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

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

The Relationship between the Exchange Rate, Interest Rate and Inflation: The Case of Turkey

The purpose of the study is to measure the effects of changes in exchange rates and interest rates on inflation and to determine which of the exchange rates or interest rates has a greater impact on inflation rate following the July 15, 2016 coup attempt in Turkey. Our expectation is that similar to most authors is to find that there is a long-term relationship between the inflation rates and both the exchange rate and interest rates and that the effect of the exchange rate on the Producer Price Index (PPI) is greater than that of the interest rates. Moreover, we expect to find a unidirectional causality relationship between the Interest Rate of Commercial Banks Credit (IRBC), Over Night Interest Rate (O/N) and United States Dollar (USD) and the PPI, but not between the IRBC, O/N, USD and the Consumer Price Index (CPI).JEL Codes - F31; O24; E4; E31; E43; P24; P4

Determining the Return Volatility of Major Stock Markets Before and During the COVID-19 Pandemic by Applying the EGARCH Model

With this study, we aim to determine the effect of the Covid-19 pandemic on the return volatility of the DJI, the DAX, the FTSE100 and the CAC40 stock indexes. We take return volatility between 1st January 2019 and 17th July 2020 and split it into two separate periods - before the Covid-19 pandemic outbreak and the first wave of the ‘In-Pandemic’ period. Only the so-called first wave of the pandemic was chosen to avoid the influence of knowledge of possible vaccines and antiviral solutions. Data were analysed by using the exponential GARCH (EGARCH) model. Findings show excessive volatility in the major stock markets with short volatility persistence and the presence of leverage in returns during the first wave of the Covid-19 pandemic outbreak. Moreover, during the pandemic period, positive shocks have been observed to have a greater effect than negative socks on the stock index return volatility

Modelling of disodium octaborate drying in a spray dryer

Stokiometrik oranlarda borik asit ve borakstan hazırlanan çözeltiden suyun püskürtmeli kurutucuda uzaklaştırılması ile üretilen hidrate disodyum oktoboratın kuruma davranışının belirlenmesi için gerçekleştirilen matematiksel modelleme çalışmalarında en az varsayımın yapıldığı en üst düzey kabul edilen hesaplamalı akışkanlar dinamiği modeli uygulanmıştır. Modellemede, sürekli faza ait kütle, momentum ve enerji korunum eşitlikleri ile dispers faza ait temel korunum eşitlikleri ve türbülans büyüklüklerini içeren diferansiyel denklem setlerinin çözümü için sonlu hacimler metodu ile çalışan STAR-CD yazılımı kullanılmıştır. Damlacıkların kurutulması esnasında aynı anda iki süreç gerçekleşmektedir. Bunlardan birincisi damlacıklara dışarıdan transfer edilen enerji ile yüzeydeki suyun hava akımı içerisine buharlaştırılması, ikinci süreç ise suyun yüzeyden buharlaşmaya başlaması ile aynı zamanda damlacığın iç kısımlarındaki nemin sıvı veya buhar halinde yüzeye transferidir. Partikül içerisindeki nem taşınımı kararsız hal difüzyon eşitliği ile ifade edilerek, lokal nem içeriği ve sıcaklığa bağlı difüzyon katsayısı hesaplanmış literatürden elde edilen matematiksel eşitliğe uyarlanmıştır. Ayrıca, iki farklı sıcaklıkta ve bağıl nem 0.1 – 0.9 aralığında su buharı desorpsiyon izotermleri oluşturularak denge nem oranları hesaplanmıştır. Difüzyon eşitliğine ait katsayılar, damlacık boyut dağılımı, damlacıkların ilk hızları, türbülans model katsayıları, kurutma havası ve besleme çözeltisi özellikleri yazılımın ön işlemcisinde tanımlanarak, kurutucu içerisinde sürekli faza ait hız, yörünge, sıcaklık ve nem değerleri ile dispers fazda, damlacık kuruma hızları ve kurutucuda kalma süreleri belirlenmiştir. Püskürtmeli kurutucunın üç seviyesinde her seviye için altı noktada nem ve sıcaklık değerleri ölçülerek, elde edilen model sonuçları ile deneysel ölçümler karşılaştırılmış, model sonuçları ile deney sonuçlarının birbirine uyum gösterdiği saptanmıştır. Anahtar Kelimeler: Püskürtmeli kurutma, hesaplamalı akışkanlar dinamiği, disodyum oktaborat.Spray drying is one-step continuous unit processing operation for transformation of feed from a liquid form to a dry powder. The feedstock prepared by aqueous solution of borax and boric acid mixtures was atomized into a drying chamber where the resulting spray mixes with hot gas, which evaporates the liquid component of the droplets. The spray dried powders have the appropriate composition of disodium octaborate tetrahydrate. A computational fluid dynamic study was carried out to investigate airflow pattern, temperature, and humidity profile at different levels in the drying chamber. The effects of operating and boundary conditions on the gas flow pattern, droplet trajectories, and overall dryer performance also were investigated. Results are presented and discussed in terms of the gas velocity, temperature, and humidity profiles within the chambers. The analysis were performed on spray dryer fitted with rotary atomizer using STAR-CD code by Euler  Lagrange approaches in which the conservation equations of mass, momentum and energy for the gas flow in the dryer are expressed in the Eulerian form and the droplets in the Lagrangian. In the case of turbulent flow, the conservation equations were solved to obtain time  averaged equations. Additional terms in these equations represent the transport of momentum, heat and mass solved by RNG k  turbulence model. The droplets temperature, mass and velocity were determined at every location of their trajectories from the local time-averaged solution for the gas. In order to describe the internal mass transfer, one-dimensional diffusion equation was solved to model the internal distribution and diffusion of water moisture inside the particle which is assumed as spherical shaped. The diffusion coefficient was determined as function of moisture content and temperature. The partial water pressure at the droplet surface is related to the surface moisture content and droplet temperature by desorption isotherms which mathematically represented with three-parameter Guggenheim -Anderson - De Boer (GAB) equation that represents a kinetic model based on multilayer and condensation. Atomization from a rotating disc was modeled by putting 100 injection points along the peripheral of the size of the atomizer.  The total feed rate was distributed evenly between the injection points.  For each injection, the initial droplet size distribution was back calculated from the size of particles collected from the drying experiments.  This back-calculation method assumes uniform shrinkage of the droplet and that there is no inhibition to shrinkage due to the sudden reduction in moisture.  In actual condition, depending on the operating parameters, a crust may form from the sudden initial removal of moisture, preventing further shrinkage of the droplet.  Since such mechanism is difficult to quantify in an actual dryer, the shrinkage model used as a simplifying assumption. The volume of product changes with the moisture content can be calculated from the actual density of the product and actual particle weight. For carrying out a simulation, first of all the geometry of the dryer was required to be able to make the mesh for the CFD calculations. A calculation grid of the drying chamber was generated with the help of the grid generator. During the calculations the CFD model interacts with the material property database. The gas flow solver calculates the gas conditions, such as temperature, moisture, velocity and degree of turbulence, in each cell of the grid. The particle tracker reads in these data in order to calculate the trajectories and the drying behavior. When the particles pass a cell of the grid the amounts of energy, mass and momentum transferred to the gas are calculated. In the next iteration program uses these transfer terms for a new calculation. The calculation loop is repeated until sufficient convergence is achieved. Accuracy of the drying models is largely affected by the prediction of the airflow within patterns in the drying chamber. The coupling effects from the transfer of mass and energy through the droplet-air interface which will further affect the properties of the air. A simple case study was used to illustrate the ability of CFD in performing optimization analysis. The model was validated by experimental tests on a pilot scale dryer on the base of temperature and water vapor concentration field measurements. The results showed that, this model is potentially usable for spray dryer chamber design for optimization, deposit prevention and scale up. Keywords: Spray drying, computational fluid dynamics, disodium octaborate

Sovereign Credit Default Swap Market Volatility in BRICS Countries Before and During the COVID-19 Pandemic

SCDS (Sovereign Credit Default Swaps) are becoming more widely used as a country risk indicator after 2008 and stand out for providing real-time information rather than periodic reporting. The COVID-19 pandemic has led to economic disruptions and a decline in international trade. Understanding how the Pandemic affects SCDS return volatility in emerging economies like BRICS forms the motivation for our research. With this study, we aim to determine the impact of the COVID-19 Pandemic on SCDS return volatility in Brazil, Russia, India, China and South Africa, known as the BRICS countries. We used the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model to analyze the data, which consisted of the daily closing price data for SCDS. The date of the first COVID-19 case in each country has been taken as the beginning of the COVID-19 Pandemic in each country. The results of the estimated GARCH models show that the volatility processes of the SCDS return series differ between periods. EGARCH model results indicate that shocks created by news in these countries during the Pandemic have a small and persistent effect on Brazil and Russia's SCDS return volatility, while they have a large and enduring effect on China and South Africa's SCDS return volatility. The findings will guide policymakers and portfolio managers in determining risk management models

The relationship between the exchange rate, interest rate, and inflation : the case of Turkey

The purpose of the study is to measure the effects of changes in exchange rates and interest rates on inflation and to determine which of the exchange rates or interest rates has a greater impact on inflation rate following the July 15, 2016 coup attempt in Turkey. Our expectation is that similar to most authors is to find that there is a long-term relationship between the inflation rates and both the exchange rate and interest rates and that the effect of the exchange rate on the Producer Price Index (PPI) is greater than that of the interest rates. Moreover, we expect to find a unidirectional causality relationship between the Interest Rate of Commercial Banks Credit (IRBC), Over Night Interest Rate (O/N) and United States Dollar (USD) and the PPI, but not between the IRBC, O/N, USD and the Consumer Price Index (CPI).peer-reviewe

Assessment Of The Vitamin B12 Status Of Pregnant Women And Their Infants

Aim:Vitamin B12 deficiency is an important problem in pregnancy because it affects not only mothers but also their infants. Although vitamin B12 deficiency is seen all over the world and all age groups, its frequency is much higher in population which has low socio-economic level. The aim of this study was to evaluate the maternal vitamin B12 status and their effect on neonatal vitamin B12 status and to detect risk factors for vitamin B12 deficiency in Bağcılar where is a low socio-economic region in Istanbul.Materials and Methods:A total of 71 pregnant women and 71 infants were included in this study between March 2016 and March 2017. Age, gender, weight, gestational age, weight gain during pregnancy, body mass index (BMI), number of parity, socio-economic status, diet, daily vitamin intake were recorded. Blood samples for whole blood count and vitamin B12 were taken all subjects. The pregnant women and newborns were divided into groups based on their vitamin B12 levels. The risk factors were analyzed for vitamin B12 deficiency.Results:The mean vitamin B12 level was 172.23±102 pg/ml for pregnant women. The number of pregnant women in deficient group (<200 pg/ml) were 73% and 46% of the mothers had a serum vitamin B12 level lower than 150 pg/ml. B12 level of pregnant women those who have consumed sufficient amount of animal products were found as significantly higher than the consumed insufficient (p=0.001). The mean vitamin B12 level of infants was found as 352.1±339.2 pg/ml and the number of infants in deficient group were 26.6%. Also, 14% of the infants had a serum vitamin B12 level lower than 150 pg/ml. There was no correlation between the mothers’ B12 level and newborns’ body measurements and gestational age.Conclusion:The prevalence of vitamin B12 deficiency in pregnant women in our region was very high and mainly cause was sub-optimal nutrition. Therefore, we suggest that the vitamin B12 status may be assess at the beginning of pregnancy in all women live in low socioeconomic region status

Assessment Of The Vıtamın B12 Status Of Pregnant Women And Theır Infants

Vitamin B12 deficiency is an important problem in pregnancy because it affects not only mothers but also their infants. Although vitamin B12 deficiency is seen all over the world and all age groups, its frequency is much higher in population which has low socio-economic level. The aim of this study was to evaluate the maternal vitamin B12 status and their effect on neonatal vitamin B12 status and to detect risk factors for vitamin B12 deficiency inGebelerde vitamin B12 eksikliği yalnızca anneleri değil aynı zamanda bebeklerini de etkileyen önemli bir sağlık sorunudur. Her ne kadar vitamin B12 eksikliği tüm dünyada ve tüm yaş gruplarında görülse de sosyoekonomik düzeyi düşük toplumlarda görülme sıklığı daha yüksektir. Bu çalışmanın amacı, İstanbul’un sosyo-ekonomik düzeyi düşük bir bölgesi olan Bağcılar’da, gebe kadınların vitamin B12 düzeylerini belirlemek, annelerin vitamin B12 düzeyinin yenidoğan bebeklerin düzeyine etkisini ve vitamin B12 eksikliği için risk faktörlerini belirlemektir

Karadeniz’de avlanan çaça (Sprattus sprattus L.) ve hamsi (Engraulis encrasicolus, L.) balıklarının büyüme parametreleri ve ölüm oranlarının tahmini

Length composition of anchovy (Engraulis encrasicolus, L.) and sprat (Sprattus sprattus L.), important small pelagic species of Black Sea, were determined in this study. Growth parameters and mortality rates for anchovy and sprat, using length composition data of fishes, were estimated. A total of 150 tons anchovy and 75 tons sprat (225 tons fish) were caught end of the 13 midwater trawl tows in the study. Length of 1516 numbers anchovy and 4214 numbers sprat were measured in the study. Maximum, minimum and average length of species were established 15.2 cm, 5.2 cm, 11.28±0.04 cm; 12.8 cm, 5.7 cm, 8.5±0.01 cm respectively.Growth and population parameters of anchovy and sprat were calculated; asymptotic length (L∞) 17.01 cm, 13.38 cm, Brody growth coefficient (K) 0.28, 0.23; instantaneous rate of mortality (Z) 2.73 year-1, 2.88 year-1; rate of natural mortality (M) 0.41 year-1, 0.52 year-1, rate of fishing mortality (F) 2.18 year-1, 1.51 year-1, exploitation rate (E) 0.80 year-1, 0.82 year-1 respectively. Growth and population parameters, calculated by the length composition for species, were compared with other studies.Bu çalışmada Karadeniz’in önemli küçük pelajik türleri olan hamsi (Engraulis encrasicolus, L.) ve çaça (Sprattus sprattus L.) balıklarının boy kompozisyonu verileri kullanılarak büyüme parametreleri ve ölüm oranları tahmin edilmiştir. Araştırmada 13 ortasu trol ağı çekimi yapılarak 150 tonu hamsi, 75 tonu çaça olmak üzere toplam 225 ton balık avlanmıştır. Yapılan örneklemede 1516 adet hamsi ve 4214 adet çaça balığının boyu ölçülmüştür. Türlerin maksimum, minimum ve ortalama boyları sırasıyla 15.2 cm, 5.2 cm, 11.28± 0.04 cm; 12.8 cm, 5.7 cm, 8.5± 0.01 cm olarak tespit edilmiştir. Hamsi ve çaçanın büyüme ve populasyon parametreleri sırasıyla; asimptotik boy (L∞) 17.01 cm, 13.38 cm; büyüme katsayısı (K) 0.28, 0.23; anlık ölüm katsayısı (Z) 2.73 yıl-1, 2.88 yıl-1; doğal ölüm katsayısı (M) 0.41 yıl-1, 0.52 yıl-1, balıkçılık ölüm oranı (F) 2.18 yıl-1, 1.51 yıl-1 ve sömürülme oranı (E) 0.80 yıl-1, 0.82 yıl-1 olarak hesaplanmıştır. Türler için boy kompozisyonundan hesaplanan büyüme ve populasyon parametreleri yapılan diğer çalışmaların sonuçları ile karşılaştırılmıştır