Dialogic Teaching Model For Ninth Class Students To Conceptualize Inequalities

It is known that difficulties are often experienced in conceptual learning of mathematics, which is an abstract lesson. For this reason, it is difficult for students to conceptually learn inequalities, one of the difficult subjects of mathematics. The aim of this study is to investigate the effect of dialogic teaching to overcome the general mistakes and difficulties of 9th grade students in deepening the conceptual teaching of inequalities. This study was designed as an action research. The answers and solutions given to 7 open-ended questions prepared to determine students’ misconceptions and mistakes were scored between 0 and 2 points. When a detailed analysis of solutions written by the students was done, it was determined that the students had difficulty in establishing the concept of numbers, that they ignored the real numbers in a defined range and only focused on integers, that they ignored zero when finding the square of the inequality in a defined range, and that they had difficulty in understanding the principle of reversing when the inequality was multiplied by a negative number and also had difficulty in the solution of inequalities when two inequalities were combined into a single inequality. According to the results of the research, dialogic teaching played a supporting role for the students to reach the conceptual learning of inequalities. It was also seen that high school students were able to reconstruct the concept of inequality conceptually in the learning process. Keywords: dialogic teaching, inequalities, conceptual teaching, reconstructin

Linear motor for multi-car elevators, design and position measurement

Multi-car elevator is an emerging technology consisting of two or more elevator cars moving independently in an elevator hoistway, which has become more appealing as building heights increase. In this paper, the design and drive methodologies for a linear motor driven multi-car elevator system with independently moving cars is introduced together with experimental results. Additionally, a safety method developed for the linear motor elevator and the conditions necessary for its proper operation are discussed. The new results introduced in this paper are in the areas of the design method of the linear motor for multi-car elevator system, and the preliminary results for the position measurement system

An inventory model with two suppliers under yield uncertainity

Cataloged from PDF version of article.In this study, an inventory model with one retailer and two suppliers is considered for a single item. Di erent from most of the models in inventory literature, we do not make the assumption that we receive all the quantity that we ordered. It is assumed that a random fraction of the lot size is actually delivered by the suppliers. Hence, the model is constructed under yield uncertainty for both binomial yield and stochastically proportional yield model. The demand rate is constant, and backordering is allowed. The ob jective is to minimize the long-run average cost and nd the near optimal values for the decision variables; order quantities and reorder point. Furthermore, the regions where diversi cation among suppliers is bene cial are investigated. The results are generalized to \M" suppliers (M>2) and solution method is proposed. Finally, experimental study is carried out for the two-suppliers problem.Gürbüz, Mustafa ÇağrıM.S

AN ANALYSIS OF HOW PRESERVICE MATH TEACHERS CONSTRUCT THE CONCEPT OF LIMIT IN THEIR MINDS

Recently, people prefer learning information operationally rather than conceptually. In this context, this study was carried out to uncover how preservice math teachers construct in their minds the conceptual definition of limit within the scope of the Calculus Course. The participants of this study consisted of 62 (30 female, 32 male) sophomore students studying in the Elementary Mathematics Teacher Education Department at Uludağ University Faculty of Education in the 2016–2017 academic year. Midterm and final exam questions requiring the use of prior knowledge were used to help collect data. Interviews were conducted with three participants who were chosen for their success. In these interviews, five questions were asked by the researchers to uncover the mathematical thinking levels and abstraction processes of the participants. The methods of semi-structured interviews and observations were used to collect data. The data were video-recorded and transcribed. The transcripts were analyzed and interpreted according to the cognitive actions of the RBC- model and the steps in Sfard’s theory of mathematics learning. Based on the analysis, the participants were found to be more successful in operational information than in conceptual information. Although the preservice teachers were able to accomplish operational learning, it can be said that they could not fully accomplish conceptual learning because they could not identify algebraic representations and could not use reasoning on these representations. Interviews with the participants revealed that they memorized the characteristics of the concept of limit to be successful in the exams. However, conceptual learning did not take place. Understanding how participants learn is believed to benefit the educators who teach the concept of limit.  Article visualizations

Active position measurement method for ropeless linear motor elevators

Elevators in modern high-rise buildings face two main difficulties: physical limitation of the traction cable that actuates the elevator car because of stretch, and loss of floor-space because numerous elevator hoistways are required to keep passenger waiting time low. Ropeless elevators where the elevator car is propelled by a linear motor that spans the whole hoistway is one strong solution candidate. They eliminate the traction cable and enable several elevator cars to travel independently in one hoistway. For freedom of movement, however, no cables must be attached to the traveling elevator car. Although the traction can be designed to satisfy this requirement, measurement of the position of the elevator car for the purpose of motor drive using the conventional techniques requires a linear encoder, which must have an electrical connection. In this thesis we propose LinearMotor Active PositionMeasurement Method (LIMAP) which is based on the principle of linear variable differential transformer. It utilizes the coils of the motor just ahead of the elevator car that are not used for traction and a magnetic shunt fixed at a known distance from the elevator car, for position measurement. The position can be determined by exciting one of the coils under the shunt while measuring the mutual inductance with the neighboring coils. Our second contribution is a design method based on finite element methods that can be used to determine the best size magnetic shunt to meet the design criteria. The third important contribution is a position search algorithm that can work under the nonlinear characteristics of the sensor in real-time. Results based on the finite element simulations of an existing motor are given, followed by actual experiments on a real motor. The results agree well to demonstrate the validity of the proposed approach

Investigating secondary school students' abstraction processes of algebraic concepts

Öğrencilerden günümüzde çok bilgiye sahip olmalarından ziyade mevcut bilgilerini problem çözme, akıl yürütme, iletişim gibi matematiksel düşünmenin temelini oluşturan becerileri kullanarak çeşitli amaçları gerçekleştirmeleri beklenmektedir. Çalışmada matematiksel düşünme, öğrencinin matematik kavramlarını zihninde nasıl yapılandırdığını açıklamaya yönelik olarak ele alınmıştır. Bu yapılandırma süreci ise matematiksel soyutlama çerçevesinden izlenmiştir. Matematiksel soyutlama, matematik kavramının genelleştirilmesi yoluyla kavrama daha kapsamlı bir uygulama alanı oluşturulması, diğer bir ifade ile kavramın özünü ortaya çıkarması işlemidir. Öğrencilerin zihninde bilginin oluşum sürecini doğrudan gözlemlemek oldukça zor bir durum olarak karşımıza çıkmaktadır. Bilginin öğrencinin zihninde nasıl oluştuğu, soyutlandığı ve hangi içsel süreçlerden geçtiği bilinirse öğrenme sürecine etkili müdahalelerde bulunmak kolaylaşacaktır. Bu çalışmada, ortaokul öğrencilerinin temel cebir kavramlarına yönelik soyutlama süreçlerinin incelenmesi amaçlanmıştır. Soyutlama süreçlerinin incelenmesinde RBC+C (Recognizing, Building with, Construct, Consolidation) teorisinde yer alan epistemik eylemler dikkate alınmıştır. Ayrıca araştırma sürecinde öğrencilerin soyutlama süreçlerinin daha iyi gözlenmesini sağlamak için Tahmini Öğrenme Yörüngeleri kullanılmıştır. Öğrenme yörüngelerinin öğrencilerin temel cebir kavramlarındaki başarılarına etkilerinin ve soyutlama süreçlerine olan yansımalarının tespit edilmesi araştırmada ortaya koyulması amaçlanan diğer bir husustur. Araştırma, belirlenen amaçlara ulaşmak için iki aşamalı tasarlanmıştır. İlk olarak öğrencilerin cebirin iki temel kavramı olan denge ve değişken kavramlarını soyutlama süreçlerini daha net görebilmek ve süreçte onların soyutlama yapmalarını desteklemek amacıyla tasarım tabanlı araştırma modelinden faydalanılmıştır. Tasarım tabanlı araştırma, öğrencilerin soyutlama süreçlerinin daha iyi anlaşılabilmesi için öğrenme ortamına müdahale edilmesine olanak sağlamaktadır. Araştırmanın ikinci aşaması ise bir durum çalışması olarak değerlendirilmiştir. Tasarımın uygulanabilirliği ve eksiklikleri sınıf içi gözlemler yoluyla; öğrencilerin soyutlama becerileri ise yarı yapılandırılmış öğrenci görüşmelerinden elde edilen veriler ile analiz edilmiştir. Katılımcılar Bursa İli, Nilüfer İlçesi’nde bir devlet okulunda öğrenim gören 6. sınıf öğrencileri arasından amaçlı örnekleme ile seçilmiştir. Aynı öğrencilerle 7. sınıf düzeyine geçtiklerinde veri toplama sürdürülmüştür. 2016-2017, 2017-2018 eğitim öğretim dönemlerinde araştırmacı ve öğretmen ile birlikte bu sınıfların matematik derslerinde araştırma gerçekleştirilmiştir. Araştırmada veriler; doküman, gözlem, görüşme veri toplama araçlarıyla veri çeşitlemesi yapılarak toplanmıştır. Gözlem ve görüşme verileri içerik analizine, öğrenme yörüngeleri ise geçmişe dönük analiz sürecine tabi tutulmuştur. Bu çalışma, başarı düzeyi yüksek olan öğrencilerin değişkenler arasındaki doğrusal ilişkiyi tanımlayabildikleri ve denklemleri çözebildiklerini göstermektedir. Öğrencilerin, cebirsel ifade ve doğrusal denklem oluşturma gibi genelleme gerektiren durumlar için verilen tüm bilgileri koordine edebildiği, ayrıca doğrusal model kavramını daha soyut durumlarda oluşturabildikleri ve yeni doğrusal model için bir kural ortaya koyabildikleri görülmüştür. Buna ek olarak, bağlamsal problemlere çözümler bulmak için belirledikleri yöntemleri daha tutarlı kullanabildikleri gözlemlenmiştir. Bu durum soyut düşünebilen öğrencilerin veriyi genelleştirebildiğini ve temsili olarak cebirsel ifade kullanabildiğini göstermiştir. Öğrencilerin bağlam içerisinde karşılaştıkları problemleri matematiksel bir yolla açıklamaları soyutlama sürecini analiz etmelerine yardımcı olmuştur. Bu araştırmada öğrencilerin cebir kavramlarını soyutlama becerileri, problem çözme süreçlerinin ve görüşmelerdeki açıklamalarının epistemik olarak analiz edilmesiyle ortaya çıkarılmıştır. Öğrencilerin uygulama öncesinde daha kısır bir düşünceye sahipken süreçte farklı düşünme yollarının farkına vardıkları, farklı cebirsel düşünme yolları ortaya koydukları, başlangıçta sözel veya aritmetik olarak ifade ettikleri matematiksel durumları cebirsel açıklamalara dönüştürdükleri görülmüştür. Araştırmada soyutlama becerisi ile zihnin cebirsel alışkanlıkları arasında birbirini destekleyici argümanlar bulunmuştur. Öğrencilerin cebir ilişkilerindeki gelişimlerini sağlayan iki matematiksel alışkanlık tespit edilmiştir. Bunlar, işlemleri düzenleyerek bir soyutlamaya ulaşmak ve matematiksel bir dil kullanarak genelleme yapmaktır. Bu alışkanlıklar, öğrencilerin aritmetikten cebire geçmelerini kolaylaştırmıştır. Yapma ve fonksiyonel kural oluşturma alışkanlıklarına sahip olan öğrencilerin cebir kavramlarını soyutlama süreçlerinde daha avantajlı olduğu söylenebilir. Soyutlama sürecinde yeni bir yapı ve matematiksel dilden bahsedildiği için soyutlama sürecindeki ilişkilerin anlaşılması fonksiyonel kural oluşturma alışkanlığına sahip öğrencilerin daha kolay inşa etmelerine olanak sağlamıştır. Cebirsel alışkanlıklarda ise öğrencilerin işlemlerden soyutlama girişimleri genellikle yeni bir dil yerine kısa bir yol bulmak ve açıklayabilmek üzerine inşa edilmektedir. Cebirin iki temel kavramınu öğretmeye yönelik bir yaklaşım üzerine kurulan araştırma, etkili bir cebir eğitimini teşvik etme çabalarını koordine etme ve öğrencilerin düşüncelerindeki önemli kilometre taşlarını belirlemek amacıyla önemlidir. Öğrenme yörüngeleri, öğretmenlere ve uygulayıcılara kendi eğitsel uygulamalarına entegre edilebilmesi için sistematik bir yol sunar. Öğrencilerin cebir kavramlarını soyutlamaları öğretimde etkili bir araç olarak kullanılabileceğine yönelik öğretmenlere hizmet içi eğitimler verilebilir ve soyutlama mekanizması, daha açıklayıcı ve kullanışlı bir biçimde matematik dersi öğretim programlarına yansıtılabilir.Students are expected to achieve various purposes by using skills such as problem solving, reasoning, and communication, which are the basis of mathematical thinking of their current knowledge, rather than having much knowledge today. In the study, mathematical thinking is discussed to explain how the student constructs mathematics concepts in his mind. This construction process was followed from the framework of mathematical abstraction. Mathematical abstraction is the creation of a more comprehensive application area of comprehension through the generalization of the concept of mathematics. In other words, it is to extract the essence of the concept. It is quite a difficult situation to observe the formation process of information directly in the students' minds. Effective interventions in the learning process will be easier if it is known how the knowledge is formed, abstracted, and what internal processes go through in the student's mind. In this study, it is aimed to analyze the abstraction processes of secondary school students towards basic algebra concepts. Epistemic actions in RBC + C (Recognizing, Building with, Construct, Consolidation) theory were taken into consideration in the analysis of abstraction processes. In addition, Hypothetical Learning Trajectories were used in the research process to provide better observation of students' abstraction processes. Determining the effects of the experimental application on students' achievements in basic algebra concepts and their reflections on abstraction processes is another aim to be revealed in the research. The research is designed as two-stage and longitudinal to achieve the determined goals. Firstly, design-based research model was used in order to see more clearly the processes of abstraction of the concepts of balance and variable, which are the two basic axioms of algebra, and to support them in abstraction in the process. Design-based research allows students to intervene in the learning environment in order to better understand the abstraction processes of students. In this regard, it is believed that it will be more useful than other types of research. Design-based research focuses on learning studies as well as intervention in the learning environment. The second stage of the research was evaluated as a case study. Design applicability and deficiencies through classroom observations; The abstraction skills of the students were analyzed from the data obtained from semi-structured student interviews. Participants were selected by purposeful sampling among 6th grade students studying at a public school in Nilüfer District of Bursa Province. Data collection was continued when they moved to the 7th grade level with the same students. During the 2016-2017, 2017-2018 academic years, researchers and teachers together carried out research in the mathematics classes. In the research, data was collected by data triangulation, data collection tools compatible with the nature of qualitative research, such as documents, observations, and interviews. Observation and interview data were subjected to content analysis, and learning road maps were subjected to historical analysis. This study shows that students with a high level of success can define the linear relationship between variables and solve equations. It was observed that students were able to coordinate all the information given for situations requiring generalization, such as algebraic expression and linear equation creation, as well as create the concept of linear model in more abstract situations and set a rule for the new linear model. In addition, it has been observed that they can use the methods they have determined to find solutions to contextual problems more consistently. This shows that students who can think abstractly can generalize the data and use algebraic expression as a representation. Explaining the problems faced by students in a mathematical way helped them analyze the process of abstraction. In this study, students' skills of abstracting algebra concepts were revealed by epistemic analysis of problem-solving processes and their explanations in interviews. While the students' algebraic habits of mind had a more vicious thought before the application, it was observed that they realized different ways of thinking in the process, presented different algebraic ways of thinking, and initially converted mathematical situations that they expressed verbally or arithmetically into algebraic explanations. In the study, supportive arguments were found between abstraction skills and algebraic habits. Two mathematical habits have been identified that ensure the development of students in algebra relationships. These are to achieve an abstraction by arranging operations and to generalize using a mathematical language. These habits made it easier for students to switch from arithmetic to algebra. It can be said that students who have the habit of making and creating a functional rule are more advantageous in the process of abstracting algebra concepts. As a new structure and mathematical language are mentioned in the abstraction process, understanding the relations in the abstraction process has enabled students with the habit of forming a functional rule to build more easily. In algebraic habits, students' attempts to abstraction from transactions are generally based on finding and explaining a short path rather than a new language. Research, based on an approach to teaching the two basic axioms of algebra, is important to coordinate efforts to promote effective algebra education and to identify important milestones in students' thoughts. Learning trajectories offers teachers and practitioners a systematic way to integrate them into their educational apps. In-service trainings can be given to the teachers that students can be used as an effective tool in teaching abstraction concepts and the abstraction mechanism can be reflected in mathematics curriculum in a more descriptive and useful manner

A research on teacher professional law on the basis of teachers' rights and freedoms

The “Teaching Profession Law” came into force in February 2022 to regulate the professional rights of teachers. The scope and purpose of this law are to regulate the professional development and career steps of teachers. This research aimed to determine the opinions of teachers about the new law of the profession. It is a descriptive study in survey design. Teachers (379 female, 285 male) from all school types, teaching levels, geographical regions, and seniority participated voluntarily in this study. Teachers think that the new professional law will not improve their rights and increase the prestige of the profession. Teachers think that the new law of professional development is not adequately discussed or discussed based on scientific data. According to teachers, the new professional law does not encourage professional development. Teachers stated that though they generally support the need for such a profession law, the new law should be discussed more opportunities that are promising should be offered to teachers

A new active position sensing method for ropeless linear motor elevators

Linear motor driven elevators are desirable in high-rise buildings because of two main reasons: First, there are no theoretical limits to their length and second, more than one elevator cage can be driven by the same stator; multi-car elevators. Position sensing in multi-car elevators is difficult because no cables should be attached to the mover in a multi-car system. In this paper we propose a linear motor active position sensing method (LIMAP) inspired by linear variable differential transformer (LVDT), in which the position of the mover of a permanent magnet linear synchronous motor (PMLSM) can be measured using no electrical components on the mover, obviating the necessity of wires. A magnetic shunt is positioned at a fixed distance ahead of the mover, and the deformation it creates on the magnetic field produced by exciting one of the coils of the stator is measured through the voltages induced on the neighboring stator coils to calculate the position of the shunt, and thus the mover. A novel method on optimizing the dimensions of the magnetic shunt to give long measurement range and small position error, and a real-time measurement algorithm are also proposed. We verify our method by simulations and experimental results