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The Role of Proof and Reasoning in Solving Real-Life Math Problems
, M.Sc. Thesis Sharif University of Technology ; Zohuri-Zangeneh, Bijan (Supervisor) ; Gooya, Zahra (Supervisor)
Abstract
The purpose of the present study was to investigate the Grade 9 students' ability to solve real-life and modelling problems, focusing on proof and reasoning. The study conducted using qualitative method in which, six volunteer students participated. The data collected via eight problems mostly chosen from Chapter 3 of the 9th grade mathematics textbook and using Adobe Connect Platform, because of Covid-19 Pandemic and schools clousure. The data were analyzed using a problem solving framework developed by Mason, Burton and Stacey (2010) including three stages of entry, attack and review. The results showed that considering these three steps, is effective to understand students' problem...
Estimating the parameters of mixed shifted negative binomial distributions via an EM algorithm
, Article Scientia Iranica ; Volume 26, Issue 1E , 2019 , Pages 571-586 ; 10263098 (ISSN) ; Akhavan Tabatabaei, R ; Salmasi, N ; Modarres, M ; Sharif University of Technology
Sharif University of Technology
2019
Abstract
Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show its flexibility in producing a wide range of variances as well as its adequacy in fitting fat-tailed distributions. These properties render MSNB...
Estimating the parameters of mixed shifted negative binomial distributions via an EM algorithm
, Article Scientia Iranica ; Volume 26, Issue 1E , 2019 , Pages 571-586 ; 10263098 (ISSN) ; Akhavan Tabatabaei, R ; Salmasi, N ; Modarres, M ; Sharif University of Technology
Sharif University of Technology
2019
Abstract
Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show its flexibility in producing a wide range of variances as well as its adequacy in fitting fat-tailed distributions. These properties render MSNB...