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KABUL EDİLDİIn this study, the solvability of a problem of the heat conduction theory with two nonlocal boundary conditions is investigated. Systems of eigenfunctions of the corresponding operator with two nonlocal boundary conditions are taken into consideration. A theorem on the solvability of the problem of the theory of heat conduction with two nonlocal boundary conditions is given.

© Soybaş D., Joshi S.B., Pawar H.H., 2022.The aim of present paper is to find out different interesting properties and characterization of unified class Pγ (A, B, α, σ) of prestarlike functions with negative coefficients in the unit disc U. Furthermore, distortion theorems involving a generalized fractional integral operator involving well-known Fox’s H-function for functions in this class are proved.

The Grüss-Voronovskaya-type approximation results for the modifiedGupta-Srivastava operators are considered. Moreover, the magnitude of differencesof two linear positive operators defined on an unbounded interval has been estimated.Quantitative type results are established as we initially obtain the moments ofgeneralized discrete operators and then estimate the difference of these operatorswith the Gupta-Srivastava operators.

The time-fractional generalized biological population model and the (2, 2, 2) Zakharov-Kuznetsov (ZK) equation are significant modeling equations to analyse biological population, ion-acoustic waves in plasma, electromagnetic waves, viscoelasticity waves, material science, probability and statistics, signal processing, etc. The new generalized (G'/G)-expansion method is consistent, computer algebra friendly, worthwhile through yielding closed-form general soliton solutions in terms of trigonometric, rational and hyperbolic functions associated to subjective parameters. For the definite values of the parameters, some well-established and advanced solutions are accessible from the general solution. The solutions have been analysed by means of diagrams to understand the intricate internal structures. It can be asserted that the method can be used to compute solitary wave solutions to other fractional nonlinear differential equations by means of fractional complex transformation.

The aim of this study was to determine learning difficulties and misunderstanding in multipliersand factors of middle school students in Kayseri, Turkey. One hundred and seven students from6th grade and 48 students from 8th grade were selected randomly from three middle schools forthe study. A questionnaire, which was developed by the first researcher, including two openended questions, eleven multiple choice questions, and one true-false question was prepared foreach group. Students solved each question and explained how they solved them. Also, it wasrequested verbally to fill in the solutions. Besides these questions, it was requested from thestudents to answer how they use the subjects of multiplication and factors in their daily lives andhow these subjects affected their attitudes and treatments towards mathematics. According to theevaluations of this research, some suggestions were made for students’ learning difficulties andconcept misunderstanding about multipliers and factors.&nbsp

The present paper deals with some convergence results concerning Gupta-type operators. Varied sequences of linear positive operators have been discussed and their approximation properties been studied in literature. This work is a collection of these operators introduced over the past three decades.

This study aims to not only determine the views of prospective elementary teacher about Polya’s four-step problem-solving process used in mathematics teaching, the problem concept and characteristics of nonroutine problems and their solutions, but also to investigate the level of knowledge about some important points concerning these concepts that prospective elementary teacher need to sufficiently know. The research sample consists of 43 prospective elementary teachers from an education faculty of a state university in Turkey. The data were obtained from the answers the prospective elementary teachers wrote on the working papers that include various styles (multiple choice, true–false judgments selection, and open-ended) of questions. Both quantitative and qualitative assessment tools were employed in the analysis of the data.

This study was carried out with 370 elementaryschool students at 8th grade to investigate the skills of 8th grade elementaryschool students. The dataset were analyzed using both quantitative andqualitative methods. The obtained results were grouped as "correct, partlycorrect, false, blank". Some solutions or equations of the problems aregiven to students and they were asked to establish an appropriate problem forthese given solutions or equations. The results indicated that the generalachievements of the students concerning these problems were inadequate. On theother hand, students are relatively more successful at finding the missing orunnecessary information in the problem or completing the missing-part problemcompared to their skills for posing an appropriate problem when a solution oran equation is given before. The majority of the problems posed by the studentswere not original and they did not request critical and creative thinking.During free problem-solving activities, most of the students did not writeproblems deeply and their writing abilities were not ambitious. Most of theposed problems were not sophisticated and not written in a comprehensive way.The study suggested problem solving activities should be increased forimprovement of problem solving abilities of students., Bu araştırmada 8. sınıf öğrencilerinin; problem kurmada önemli bir yeresahip olan niceliksel bilgiyi düzenleme, seçme, kavrama ve aktarma becerileriincelenmiştir. Matematiksel gelişimin önemli bir bileşeni olarakdeğerlendirilen problem kurma, verilen bir problemin tekrar biçimlendirilmesiveya verilen bir durumdan yeni bir problem oluşturma becerisi olaraktanımlanmakta, öğrenmenin içe dönük bir aktivitesi olarakdeğerlendirilmektedir. Araştırma; Aynıil içinde 4 farklı ilçede toplam 370 öğrenciye 1 ders saati verilerek 11soruluk problem tarama etkinliği uygulanmıştır. Bu öğrenciler arasından seçilen12 öğrenciyle mülakatlar gerçekleştirilmiştir. Toplanan veriler, nitelyöntemler kullanılarak analiz edilmiş ve belirlenen ölçütlere göredeğerlendirmeler yapılmıştır. Sonuçlar; “doğru, kısmen doğru, yanlış, boş”şeklinde dört grupta ele alınmıştır. Öğrencilere uygulanan problemetkinliklerinde bazı soruların çözümleri veya denklemleri verilmiş ve busorularla ilgili çözüm veya denkleme uygun problem kurulması istenmiştir. Busorularda öğrencilerin genel başarılarının yetersiz olduğu görülmüştür. Fakatproblem içerisindeki eksik veya fazla bir bilgiyi bulma veya yarım bırakılmışbir problemi tamamlama konusunda ise verilen bir çözüm veya denkleme uygun problemkurma becerilerine nispeten daha başarılı oldukları anlaşılmıştır. Öğrencilerinkurduğu problemler incelendiğinde elde edilen bulgular, öğrencilerinçoğunluğunun özgünlük ve yaratıcılık seviyelerinin olması gerekene göre dahadüşük olduğunu göstermektedir. Tamamen serbest problem kurma etkinliğindeöğrencilerin büyük bölümünün çok basit problemler yazdıkları görülmüştür.

This study was carried out to examine the integration of the calculator TI-92 in the secondary level. As a symbolic calculator, the TI-92 is equipped with Derive which is a symbolic calculation program and Cabri which is a geometry program. This study only dealt with the part concerned with the program Derive. First of all we determined the potentials and limitations, then we seek a response to the question which «benefits» can we expect at the learning level of the students?, Bu araştırma, TI-92 hesap makinesinin ortaöğretim seviyesine entegrasyonunu incelemek üzere yapılmıştır. TI-92 hesap makinesi bir sembolik hesap programı olan Derive ve bir geometri programı olan Cabri programlarıyla donatılmıştır. Bu araştırmada sadece Derive programı ile ilgili olan kısmı incelenmiştir. İlk olarak yeterliliklerini ve sınırlılıklarını belirledikten sonra, öğrencilerin öğrenme aşamasında, ne gibi « faydalarını » bekleyebiliriz sorusuna cevap arayacağız.