O uso de um jogo de treinamento no ensino dos conceitos de média e variância. The use of a training game in the teaching of the concepts of mean and variance

Apresentamos, neste artigo, o relato de uma experiência de ensino que utilizou, em sala de aula, um jogo de dados, para o reforço no aprendizado dos conceitos de média e variância. O jogo é original e utiliza, simultaneamente, esses dois importantes conceitos da Estatística Descritiva. Formulamos também alguns problemas, envolvendo situações de jogo, cujas soluções, obtidas pelos próprios alunos, têm por objetivo reforçar os conceitos matemáticos presentes nas definições de média e de variância. Pelos relatos dos alunos e das professoras que aplicaram o jogo, acreditamos que a atividade desenvolvida tenha contribuído para a apreensão dos conceitos de média e variância pelos alunos. Esperamos que a sequência didática aqui apresentada possa auxiliar o professor do Ensino Médio no seu trabalho com esses conceitos. In the present study, we describe a classroom teaching experience with a dice game to reinforce the learning of the concepts of mean and variance. The game is an original proposal and uses these two important concepts of Descriptive Statistics. We have also formulated some problems involving game situations. The solutions of these problems, obtained by the students, are intended to reinforce the mathematics concepts present in the definitions of mean and variance. Based on the reports of the students and teachers that applied the dice game, we believe that the activity contributed for the learning of the concepts of means and variance by the students. Therefore, we hope that the didactics sequence presented herein can help high school teachers in their work with these concepts

Psycholinguistic Correlates of Symbol Grounding in Dictionaries

A dictionary can be represented as a directed graph with links from defining to defined words. The minimal feedback vertex sets (MinSets, Ms) of a dictionary graph are the smallest sets of words from which all the rest can be defined. We computed Ms for four English dictionaries. The words in the dictionary components revealed by our graph-theoretic analysis differ in their psycholinguistic correlates. Every MinSet has a C-part that is younger and more frequent and an S-part, that is more concrete. To understand the functional role of these components will require a close study of the words themselves, and how they are combined into definitions. We can already conclude that the closer a word is to the MinSets that can define all other words, the more concrete and frequent the word is likely to be, and the earlier it is likely to have been learned. This is what one would expect if the words in the MinSets were the ones that had been acquired through direct sensorimotor grounding

Do Bottom-up Effects Define The Structuring Of Ant (Hymenoptera: Formicidae) Communities In A Restinga Remnant?

Restingas are lowland sandy ecosystems located between mountain ranges and the sea. For living organisms in this ecosystem, restingas can be seen as habitats formed by islands of vegetation separated by a sandy matrix. These organisms are highly influenced by the environmental conditions and physical characteristics of the landscape, including size, connectivity and environmental heterogeneity. Given the recognized effectiveness of ants as bioindicators, this study uses these organisms as a model to assess how vegetation complexity affects ant communities. The study was carried out in the Parque das Dunas, Salvador - Bahia. Within this park, four categories of vegetation islands (Small, Medium, Large and Continuous) were delimited, where the ant fauna was sampled and the forms of vegetal life were analyzed, using the Raunkiaer analysis. A total of 69 ant species were collected from 31 genera and six subfamilies. We found a positive relationship between the diversity of plant life forms (H') and ant richness. In general, there was a significant difference in the composition of ant species in each microhabitat and between the areas of continuous vegetation and the different vegetation islands. There is a bottom up effect mediating the ant community associated with dune vegetation, the local richness of ant species responds to vegetation heterogeneity

Hidden Structure and Function in the Lexicon

How many words are needed to define all the words in a dictionary? Graph-theoretic analysis reveals that about 10% of a dictionary is a unique Kernel of words that define one another and all the rest, but this is not the smallest such subset. The Kernel consists of one huge strongly connected component (SCC), about half its size, the Core, surrounded by many small SCCs, the Satellites. Core words can define one another but not the rest of the dictionary. The Kernel also contains many overlapping Minimal Grounding Sets (MGSs), each about the same size as the Core, each part-Core, part-Satellite. MGS words can define all the rest of the dictionary. They are learned earlier, more concrete and more frequent than the rest of the dictionary. Satellite words, not correlated with age or frequency, are less concrete (more abstract) words that are also needed for full lexical power.Comment: 11 pages, 5 figures, 2 table

The Latent Structure of Dictionaries

How many words (and which ones) are sufficient to define all other words? When dictionaries are analyzed as directed graphs with links from defining words to defined words, they reveal a latent structure. Recursively removing all words that are reachable by definition but that do not define any further words reduces the dictionary to a Kernel of about 10%. This is still not the smallest number of words that can define all the rest. About 75% of the Kernel turns out to be its Core, a Strongly Connected Subset of words with a definitional path to and from any pair of its words and no word’s definition depending on a word outside the set. But the Core cannot define all the rest of the dictionary. The 25% of the Kernel surrounding the Core consists of small strongly connected subsets of words: the Satellites. The size of the smallest set of words that can define all the rest (the graph’s Minimum Feedback Vertex Set or MinSet) is about 1% of the dictionary, 15% of the Kernel, and half-Core, half-Satellite. But every dictionary has a huge number of MinSets. The Core words are learned earlier, more frequent, and less concrete than the Satellites, which in turn are learned earlier and more frequent but more concrete than the rest of the Dictionary. In principle, only one MinSet’s words would need to be grounded through the sensorimotor capacity to recognize and categorize their referents. In a dual-code sensorimotor-symbolic model of the mental lexicon, the symbolic code could do all the rest via re-combinatory definition