11. Sınıf Öğrencilerinin Matematiksel Düşünmenin Aşamalarındaki Yaşantılarından Yansımalar

This study aimed to reveal the experiences of 11th grade students related to specializing, generalizing, conjecturing and proving stages of mathematical thinking. Worksheets, each consisting of 9 questions included the stages of mathematical thinking, and this pilot study was applied to 24 students. The results of the study demonstrated that student achievement decreased as the stages of mathematical thinking progressed. From this point of view, students were found to demonstrate a good performance in specializing stage and to have a big difficulty in proving stage. Moreover, the students’ answers in generalizing and conjecturing stages were observed to accumulate under verbal and algebraic codes and in proving stages the answers were found to accumulate under the codes of arithmetic, geometric and algebraic. Suggestions are made based on the results of the study.Bu çalışmada, nitel araştırma yaklaşımı kullanılarak 11. sınıf öğrencilerinin matematiksel düşünmenin özelleştirme, genelleme, varsayımda bulunma ve ispatlama aşamalarıyla ilgili yaşantılarını ortaya çıkarmak amaçlanmıştır. Matematiksel düşünmenin aşamalarını dikkate alan ve her biri dokuzar sorudan oluşan çalışma yaprakları geliştirilmiş ve pilot çalışmadan sonra 24 lise öğrencisine uygulanmıştır. Çalışmanın sonuçları matematiksel düşünmenin aşamaları ilerledikçe öğrenci başarısının düştüğünü ortaya koymuştur. Bu bakımından, öğrencilerin özelleştirmede iyi performans sergiledikleri, ispatlamada ise büyük sıkıntı çektikleri tespit edilmiştir. Ayrıca, genelleme ve varsayımda bulunma aşamalarında öğrencilerin cevaplarının sözel ve cebirsel, ispatlama aşamasında ise aritmetik, geometrik ve cebirsel kodları altında toplandıkları belirlenmiştir. Çalışmanın sonuçlarına dayanarak çeşitli öneriler sunulmuştur

Optimisation and Constraint Based Heuristic Methods for Advanced Planning and Scheduling Systems

Manufacturing Resources Planning (MRPII) systems are unable to prevent capacity problems occurring on the shop floor such as varying workloads, changing bottlenecks, high Work-in-Process (WIP) levels, lower machine utilisation, less throughput, late deliveries that cannot be resolved easily in the short term because production scheduling is based on fixed lead times and backward scheduling logic. For this reason, a new breed of concepts called APS (Advanced Planning and Scheduling) systems emerged which include finite capacity planning at the shop floor level through constraint based planning. In this paper, we present a Constraint Programming (CP) model to show how optimisation models could be used in this context. We also present a two phase heuristic to solve this complicated APS problem. While jobs are assigned to the best eligible machines to smooth the workload on the machines in the first phase, a constraint based scheduling heuristic schedules jobs once they are assigned to eligible machines in the second phase. We provide numerical tests and discuss the results for both models and the heuristic. The concluding remarks and suggestions for future research are stated in the final section of the paper

Reflections from the Experiences of 11th Graders during the Stages of Mathematical Thinking

Bu çalışmada, nitel araştırma yaklaşımı kullanılarak 11. sınıf öğrencilerinin matematiksel düşünmenin özelleştirme, genelleme, varsayımda bulunma ve ispatlama aşamalarıyla ilgili yaşantılarını ortaya çıkarmak amaçlanmıştır. Matematiksel düşünmenin aşamalarını dikkate alan ve her biri dokuzar sorudan oluşan çalışma yaprakları geliştirilmiş ve pilot çalışmadan sonra 24 lise öğrencisine uygulanmıştır. Çalışmanın sonuçları matematiksel düşünmenin aşamaları ilerledikçe öğrenci başarısının düştüğünü ortaya koymuştur. Bu bakımından, öğrencilerin özelleştirmede iyi performans sergiledikleri, ispatlamada ise büyük sıkıntı çektikleri tespit edilmiştir. Ayrıca, genelleme ve varsayımda bulunma aşamalarında öğrencilerin cevaplarının sözel ve cebirsel, ispatlama aşamasında ise aritmetik, geometrik ve cebirsel kodları altında toplandıkları belirlenmiştir. Çalışmanın sonuçlarına dayanarak çeşitli öneriler sunulmuştur.This study aimed to reveal the experiences of 11th grade students related to specializing, generalizing, conjecturing and proving stages of mathematical thinking. Worksheets, each consisting of 9 questions included the stages of mathematical thinking, and this pilot study was applied to 24 students. The results of the study demonstrated that student achievement decreased as the stages of mathematical thinking progressed. From this point of view, students were found to demonstrate a good performance in specializing stage and to have a big difficulty in proving stage. Moreover, the students’ answers in generalizing and conjecturing stages were observed to accumulate under verbal and algebraic codes and in proving stages the answers were found to accumulate under the codes of arithmetic, geometric and algebraic. Suggestions are made based on the results of the study

Effect of ultrasound and microwave pretreatments on some bioactive properties of beef protein hydrolysates

WOS:000901695700002This study was aimed to determine antioxidant, antibacterial and angiotensin converting enzyme I inhibition activities of protein hydrolysates. Ultrasound and microwave pretreatment was applied to the beef. Hydrolysates were obtained by enzymatic (alkalase) hydrolysis at different times (60 min, 90 min, 120 min). Results showed that protein hydrolysates exhibited high percentages of hydrolysis of protein hydrolysates ranging from 64.1 to 88.93%. Angiotensin converting enzyme I inhibition activity ranging from 45.5 to 86.79%. DPPH inhibition values ranging from 9.25 to 29.32% and ABTS values ranging from 6.35 to 14.43 mg TEAC/g. E.coli and S.aureus were used in antibacterial activity at concentrations of 5 log cfu/ml and 7 log cfu/ml. It has been found that hydrolysates showed inhibitory activity against the tested pathogens. The results were significantly (P < 0.01) affected by ultrasound and microwave. These results indicated that ultrasound and microwave processes markedly increased the bioactive properties of protein hydrolysates obtained from an enzymatic hydrolysis

Analysis Of The Teaching Process Of Place Value Concept

Bu araştırmada, ilk olarak Basamak Değeri (BD) kavramının önemi, konuyla ilgili yaşanan zorluklar ve bu zorlukların aşılmasına yönelik ortaya atılan çözüm önerileri literatüre dayalı olarak kısaca tanıtılmıştır. Ardından bu önerilere BD öğretiminde ne derece uyulduğu müfredat ve ders kitabı analizi ile öğretmen görüşleri ışığında ortaya konulmaya çalışılmıştır. Buna göre, BD öğretiminde zengin etkinlikler yer almakta ve ayrıca abaküs, sayı blokları, birim küpler vb. materyalden yararlanılmaktadır. Diğer yandan BD öğretiminde sayıların çokluk değerinden ziyade sayı değeri ön plana çıkmaktadır. Ayrıca müfredat ve ders kitaplarında 1. sınıftan itibaren yer almasına karşın öğretmenlerin çoğunun BD‟yi 2. sınıfta öğretmeye başladığı ve BD öğretiminin uzun bir sürece yayılması ve diğer konularla ilişkilendirilerek anlatılmasının gerekli olduğunu düşündükleri belirlenmiştirThis research aims firstly identifying the importance of Place Value (PV) concept, learning difficulties on this subject and suggestions offered to get over these difficulties based on the literature. It aims secondly showing how these suggestions are put into practise via curriculum and textbooks‟ analysis and teachers‟ opinions. Obtained data underlines the abundance of the activities about PV and shows that teaching PV makes use of many materials such as abacus, number blocks, digit cubes etc. It was also revealed that in teaching activities usually column value is taken front more than the quantity value. In addition, althought PV concept exists from 1st class in the curriculum and textbooks, the teachers mostly teach PV from 2nd class; and they think that teaching PV process must be spreaded to a long period of time and it must be realised in relation with other concepts and subjects

Meyve ve sebzelerin diyet lifi bakımından et ve et ürünlerinde kullanımı

Fruits and vegetables contain different amounts of dietary fiber. Fruit and vegetable wastes that are considered as food waste and have high added value are important in many aspects. Wastes with added value are used as dietary fiber. Dietary fiber added meat and meat products are effective for health and these additives improves meat in terms of technological properties. Dietary fibers have properties such as increasing water retention capacity, reducing formulation expenses, modifying texture, and improving storage stability in low-fat products. Dietary fibers have the opportunity to be used in meat products due to their technological features such as preventing cooking losses and improving texture as well as being functional. Consumers are increased in the awareness that there is a relationship between nutrition and health day after day. However, there are also concerns that diseases increase with improper diet. For this reason, it is recommended to increase the dietary fiber addition in the daily diet The use of dietary fiber as a filler in meat products can be a satisfying factor for conscious consumers. For this reason, production of meat and meat products rich in dietary fiber will guide new studies by using fruit and vegetable waste.Meyve ve sebzeler farklı miktarlarda diyet lifi içerir. Gıda atığı sayılan ve katma değeri yüksek meyve ve sebze atıkları pek çok açıdan önemlidir. Katma değeri olan atıklar diyet lifi olarak kullanılmaktadır. Diyet lifi katkısı olan et ve et ürünleri sağlık için etkilidir ve eti teknolojik özellikleri açısından iyileştirir. Diyet lifleri, az yağlı ürünlerde su tutma kapasitesini artırma, formülasyon maliyetlerini azaltma, dokuyu değiştirme ve depolama kararlılığını geliştirme gibi özelliklere sahiptir. Diyet lifleri, fonksiyonel olmasının yanı sıra pişirme kayıplarını önleme ve dokuyu düzeltme gibi teknolojik özellikleri nedeniyle et ürünlerinde kullanılma imkânına sahiptir. Tüketiciler beslenme ile sağlık arasında her geçen gün bir ilişki olduğu bilincinde artmaktadır. Bununla birlikte, yanlış beslenme ile hastalıkların arttığına dair endişeler de vardır. Bu nedenle günlük diyette diyet lifi ilavesinin artırılması önerilmektedir. Et ürünlerinde dolgu maddesi olarak diyet lifinin kullanılması bilinçli tüketiciler için tatmin edici bir faktör olabilir. Bu nedenle diyet lifi yönünden zengin et ve et ürünlerinin üretimi, meyve ve sebze atığını kullanarak yeni çalışmalara yön verecektir

A note on "A mixed integer programming model for advanced planning and scheduling (APS)"

In a recent paper, Chen and Ji [Chen, K., Ji, P., 2007. A mixed integer programming model for advanced planning and scheduling (APS). European Journal of Operational Research 181, 515-522] develop a mixed integer programming model for advanced planning and scheduling problem that considers capacity constraints and precedence relations between the operations. The orders require processing of several operations on eligible machines. The model presented in the above paper works for the case where each operation can be processed on only one machine. However, machine eligibility means that only a subset of machines are capable of processing a job and this subset may include more than one machine. We provide a general model for advanced planning and scheduling problems with machine eligibility. Our model can be used for problems where there are alternative machines that an operation can be assigned to.Scheduling MRP Advanced planning and scheduling Mixed integer programming

Antibacterial and antioxidant activity of peach leaf extract prepared by air and microwave drying

WOS:000682872500001In this study, antioxidant and antimicrobial effects of methanol and water extracts of peach leaves dried in air and microwave drying on E. coli ATCC 25922 and L. monocytogenes ATCC 7644 were investigated. Pathogens were inoculated into broth medium prior to the extract addition. Samples were then kept at 4°C for 15 min. The highest inhibitory effect on the samples inoculated with E. coli at 5.44 ± 0.03 cfu/ml and 7.44 ± 0.03 cfu/ml levels was obtained from the treatment of microwave-water; the final enumeration counts of E. coli were 3.80 ± 0.01 cfu/ml and 5.44 ± 0.07 cfu/ml, respectively. Similarly, the highest inhibitory effect on the samples inoculated with L. monocytogenes at 5.18 ± 0.02 cfu/ml and 7.18 ± 0.02 cfu/ml levels was obtained from the treatment of microwave-methanol; the final enumeration counts of L. monocytogenes were 4.40 ± 0.03 cfu/ml and 6.03 ± 0.07 cfu/ml, respectively. Inhibitory activity of microwave-dried peach leaf extracts was higher. The highest TPC (4.08 mg GAE/ml) values were obtained from air-dried samples extracted by water. The DPPH value of both extracts of microwave-dried samples was higher than the air-dried samples. The results indicate methanol extracts as an antimicrobial and antioxidant agent may be used to reduce microbial population. Novelty Impact Statement: The highest Total phenolic content (4.08 mg GAE/g) values was seen samples that dried in the air extracted with water. All samples TEAC values changed from 0.86 to 5.35 mg TEAC/g. The Inhibitory effect of all peach leaf extracts on E. coli and L.monocytogenes was found statically important (p <.05)