In early childhood, planning provides a basis for organizational skills that are useful for future school performance (Perez & Gauvain, 2009). However, research shows that preschoolers’ planning abilities are limited because they often fail to consider task demands, are inefficient at self-monitoring, and are unlikely to use strategies to their advantage (Gardner & Rogoff, 1990). The present study examined whether preschoolers could improve their planning skills by consciously drawing connections between objects and events through the use of verbal self-explanations. A microgenetic design was used in order to repeatedly measure preschoolers’ performance on the Tower of Hanoi (ToH) task over a period of 6 to 8 weeks. Forty-five children between the ages of 4 and 6 years were randomly assigned to 1 of 3 conditions: self-explanation, no self-explanation, and control. Each child was administered a pretest, 3 micro sessions based on condition, and a posttest. In addition to ToH performance, children also were measured on inhibitory control, working memory, short-term memory, and verbal ability at pretest, and on a novel planning task, the Box-ToH, at posttest. Multilevel models were used to analyze the data at the between- and within-person levels. Although no differences were found in ToH performance over time between conditions, preschoolers’ use of self-explanations and strategies were independently related to individual improvements in ToH performance over time. Moreover, preschoolers’ improvements in ToH performance were not reducible to age-related increases, inhibitory control demands, working memory, short-term memory, or verbal ability. Lastly, findings did not support preschoolers’ ability to transfer their knowledge of strategies on the ToH to the Box-ToH. Overall, the present study demonstrated that self-explanations and strategy use are both important predictors of understanding individual changes in planning performance during the preschool years. These findings have important implications in terms of improving preschoolers’ executive function skills and preparing children for early academic success. / Graduate

The Apprentices' Tower of Hanoi is introduced in this thesis. Several bounds are found in regards to optimal algorithms which solve the puzzle. Graph theoretic properties of the associated state graphs are explored. A brief summary of other Tower of Hanoi variants is also presented.

Made available in DSpace on 2016-07-27T14:20:12Z (GMT). No. of bitstreams: 1 LARISSA DE OLIVEIRA E FERREIRA.pdf: 1804099 bytes, checksum: d2b4dba42341c787eb8c9b6b9ba6a815 (MD5) Previous issue date: 2013-11-08 / Neuropsychology in recent years has increased the number of research on executive function function. The increase in research was necessary because it is a subject that covers . functions directly linked to cognitive processes necessary for good per performance in daily ormance activities activities, and tasks that require a more elaborat , elaborate reasoning e reasoning. But most research, found . found, has as its object of study groups of children and adolescents with neuropsychi neuropsychiatric atric disorders or dysfunctions dysfunctions. In Brazil there are few standardized ba batte ttery to assess ry executive function. One of the instruments used is the Tower of Hanoi, but there is no consensus on how to apply and which components of this instrumen instrument assesses t executive function function. From this perspective we chose to study the Tower of Hanoi in the assessment of executive function with group of children with normal development . This study tested 55 children and adolescents between 10 and 16 years, with the aim to evaluate the relationship between time and performance in the Tower of Hanoi to assess executive function function. As convergent validity was used to scale . the implementation of WISC III III, which is a w , widely studied intelligence test idely test, which evaluates all components , of executive function and that has to count time as a key factor in the fi final s nal score of all core subtests subtests. The results provide data that seem to show that the number of movements . and me measure the execution time in ToH asure ToH, with children 10 , - 16 years o old, has no ld, discriminative power power, the comparison between the groups 10 , 10-13 years and 14 -16 year years and between genders s genders. We conclude that the ToH unlike many studies showed . that it is not an effective tool in the assessment of executive function in children 10 10-16 years. The measurement of time in carrying out the ToH is not necessary since no significa significant correlation in any of the comparisons made in this study. nt / Em neuropsicologia neuropsicologia, nos últimos anos tem aumentado o número de pesq pesquisas sobre a uisas função executiva. O aumento das pesquisas fez fez-se necessário por tratar tratar-se de um assunto que abrange funções diretamente ligadas a processos cognitivos necessário necessários para o bom desempenho em atividades cotidianas, e em tarefas que exij exijam um am raciocínio mais elaborado. No entanto, a maioria das pesquisas encontrada encontradas tem como s objeto de estudo grupos de crianças e adolescentes com disfunções ou transtornos neuropsiquiátr neuropsiquiátricos, icos, o que não permite esclarecer o que seria o desenvolvimento e o funcionamento da função executiva em grupos sem comprometimentos. No Brasil Brasil, existe existem poucas bateria baterias padronizadas para avaliar a função executiva. Um dos instrumentos muito usado é a Torr Torre de Hanói e (TOH) TOH), porém porém, não existe consenso quanto a forma de aplicação e quais componentes da função ex executiva esse ecutiva instrumento avalia. Com essa perspectiva perspectiva, optou optou-se por estudar a Torre de Hanói na avaliação da função executiva com grupo de crianças com desenvolvimento normal. Foram testadas 55 crianças e adolescentes, entre 10 e 16 anos, com o objetivo de avaliar a relação entre tempo e o d desempenho na Torre de Hanói para a esempenho avaliação da função executiva. Como medida de correlação usou usou-se a escala de ex execução do Wisc ecução III III. Os resultados fornecem dados que parecem demonstrar que o número de movimentos e a medida do tempo na execução na ToH, com crianças de 10 a 16 anos, não tem poder discriminativo, na comparação do desempenho do número e do tempo de execu execução ção ent entre os grupos de 10 a 13 anos, re de 14 a 16 anos e entre os gêneros. Conclu Conclui-se que a medida do tempo na realização da ToH ToH, de acordo com os , dados levantados e em grupos de crianças e adolescentes da 10 a 16 anos não se faz necessária necessária, uma vez que não apre apresentou correlação significativa. sentou

This work is concerned with five problems in combinatorics. In Josephus problem, people are standing in a circle or in a row and every q-th is executed until only one person remains. We show how to find the survivor, and discuss the generalization when each person has more lives. In Tower of Hanoi, we study the numbers and properties of moves necessary to transport the tower from one rod to another, where the total number of rods is either three or four. We mention related problems with restrictions on the legal moves. In ménage problem, we calculate the number of seatings of couples around a table such that men and women alternate and nobody sits next to his or her partner. We also discuss permutations with restricted positions and rook polynomials. In ballot problem, we consider two candidates competing against each other and calculate the probability that, throughout the count, the first candidate always had more votes than k times the number of votes of the second one; we also mention the relation to Catalan numbers. In Kirkman's schoolgirl problem, the task is to find a weekly schedule for fifteen girls walking daily out in triads so that no two go together more than once. We also discuss the social golfer problem and Schurig's tables.