Let a discrete time semi-Markov process Z ∈ with finite state space an alphabetDefining the process U ∈ to be the backward recurrence time of the process Z ∈ we study the Markov process Z U ∈ We give its transition probabilities of first and higher order, the limiting distribution, and the stationary distribution. Using this Markov process we construct a k-dimensional process Z U ∈ and we study its basic properties. As an application we consider a finite set of words W = w 1 w 2 w of equal length k which are produced under the semi-Markovian hypothesis and we focus on the waiting time for the first word occurrence from the set W . The corresponding probability distribution, the generating function, as well as the mean waiting time and variance are obtained.
In this paper we investigate students’ outcomes regarding the use of a dual modality programming environment that combines both text mode and block mode in class. The survey targets students of the 3nd grade of Junior High School (Gymnasium) in Greece and attempts to answer research questions regarding their perceptions after a one year course using the programming environment Pencil Code. The analysis of the collected data clearly indicates that the vast majority of students have used both modes during their work. The students find the block mode easier than the text mode but prefer to modify or correct the code using the text mode. We also noticed significant correlations between the mode used and the students’ gender, their school grades and their future course choice. The findings of this study can be useful when redesigning new Informatics curricula for the secondary education.
In this paper we investigate teachers’ perceptions regarding the use of block and text programming environments in the class. The survey targets teachers of informatics in primary and secondary schools in Greece and attempts to answer research questions regarding the suggested duration of block-based programming practice and the difficulty of students’ transition from block-based to text-based programming. In contrast to the majority of research works that consider students’ opinions, in this paper we investigate the perceptions of their teachers and take advantage of their experience on the taught subject. Although the curriculum mandated by the Ministry of Education provides no specific directive, teachers agreed that block-based environments are appropriate introductory tools to programming. One of the primary tasks of this work was to determine the recommended age for students to move from block-based to text-based programming. The analysis of the collected data clearly indicated a specific age for this transition: teachers believe that students in primary school and the lower secondary school (ICSED levels 1 and 2 respectively) should use a block-based programming environment and should be introduced to text-based programming during the upper secondary school (ICSED level 3), after the age of 14. The findings of this study can be useful when designing new Informatics curricula for the secondary education, all-over the world.
Abstract. Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process {Zγ ; γ ∈ N}. We derive the probability of a word occurrence in the sequence. We also obtain results for the mean and variance of the number of overlapping occurrences of a word in a finite discrete time semi-Markov sequence of letters under certain conditions. Mathematics Subject Classification. 60K10, 60K20, 60C05, 60E05.
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