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This dissertation investigates the interplay between second and fourth graders’ use of rulers and paper strips to solve number line measurement problems. Drawing upon and extending Vygotsky’s (1978, 1986) approach to mediation in problem solving, and Saxe’s (2012) treatment of microgenesis of representational activity, I analyzed 36 second and 39 fourth graders’ measurement activity as they participated in videotaped semi-structured interviews. At each grade, students were randomly assigned to ruler, short paper strip, or long paper strip conditions, and solved five number line problems first without the tool available and then five similar problems with the tool available. For each problem, two numbers were labeled (e.g., 4 and 6) and students were asked to place a third number appropriately (e.g., 9). Problems and tools were designed to elicit unitizing strategies (splitting, iterating, counting) as students coordinated tool with target to produce a linear measure. I report findings related to the precision of students’ estimates contrasting tool absent and present conditions, and findings related to students’ adaptation of tools to serve measurement functions. Analyses of students’ precision revealed that with or without the support of tools, fourth graders were more precise than second graders, though the utility of tool varied with tool and problem type. The long paper strip was particularly difficult for second graders, and at both grades, many students rejected using the long paper strip. Students generally became precise with tools when a solving a problem type that displayed a linear unit of 1 instead of a larger unit, though this varied with tool type. On other problem types, tools interfered with precision, and on still other problem types, tools interfered with the precision of second, but supported the precision of fourth graders. Analyses of strategies revealed three levels in students’ ability to coordinate a unitization of tool and target as they tried to adapt tools to serve measurement functions. I argue that these findings can productively inform our understanding of the interplay between tool use in students’ developing measurement activity as well as the design of instructional problem environments to support students’ tool using in linear measurement.

In this research, the aim is to analyze evaluating of estimation skill of the elementary school sixth, seventh and eighth year mathematic curriculum in term of teachers’ views. In this research, a descriptive research was designed as a cross hatching model. The quantitative data of the research was obtained from questionnaire form and the qualitative data was obtained from semi-structured interview form and unstructured observation. The quantitative sample of the research was done in a province located in the south of Turkey. There were 190 instructors, teaching the sixth, seventh and eight grade the teacher. The qualitative data in the research was obtained from 10 math teachers who are study in 5 different middle schools. The observation data was obtained following a teacher from each grade level. The quantitative data of the research were analyzed with descriptive statistical techniques, and were calculated frequency, percentage and mean values. The analysis of qualitative data made with descriptive analysis. Research findings reveal that they have a positive opinion for the estimation skills in mathematic curriculum. And also, according to the teachers’ opinions, the acquisitions of estimation skill in curriculum are not suitable for students’ levels cognitively.

This is a post-peer-review, pre-copyedit version of an article published in European Journal of Psychology of Education. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10212-015-0251-z, The conduct of this study was supported by grant GOA 2012/010 of the Research Fund KU Leuven, Belgium, and by grant DFG: EB462/1-1 of the German Research Foundation to the fourth author.

6. Sınıf Öğrencilerinin Ölçmeye Dayalı Tahmin Becerilerinin ve Bu Beceriye İlişkin Görüşlerinin İncelenmesiİmren AYDOĞDUEskişehir Osmangazi Üniversitesi Eğitim Bilimleri EnstitüsüMatematik ve Fen Bilimleri Eğitimi Anabilim DalıDanışman: Dr. Öğr. Üyesi Emre EV ÇİMEN2020Amaç: Günlük hayatta sıkça kullanılan matematiksel tahmin etme becerisi matematik eğitiminde önemi gittikçe artan bir araştırma konusudur. Tahmin becerisininönemli bir alt bileşeni olan ölçmeye dayalı tahmin becerisi matematiksel problem çözme başarısını etkileyen bir beceridir. Ölçmeye dayalı tahmin becerisinin alanyazındahenüz yeterince araştırılmadığı görülmektedir. Buradan hareketle, altıncı sınıf öğrencilerinin ölçmeye dayalı tahmin becerilerinin ve bu beceriye ilişkin görüşlerinin incelenmesi bu araştırmanın ana amacıdır. Araştırmada öğrencilerin ölçmeye dayalı tahminbecerileri, kullandıkları tahmin stratejileri ve yaptıkları tahminlerini ölçümlerle eldeettikleri değerlerle karşılaştırma süreçleri incelenmiştir. Ayrıca öğrencilerin söz konusubeceriye ilişkin görüşleri ile araştırma kapsamında yapılan uygulamalara yönelik görüşlerinin incelenmesi de amaçlanmıştır.Yöntem: Araştırmada nitel yöntemlerden durum çalışması deseni kullanılmıştır.Çalışma grubunu Ankara İlinin bir merkez ilçesinde bulunan bir ortaokulda altıncı sınıfta okuyan altı öğrenci oluşturmuştur. Çalışma grubunun belirlenmesi için altıncı sınıftaokuyan 35 öğrenciye ölçmeye dayalı tahmin becerilerini belirlemeye yönelik etkinlikleruygulanmıştır. Bu öğrenciler arasından yüksek, orta ve düşük tahmin becerisine sahipbir kız ve bir erkek öğrenci olmak üzere toplam altı öğrenci çalışma grubu için seçilmiştir. Öğrencilerle birer seans klinik görüşmeler yapılmış ve tahmin becerileri ile tahminlerini ölçümleriyle karşılaştırma süreçleri incelenmiştir. Ayrıca klinik görüşmelerdensonra öğrencilerin uygulamaya ilişkin görüşleri de alınmıştır. Tahminlerin değerlendirilmesinde alanyazında bulunmayan ve 'Tahminlerin Ölçümün Yüzdesine Göre Değerlendirilmesi' adı verilen bir yöntem kullanılmış olup bu yöntem detaylı bir şekilde açıklanmıştır. Klinik görüşmelerden ve öğrenci görüşlerinden elde edilen veriler de detaylıbir şekilde analiz edilmiştir. 2Bulgular: Araştırmada ulaşılan bulgular incelendiğinde öğrencilerin ölçmeyedayalı tahminde kullandıkları stratejiler referans noktası kullanma, karşılaştırma, öncekibilgiyi kullanma, gözünde canlandırma, birim tekrarlama, parçalama, sıkıştırma, rastgele tahmin ve yeniden biçimlendirme stratejileridir. En çok kullanılan strateji referansnoktası kullanma stratejisi olmuştur. Öğrencilerin yapılan etkinliklerde ölçmeye dayalıtahmin becerilerinin yüksek olmadığı belirlenmiştir. Öğrencilerin uzunluk tahminindedaha yüksek performansa sahipken alan ve hacim tahmininde daha düşük performansasahip oldukları bulgusuna ulaşılmıştır. Öğrencilerin tahmin sonuçlarını ölçüm sonuçlarıyla karşılaştırma süreçlerinde ölçüm yaparken öğrencilerin 30 cm'lik cetvel ve katlanırmezuraya kıyasla genelde metre kullandıkları belirlenmiştir. Tahmin değerlerini ölçümdeğerleri ile karşılaştırmanın öğrencilerin öğrenmelerine olumlu etkisinin olduğu belirlenmiştir. Yapılan görüşmeler neticesinde, öğrencilerin tahmin denildiğinde akıllarınagelen ilk becerinin işleme dayalı tahmin becerisi olduğu bulgusuna ulaşılmıştır.Sonuç ve Öneriler: Araştırmada ulaşılan önemli sonuçlardan ilki tahmin becerisi yüksek olan öğrencilerin daha fazla strateji kullandıkları sonucu olmuştur. Tahminbecerisi konusunda alanyazından farklı olarak bu araştırmada yeniden biçimlendirmestratejisi ortaya çıkmıştır. Öğrencilerin ölçüm sırasında zorluk yaşamaları, bu konudaeksikleri olduklarını ortaya çıkarmıştır. Bu araştırmanın ilerletilmesi için daha genişçalışma grupları, farklı özelliklere sahip öğrenciler ve farklı sınıf seviyeleri ile araştırmalar gerçekleştirilmesi önerilir. Eğitimcilere yönelik olarak da öğrencilerin ölçmeyedayalı tahmin becerilerinin gelişimine fırsat sağlayan etkinliklerin artırılması önerilmektedir.Anahtar kelimeler: Ölçmeye dayalı tahmin, Tahmin stratejileri, Tahmin becerisi, Altıncı sınıf öğrencileri, Ortaokul matematik eğitimi. An Investigation of Sixth Grade Students' Measurement Estimation Skills andTheir Views on This Skillİmren AYDOĞDUEskisehir Osmangazi University Institute of Educational SciencesDepartment of Mathematics and Science EducationAdvisor: Assist. Prof. Dr. Emre EV ÇİMEN2020Purpose: The ability to estimate mathematically, which is used extensively indaily life, is becoming an increasingly important research topic in mathematics education. Measurement estimation, which is an important subcomponent of estimation, is askill that affects mathematical problem solving success. It is seen that measurementestimation skill has not been investigated sufficiently in the literature yet. From here,the main purpose of this study is to investigate the measurement estimation skills ofsixth grade students and their opinions about this skill. In the research, the students'skills of estimation, their estimation strategies, and their processes of comparing between their estimated values and values they obtained after measuring, were investigated. We also aimed to investigate the students' views on the measurement estimationskill and their opinions about the applications performed in this research.Method: The case study design, one of the qualitative research methods, wasused in the study. The study group consisted of six students at the sixth grade level in asecondary school in the central district of Ankara Province. For the selection of thestudy group, activities aimed at determining measurement estimation skills were appliedto 35 students at the sixth grade level. A total of six students, three female and threemale, each one having high, medium and low estimation skills were selected for thestudy group. One session of clinical interviews were conducted with each of the students, and their estimation skills and their comparison process between their estimatedand measured values were investigated. In addition, after the clinical interviews, students' opinions about the applications were also obtained. A method, called 'The Assessment of the Estimations According to Percentage of Measurement' is used that isnot available for the assessment of estimations in literature and is explained in detail.The data obtained from interviews and student opinions were also analyzed in detail. 4Results: When the findings were analyzed, the strategies that students used inestimating were found to be `using reference point, comparison, using previous information, visualization, unit repetition, fragmentation, compression, random predictionand reformatting strategies`. The most commonly used strategy was the reference pointuse strategy. It was determined that students' estimation skills were not high in activities. It was found that while students had higher performance in length estimation, theyhad lower performance in area and volume estimation. It was determined that studentsgenerally used the meter compared to the 30 cm ruler and the soft tape measure whilethey compared their estimated values with the measured values. It was determined thatthe activity of comparing their estimations with the measured values had a positive effect on students' learning. After the interviews, it was found that the first skill that cameto the students' mind was operation-based estimation skill when they first heard aboutestimation.Conclusion and Suggestions: The first of the important results obtained in thestudy was that students with higher estimation skills used more strategies. Unlike theliterature on estimation skills, this research revealed the strategy of reformatting. Thefact that the students had difficulty during measurements revealed that they lackedknowledge on this subject. In order to advance this research, it is recommended to conduct research with wider study groups, students with different characteristics and different grade levels. For educators, we can suggest to increase the activities that providemore opportunity for students to develop their measurement estimation skills.Keywords: Measurement estimation, Estimation strategies, Estimation skill, Sixthgrade students, Secondary school mathematics education. 158

In this paper, two maximum-likelihood (ML) channel estimators that are robust and perform consistent channel estimation in the presence of impulsive noise (IN) for power line communication (PLC) systems are proposed and analyzed. The two estimators differ on the way they exploit the estimated IN to determine the coefficients of the channel impulse response. In the first approach, the channel estimator treats the estimated IN as a deterministic quantity; in the second as a random quantity. The performances of both estimators are analyzed and numerically evaluated. As it will be shown, between the two proposed estimators, the one that is based on the random approach outperforms the deterministic one in all typical PLC scenarios. However, the deterministic approach-based estimator can perform consistent channel estimation regardless of the IN behavior with less computational effort and becomes an efficient channel estimation strategy in situations where high computational complexity cannot be afforded. © 2018 Elsevier Ltd

© 2015, Instituto Superior de Psicologia Aplicada, Lisboa, Portugal and Springer Science+Business Media Dordrecht. This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint condition included an additional benchmark at the midpoint and children in the quartile condition were provided with a benchmark at every quartile. First, the inclusion of a midpoint resulted in more accurate estimates around the middle of the number line in the midpoint condition compared to the bounded and, surprisingly, also the quartile condition. Furthermore, the two additional benchmarks in the quartile condition did not yield better estimations around the first and third quartile, because children frequently relied on an erroneous representation of these benchmarks, leading to systematic estimation errors. Second, verbal strategy reports revealed that children in the midpoint condition relied more frequently on the benchmark at the midpoint of the number line compared to the bounded condition, confirming the accuracy data. Finally, the frequency of use of benchmark-based strategies correlated positively with mathematics achievement and tended to correlate positively also with estimation accuracy. In sum, this study is one of the first to provide systematic evidence for children’s use of benchmark-based estimation strategies in NLE with natural numbers and its relationship with children’s NLE performance. ispartof: EUROPEAN JOURNAL OF PSYCHOLOGY OF EDUCATION vol:31 issue:2 pages:117-134 status: published

In recent years, a significant interest in hybrid and battery electric vehicles has arisen globally due to reducing fuel consumption, mitigating dependence on imported oil and decreasing greenhouse gas emissions. The overall success of these vehicles mostly depends on the performance of sub-systems that they are created. In order to enhance the performances of these sub-systems, estimation of their parameters with high accuracy is required. Furthermore, estimation strategies play an important role in battery management, vehicle energy management and vehicle control by undertaking different tasks. There have been a limited number of review studies related with estimation strategies that are only focused on battery state of charge (SOC) and state of health (SOH) estimation. This paper presents a comprehensive review on various estimation strategies used in hybrid and battery electric vehicles for the first time in the literature. The existing estimation strategies are classified and different methodologies used in each estimation strategy are elaborated. Recent research advances on existing estimation strategies are clearly emphasized by reviewing numerous studies over 200 papers. © 2014 Elsevier Ltd. All rights reserved.

Number line estimation (i.e., indicating the position of a given number on a physical line) is a standard assessment of children’s spatial representation of number magnitude. Importantly, there is an ongoing debate on the question in how far the bounded task version with start and endpoint given (e.g., 0 and 100) might induce specific estimation strategies and thus may not allow for unbiased inferences on the underlying representation. Recently, a new unbounded version of the task was suggested with only the start point and a unit fixed (e.g., the distance from 0 to 1). In adults this task provided a less biased index of the spatial representation of number magnitude. Yet, so far there are no children data available for the unbounded number line estimation task. Therefore, we conducted a cross-sectional study on primary school children performing both, the bounded and the unbounded version of the task. We observed clear evidence for systematic strategic influences (i.e., the consideration of reference points) in the bounded number line estimation task for children older than grade two whereas there were no such indications for the unbounded version for any one of the age groups. In summary, the current data corroborate the unbounded number line estimation task to be a valuable tool for assessing children's spatial representation of number magnitude in a systematic and unbiased manner. Yet, similar results for the bounded and the unbounded version of the task for first- and second-graders may indicate that both versions of the task might assess the same underlying representation for relatively younger children - at least in number ranges familiar to the children assessed. This is of particular importance for inferences about the nature and development of children's magnitude representation.