directly measured, most of research studies in the literature addressed developing a TPACK survey instrument in order to indirectly measure teachers\u27 TPACK in terms of their perceptions. However, there were rare research studies focusing on development a TPACK survey instrument for pre-service secondary mathematics teachers, especially in Turkey too. Therefore, the main goal of this study is to examine Turkish pre-service secondary mathematics teachers\u27 perceptions regarding TPACK domains, as well as adapting TPACK survey instrument, developed by Zelkowski and his colleagues (2013), into Turkish language and context. Another purpose of this study is to investigate the relationships among TPACK components, and the relationships of pre-service teachers\u27 attitudes towards use of technology in education with their TPACK components. This study also aims to explore the effects of demographics differences (gender and year of enrollment) on their perceptions regarding TPACK domains and attitudes. Survey, correlational and causal-comparative research designs were used in this study. To adapt the TPACK survey instrument into Turkish, the following processes were used: forward translation, backwards translation, comparison of original TPACK survey with backward translation, expert reviews and cognitive interviews. The data were collected in terms of two studies, the pilot and main studies, during the fall semester of 2016 in Turkey. Two survey instruments, the Turkish TPACK and Attitude scale towards Computer-Aided Education (Arslan, 2006), were used to collect the data. The total of 778 pre-service secondary mathematics teachers participated in this study as volunteer. The pilot study data was used to examine translation of the Turkish TPACK survey instrument and to determine its hypothesized factor structure. The main study data was utilized to validate its factor structure and to conduct further statistical analysis related to the research questions. The results of factor and reliability analysis showed that the Turkish TPACK survey instrument is valid and reliable for five factors (TK, CK, PK, TPK, and TPACK) including 29 items. The findings of correlations analysis indicated that there were significant positive correlations among five TPACK components with small or moderate effect sizes. In addition, the relationships of pre-service teachers\u27 attitudes with TPACK components were positive and significant, with small or moderate effect sizes. The results of MANOVA displayed that the linear combination of TPACK components differentiated with respect to pre-service teachers\u27 gender and year of enrollment. According to findings of MANOVA, male pre-service teachers had significantly better perceptions about TK and CK than females. Furthermore, fifth grades showed significantly higher perceptions related to CK and TPACK than first and second grades, as well as third grades had greater perceptions on CK than first grades. The findings of ANOVA revealed that there were no statistically differences of pre-service teachers\u27 attitudes towards use of technology with respect to gender, although they had significantly mean differences in regard to year of enrollment. According to the results of ANOVA, five grades had more positive attitudes than first and second grades, as well as third grades had more positive attitudes than first grades. Regarding of finding in this study, future research may focus on which factors influence the development of pre-service teachers\u27 TPACK by means of experimental research studies; and on why male and female pre-service teachers\u27 perceptions in associated with some of TPACK components become different

Bibliometric analysis of scientific studies conducting on noticing skill in mathematics education

hil olmak üzere bibliyometrik verilerle ilgili yayınlanmış literatürü tanımlamak, değerlendirmek ve izlemek için kullanılan bir istatistiksel analiz türüdür. Bu çalışmada fark etme becerisi ile ilgili yayınlanmış bilimsel çalışmaların bibliyometrik analizi yapılmıştır. WoS veri tabanından SSCI ya da ESCI indexli 128 yayın incelenmiştir. Elde edilen bulgulara göre en fazla yayın yapan ülkelerin “Amerika Birleşik Devletleri”, “Türkiye” ve “Almanya”; en fazla yayın yapılan dergilerin “journal of mathematics teacher education”, “international journal of science and mathematics education” ve “zdm-mathematics education”; en çok yayın yapan üniversitelerin “Hamburg Üniversitesi”, “Michigan Eyalet Üniversitesi” ve “Northwestern Üniversitesi” olduğu görülmüştür. Ayrıca fark etme becerisi ile ilgili kavramsal yapı ortaya çıkarılmış ve görselleştirilerek sunulmuştur.Bibliometric analysis is the one of the statistical analysis methods, which is conducted to illustrate, evaluate and keep track of an interested literature using bibliographic data including citation information about authors, publications, institutions, journals, and countries. In this study, it was performed a series of bibliometric analysis related to the published research on noticing skills in the literature. 128 publications with SSCI or ESCI index were examined from WoS database. In the light of the findings, it was seen that the USA, Turkey and Germany are the most productive countries on noticing skills research in mathematics education. In addition, the journal with the most publications are “journal of mathematics teacher education”, “international journal of science and mathematics education” and “zdm-mathematics education”, respectively. Moreover, the most productive institutions on noticing skills research in mathematics education are “University of Hamburg”, “Michigan State University” and “Northwestern University”, respectively. Finally, it was visualized the conceptual structure of the research related to noticing skills in this study

Analysis, Design, and Optimization of Structures with Integral Compliant Mechanisms for Mid-Frequency Response

An analysis, design, and optimization methodology for structures that vibrate in the 1 kHz to 10 kHz frequency range has been developed. This methodology is the synthesis of several established research fields including structural dynamics, compliant mechanism design, finite element computational analysis, and structural optimization via an evolutionary algorithm.Ph.D.Mechanical EngineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/60284/1/Dede_Dissertation.pd

Kilohertz magnetic field focusing in a pair of metallic periodic-ladder structures

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98699/1/ApplPhysLett_99_093501.pd

Use of hidden robot concept for calibration of an over-constrained mechanism

Overconstrained mechanisms prove useful in applications where high stiffness and low weight is required against high amount of forces while keeping high precision. This study issues a planar two degrees-of-freedom overconstrained parallel manipulator for positioning the end-effector with high acceleration values (>5g) with a positioning precision in the order of 30 micrometers. Since the manufacturing errors were compatible with the end-effector positioning errors, it was required to perform some system identification before the precision and repeatability tests. For the system identification, the end-effector position and motor input values are recorded. However, since the mechanism is overconstrained, the link lengths could not be obtained due to the lack of analytical inverse kinematics solution. In order to cope with this problem, the hidden robot concept is utilized in order to fit a simple kinematic model between the task space and the joint space of the manipulator. Further calibration studies are carried out using the error correction matrix. The test results are presented

Historical Space Steps of Turkey: It Is High Time to Establish the Turkish Space Agency

This paper discusses the importance of space in today’s space driven world, the current space activities of Turkey, its space organizations with legislation background information and calls for the necessity for the establishment of the Turkish Space Agency (TSA). Firstly, the importance of space is given which is followed by a brief background and current space activities in Turkey. Then, the answers to why Turkey needs a National Space Agency are outlined by stating its expected role and duties. Additionally, the framework for space policy for Turkey is proposed and the findings are compared with other developing regional space actors. Lastly, it is proposed and demonstrated that Turkey is on the right track with its space policy and it is suggested that the establishment of the TSA is critical both for a coherent space policy and progress as well as the successful development of its national space industry, security and international space relations

Design and analysis of a parallel mechanism for kinematically redundant hybrid planar laser cutting machine

Conventional planar laser cutting machines cannot achieve high accelerations, because the required precision values cannot be achieved due to the high inertial loads. Machines configured as kinematically redundant mechanisms are able to reach 5-6 g acceleration levels since they include a parallel mechanism with a smaller workspace which is exposed to smaller inertial loads. The study presented in this paper focuses on the design of a parallel planar mechanism to be integrated to the main axes of conventional planar laser cutting machines to achieve higher accelerations of the laser head up to 6 g. Parallel mechanism’s conceptual design and dynamic balancing studies are provided along with the joint clearance effect on precision due to having more joint structures.Republic of Turkey Ministry of Science, Industry and Technology & Coşkunöz Metal Form (Project code: 01668.STZ.2012-2

Bakışımsız bir düzlemsel 5R eyleyicisinin bağlama açına göre tasarımı

İki serbestlik dereceli düzlemsel 5R (R: döner mafsal) mekanizmasının uç noktasının işlevsel çalışma alanına göre mekanizma tasarımı çok farklı başarım ölçütlerine göre yapılabilmektedir. Bu çalışmada uç noktasının yerleşimi nedeni ile kinematik yapısı ve çalışma alanı bakışımsız olan bir 5R mekanizmasının bağlama açısının dik açıya yakın tutulması ölçütü uyarınca işlevsel çalışma alanının tespiti ve de istenilen çalışma alanına boyutuna göre uzuv boyutlarının seçimi ele alınmıştır. Mekanizmanın çalışma alanının tespiti için gerekli kinematik model oluşturulmuş, bağlama açısına göre işlevsel çalışma alanı tespiti irdelenmiş, çalışma alanına gör uzuv boyutlarının belirlenmesi açıklanmış ve de bağlama açısının kuvvet iletimine etkisi tartışılmıştır.There are many performance indices defined for the design of two degrees-of-freedom planar 5R (R: revolute joint) mechanisms according to the dexterous workspace of the end effector. In this study, the performance index was chosen as the transmission angle in order to determine the dexterous workspace of an asymmetric planar 5R mechanism. Also design of link lengths according to a desired dexterous workspace is explained. First, the necessary kinematic model for determining the workspace of the mechanism is constructed. Then the formulation is presented for determining the dexterous workspace according to transmission angle. Finally the effect of the transmission angle on force transmission characteristics is discussed